tag:blogger.com,1999:blog-5439075200771881622024-03-21T03:20:25.789-07:00MathSnack/math 'snak/ - Ideas to Satisfy Your Mathematical Cravings:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comBlogger41125tag:blogger.com,1999:blog-543907520077188162.post-46828797747223954872023-02-03T20:16:00.012-08:002023-06-07T08:03:26.788-07:00Place Value: An Essential UnderstandingNo, this ain't your momma's math... It's better!<div><br /></div><div>Mathematics education has come a long way over the past 10 years. The calculations, of course, are the same (after all, 33 + 20 still equals 53), but teaching mathematics has certainly evolved. </div><div><br /></div><div>"Back in the day" knowing that the answer was 53 was typically all that teachers expected – it was mostly about getting the correct answer – I honestly cannot remember a single time that a math teacher asked <i>WHY</i> my answer was what it was. Of course, the correct answer is still important, but mathematics education of today requires that learners understand why the answer is 53 – we want our students to deeply understand the patterns and relationships of numbers that allow for greater flexibility and application of the mathematics. In other words, we are teaching our students how to become thinkers of mathematics, not just do-ers of math. </div><div><br /></div><div>Let's focus on PLACE VALUE. Did you know that "place value" is mentioned 25 times in the Common Core Standards in grades K through 5? Take a look at a brief progression of place value through the grades: </div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkRQI_cpBgMBJ_iHpVWoXriZVXumbAgxv69xXjS1CUrrbkmD3cwiyBOFxXPER2ogrjb9uwMY8kiGI8iePhszpZS8Qy7hYBYGfDZSlWzjoY_MaI42FfdfIv-G_kMyfRCGvzU5EWwRVjasCCxNEoSjPNzpdIYQbRjF3u1hZPDB6ziZH4snvCaAwS65g30g/s9000/a.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="4872" data-original-width="9000" height="346" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkRQI_cpBgMBJ_iHpVWoXriZVXumbAgxv69xXjS1CUrrbkmD3cwiyBOFxXPER2ogrjb9uwMY8kiGI8iePhszpZS8Qy7hYBYGfDZSlWzjoY_MaI42FfdfIv-G_kMyfRCGvzU5EWwRVjasCCxNEoSjPNzpdIYQbRjF3u1hZPDB6ziZH4snvCaAwS65g30g/w640-h346/a.jpg" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div>That's good information about the progression of Place Value learning, but WHAT DOES IT LOOK LIKE in the classroom?</div><div><br /></div><div>Before students even begin adding and subtracting multi-digit numbers in 2nd grade, they should first learn how to be flexible in the way they decompose numbers. Take the number 53, for example. In many 1st grade classrooms, students learn to break 53 into 50 + 3... BUT they also need to understand that 53 can be represented by 53 ones, or 4 ten and 13 ones, or 40 + 13 ➥ this flexible way of thinking about 53 lays the foundation for the work they will do in 2nd grade. </div><div><br /></div><div>Imagine students are posed with the problem 53 – 27.</div><div>What if instead of just recognizing 53 as 5 tens and 3 ones (which poses a problem when they try to imagine taking away 7 ones), they also could easily imagine 53 as 4 tens and 13 ones: </div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEituxIDjV1dj_C_tayEr2Vkq0ocvZGyXPvtEQ84V-IuWDDCP9IwZ3dW13NIfGTZkITsK2rjw8HyF294UYEPaMXMnos3V4clSuBYmi8_Sf9RUBRP1TcLfnkFSO5iywnOxLAENWPzkFrSHBS56BWGh282fePzOMGn5X2pxXhdLLxCVGcLfzAchpmU9ydlnw/s3858/IMG_9342.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1627" data-original-width="3858" height="270" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEituxIDjV1dj_C_tayEr2Vkq0ocvZGyXPvtEQ84V-IuWDDCP9IwZ3dW13NIfGTZkITsK2rjw8HyF294UYEPaMXMnos3V4clSuBYmi8_Sf9RUBRP1TcLfnkFSO5iywnOxLAENWPzkFrSHBS56BWGh282fePzOMGn5X2pxXhdLLxCVGcLfzAchpmU9ydlnw/w640-h270/IMG_9342.jpg" width="640" /></a></div><br /><div>Being flexible with place value gets even more exciting when we subtract larger numbers – this is how those who are mathematically fluent have been solving problems like this for generations (in spite of what they were being taught in school) – it's us educators who are finally catching up to them!</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhT8UCGtLdxzdmWUYQ8nvGIo2bce9P8pLOXpIJ4mq0aPBzIP3ZK_OmntGum8wbQizVL3qwDy_oPufN5xJaXl0sHaiPumtQ2Zh3D7V4_fjyxq2cbrLsoXTRRER7uANJ4bxu-QsTaEhYoUv5oajl4pec1Q7PI6yKNZ-ck98AcIx-8_uXLevjxdZsASoZq0A/s3643/IMG_9343.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1530" data-original-width="3643" height="268" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhT8UCGtLdxzdmWUYQ8nvGIo2bce9P8pLOXpIJ4mq0aPBzIP3ZK_OmntGum8wbQizVL3qwDy_oPufN5xJaXl0sHaiPumtQ2Zh3D7V4_fjyxq2cbrLsoXTRRER7uANJ4bxu-QsTaEhYoUv5oajl4pec1Q7PI6yKNZ-ck98AcIx-8_uXLevjxdZsASoZq0A/w640-h268/IMG_9343.jpg" width="640" /></a></div><br /><div>We also saw in the progressions that rounding number relies on an understanding of place value, too. Think about the number 1,742. By understanding place value, we understand that</div><div><ul style="text-align: left;"><li>1742 has 1742 ones</li><li>1742 has 174 tens -- yes, I know there's a 4 as the tens DIGIT, but there are not just 4 tens - there are 174 tens (and 2 ones). </li><li>1742 can also be thought of as 17 hundreds (and 42 ones) – Let's read that one again so we can process it fully – 1742 has 17 hundreds (not just 7 hundreds). </li></ul></div><div>The ability to think flexibly about place value in this way makes rounding much easier to understand. Imagine we were asked to round 1,742 to the nearest 10. By knowing this number has 174 tens (and a few extras), we understand that this number has a little more than 174 tens (because of the few extras) but less than 175 tens. Of all the numbers in the world, we have narrowed it down to just two specific numbers that this number must round to – either 174 tens (1740) or 175 tens (1750). Then by looking at the "extras", we know that we don't have enough to make it halfway between those two numbers (to 1745), so we must round to the lower value 1740 when rounding 1742 to the nearest 10. </div><div><br /></div><div><b>Place value understanding is foundational</b> to building a deep understanding of numbers and supporting fluency. We didn't delve into it this time, but place value should be explored and learned using concrete models. Here are a few images from other educators for inspiration as you continue on the place value journey with your students!</div><div><br /></div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzRnbF5sLEitNqEn5iydlroCu_naJjulzCTlUcbtXZCrNmH3rbH5tXN2LIwOlcSE6TUXktNygLxo73T5wZR57woo3p329RQ1pv0F0rh1E8P84BpPlC0XKbIf8mbBFP8uiqjMZjPfLoUiTDCOtj-GjyDsSXfhQ6Ne2NisbYljLiUgfgwjEs5nHUDZPswA/s2504/Screen%20Shot%202023-02-03%20at%2010.59.06%20PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1578" data-original-width="2504" height="404" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzRnbF5sLEitNqEn5iydlroCu_naJjulzCTlUcbtXZCrNmH3rbH5tXN2LIwOlcSE6TUXktNygLxo73T5wZR57woo3p329RQ1pv0F0rh1E8P84BpPlC0XKbIf8mbBFP8uiqjMZjPfLoUiTDCOtj-GjyDsSXfhQ6Ne2NisbYljLiUgfgwjEs5nHUDZPswA/w640-h404/Screen%20Shot%202023-02-03%20at%2010.59.06%20PM.png" width="640" /></a></div><br /><div><br /></div><div><br /></div><div><br /></div><div><br /></div>:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comtag:blogger.com,1999:blog-543907520077188162.post-35199278442471726512022-11-02T09:38:00.003-07:002022-11-02T09:58:33.076-07:00The NUMBER LINE – A Hidden Treasure in Plain Sight!<p></p><div style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">Just about every elementary math classroom has one - I've worked in three different school districts in my career and having a number line displayed on the wall has been the standard in each of those districts. Let's pause for a minute and think about that phrase "displayed on the wall"....</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><h1 style="clear: both; text-align: center;">WALL ART</h1><h1 style="clear: both; text-align: center;"><span style="font-weight: normal;">or</span></h1><h1 style="clear: both; text-align: center;">LEARNING CHART</h1></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1_x0eLPtPxibv_gGOPDhAU-_zefY2IovaKaxrTq4JNPtuxjFyfUyqZmKIIgPCqsLxWxudl1SWxZD9AouZeyUq04JZzTsExdTBOhI-3qAe_1Qbydvq_0VuaZdqMXdJZkLotpKY0xW65ckR9BmoN8r5iBy07cfj0wyEHxxrB1NS6IFUrMzBIWqdSPezcg/s1980/Screen%20Shot%202022-07-20%20at%208.16.49%20AM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1068" data-original-width="1980" height="356" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1_x0eLPtPxibv_gGOPDhAU-_zefY2IovaKaxrTq4JNPtuxjFyfUyqZmKIIgPCqsLxWxudl1SWxZD9AouZeyUq04JZzTsExdTBOhI-3qAe_1Qbydvq_0VuaZdqMXdJZkLotpKY0xW65ckR9BmoN8r5iBy07cfj0wyEHxxrB1NS6IFUrMzBIWqdSPezcg/w659-h356/Screen%20Shot%202022-07-20%20at%208.16.49%20AM.png" width="659" /></a></div><br /><div class="separator" style="clear: both; text-align: left;">A number line display? Is that really what we want? A<i> display </i>rather than a tool. <b>I want my number line to be a tool</b> – a number line is a powerful learning aid when it's <i>used</i>. Now think about where most teachers hang their number lines... in just about every classroom, the number line is hung on the wall wa-a-y-y up high in a location where access is challenging to our young learners who benefit from using the number line as a hands-on learning tool. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Why do we hang this amazing math tool in a place where access is difficult? Lack of wall space is certainly one of the reasons, perhaps it's just become a classroom tradition, and maybe we just don't understand the full value and the range of applications that support instruction when using a number line. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Many teachers have already discovered one of the solutions: Keep your <i>wall art</i> for reference BUT <b>make sure students have hands-on access to other number lines</b> (perhaps one is taped to their desk or maybe various number lines have been placed in their hands-on math kits). Okay, so now that we've brought the number line down to students, let's talk about a few of the many amazing (and perhaps surprising!) ways to use a number line to support learning. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><h3 style="clear: both; text-align: left;"></h3><h1 style="text-align: center;"><span style="font-size: x-large;">AMAZING</span><span style="font-size: large;"> </span><span style="font-weight: normal;"><span style="font-size: large;">(and perhaps surprising!)</span><br /></span><span style="font-size: x-large;">WAYS to USE a NUMBER LINE to SUPPORT LEARNING</span></h1><div><br /></div> <div><i>Did you know that the</i> CCSS Standards<i> which have been adopted by many states, specifically names "Number Line" as as strategy/model 30 times (!). In addition to those 30 callouts, the number line can be an effective modeling tool for many other learning moments, as well. </i></div><div><i><br /></i></div><div style="text-align: center;"><br /></div><div style="text-align: left;">Many classrooms already use the number line to model addition and subtraction, one more and one less, counting and before and after concepts, but what about multiplication? division? elapsed time? unit conversions? and rounding? Can a number line be used effectively to solve for these types of problems? </div><div style="text-align: left;">Yes, yes, yes, yes, and yes! </div><div style="text-align: left;"><br /></div><div style="text-align: left;"><br /></div><div style="text-align: center;"><h1>MULTIPLICATION</h1><h1><div style="font-size: medium; font-weight: 400; text-align: left;">If we know 4 x 20, how could we use the number line as a tool to visualize 4 x 19? Those 4 jumps of 20 would be 4 jumps of 19, so we'd need to compensate for the 4 big jumps by backing up 4 (1 for each 20 that was really a 19). What if we were calculating 4 x 18? How could we use our visual model of 4 x 20 to solve that equation? Are you thinking we could do 4 x 20 then back up 8 (compensating for the 2 extra spaces with each jump of 20)? What if the original problem had been 5 x 19 instead of 4 x 19? How might the number line model be the same? How might it be different? </div><div style="font-size: medium; font-weight: 400; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyHJnajK_2b2FK09tIJf8EQEirDyowTXCUQZNxxffSXXH-eUKKUS-VAb513ajlPDlic3NpfrqJ8nwrpfHn2E68aUMsYhjNV-NPXko0xiYwoo2PUkAYQjVoCHzdWCg7nJapPnhh3nx5N6Cgb4ia6hF9pU3E2Q6Vd0hh08Wx5B8Axb8QxpBBXd6fjQ3Aaw/s2174/Screen%20Shot%202022-11-02%20at%2011.26.08%20AM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1242" data-original-width="2174" height="325" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyHJnajK_2b2FK09tIJf8EQEirDyowTXCUQZNxxffSXXH-eUKKUS-VAb513ajlPDlic3NpfrqJ8nwrpfHn2E68aUMsYhjNV-NPXko0xiYwoo2PUkAYQjVoCHzdWCg7nJapPnhh3nx5N6Cgb4ia6hF9pU3E2Q6Vd0hh08Wx5B8Axb8QxpBBXd6fjQ3Aaw/w568-h325/Screen%20Shot%202022-11-02%20at%2011.26.08%20AM.png" width="568" /></a></div><br /><div style="font-size: medium; font-weight: 400; text-align: left;"><br /></div></h1><h1>DIVISION</h1><h1><div style="font-size: medium; font-weight: 400; text-align: left;">I love using the number line model for division. You'll likely notice that this is just a <i>partial quotient </i>method that utilizes the number line. Many students (and teachers!) find this number line model easier to understand and manage with division equations than using the box method or area model. </div><div style="font-size: medium; font-weight: 400; text-align: left;"><br /></div><div style="font-size: medium; font-weight: 400; text-align: left;">Notice how we take advantage of multiplication facts that we know to get to the quotient. Take a look for yourself, what do you think? </div><div style="font-size: medium; font-weight: 400; text-align: left;"><br /></div></h1><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAo0YTMEvSVDwfJhBGFbS2STMGLcSXVWsU5wVqbXAD-15qvzxCV9iKAQhNJKf2RWkKKt_vR9h9FRQTMziU-Jy6mt6G9NmcoatKE2kZD5Zj1T6CkqxwBVz9ku5Dj6zc9uB14_mVdPLgq8OQN93I6Vzyh2g6ankSnIG6QbucS5Nwu_Xrem3KruT6P6Zhzw/s3836/Screen%20Shot%202022-11-02%20at%2011.06.22%20AM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1558" data-original-width="3836" height="226" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAo0YTMEvSVDwfJhBGFbS2STMGLcSXVWsU5wVqbXAD-15qvzxCV9iKAQhNJKf2RWkKKt_vR9h9FRQTMziU-Jy6mt6G9NmcoatKE2kZD5Zj1T6CkqxwBVz9ku5Dj6zc9uB14_mVdPLgq8OQN93I6Vzyh2g6ankSnIG6QbucS5Nwu_Xrem3KruT6P6Zhzw/w556-h226/Screen%20Shot%202022-11-02%20at%2011.06.22%20AM.png" width="556" /></a></div><h1><br /></h1><div><br /></div><h1>ELAPSED TIME</h1><div style="text-align: left;">A number line is a simple way to straighten out our traditional analog clock. We can use a number line model by creating <i>friendly jumps</i> to make calculating elapsed time more efficient. </div><div style="text-align: left;"><br /></div><div style="text-align: left;">Check out the two models below that help students (adults, too!) calculate elapsed time. Because I use the number line model so much, I can now visualize a number line in my head when trying to figure out what time I will arrive at my destination 🚘.</div><div style="text-align: left;"><br /></div><h1><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfMtWvTf7G37TZ29PV9HjiHqwQVNgN4V22ccEfCesgrlsTYkx4amBmg7YE-Ql3_6DzviMJx_wNAcQf40zZxnrnkigCmZdTePFSRz3WedxZRHnT55cz5UCV-7drzUZ0Rh9rzhCLTdlWh-6KMy4NohbL_f8pH4xHfM8E2ANg84oP97-IuKYHnxLieePbpA/s1392/Screen%20Shot%202022-11-02%20at%209.52.01%20AM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="784" data-original-width="1392" height="274" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfMtWvTf7G37TZ29PV9HjiHqwQVNgN4V22ccEfCesgrlsTYkx4amBmg7YE-Ql3_6DzviMJx_wNAcQf40zZxnrnkigCmZdTePFSRz3WedxZRHnT55cz5UCV-7drzUZ0Rh9rzhCLTdlWh-6KMy4NohbL_f8pH4xHfM8E2ANg84oP97-IuKYHnxLieePbpA/w487-h274/Screen%20Shot%202022-11-02%20at%209.52.01%20AM.png" width="487" /></a></h1><div><b>How are these two models the same? How are they different?</b></div><div><br /></div></div><div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg62ryB82G2SFUvzbliTOQW30rupwunvx7QyVHPl2NhwQ9RbGDDD0_q0OCH25_gQEWDgXrxM-j-g2nJ6oRtFvfNfQl1JiWa3XdPB8RzWdYVrQL5dARfGB2Z-NUq0ugA_4dNx8yiBkexObNGQiTRab403uXGTpDE7x6zB3Z3KGSy16W9nVvFfg66JWwcXA/s2180/Screen%20Shot%202022-11-02%20at%209.59.01%20AM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1258" data-original-width="2180" height="283" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg62ryB82G2SFUvzbliTOQW30rupwunvx7QyVHPl2NhwQ9RbGDDD0_q0OCH25_gQEWDgXrxM-j-g2nJ6oRtFvfNfQl1JiWa3XdPB8RzWdYVrQL5dARfGB2Z-NUq0ugA_4dNx8yiBkexObNGQiTRab403uXGTpDE7x6zB3Z3KGSy16W9nVvFfg66JWwcXA/w489-h283/Screen%20Shot%202022-11-02%20at%209.59.01%20AM.png" width="489" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><div style="text-align: left;">Now we simply add the values of the <i> friendly jumps</i> to calculate that the workout was 38 minutes long (that's not a bad workout on a busy day, right?)</div><div style="text-align: left;"><br /></div><div style="text-align: left;"><br /></div> </div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><h1>ROUNDING</h1><div style="text-align: left;"><div class="separator" style="clear: both; text-align: center;"><br /></div><div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqgcH1uoBR26Zwdhgy2tL5KwcB6W03oTtDeovykd-pMZJpdpZ2gMIUL2g-tVhil-iOkhRTrXlQ2qdROS7RP2Us14orEN1np-astD1_AqUamxvwPt9-QbI5Mh80eqUIBuHLbVyVSai3D2LyjorP7FGkxT67HYnvQBFvF3YOpMiUolIsaRPJENHIvqQCGQ/s350/5af6cfad4493d68596251bf63e669575.jpeg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="350" data-original-width="263" height="219" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqgcH1uoBR26Zwdhgy2tL5KwcB6W03oTtDeovykd-pMZJpdpZ2gMIUL2g-tVhil-iOkhRTrXlQ2qdROS7RP2Us14orEN1np-astD1_AqUamxvwPt9-QbI5Mh80eqUIBuHLbVyVSai3D2LyjorP7FGkxT67HYnvQBFvF3YOpMiUolIsaRPJENHIvqQCGQ/w164-h219/5af6cfad4493d68596251bf63e669575.jpeg" width="164" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">This is a procedural TRICK!</span><br style="font-size: small;" /><span style="font-size: small;">This is NOT a good </span><span style="font-size: small;">model</span></td></tr></tbody></table>I Googled rounding strategies the other day and found mostly a bunch of rounding <i>tricks</i> (mnemonic devices to remember and various rhymes - some that were so complex that I couldn't see how that possibly made it easier!). Anyway, we don't need tricks – tricks are just that, ways of tricking people into believing that they know or understand a concept. <b>We need to teach strategies</b> that actually help students to conceptually understand the mathematical concept; after all, we want them to understand the relationship of numbers and then generalize their understandings in other applications, right?</div><div><br /></div><div>The number line model can help us give relational context to a number. Imagine we wanted to round the population of Palm Springs to the nearest thousand. I can see that there are 44 thousand (plus a few more) people who currently reside in Palm Springs. The question is whether the "plus some more" puts us closer to the next thousand???</div><div><br /></div><div><span style="font-size: medium;"><b>The Critical Importance of Benchmark Numbers</b> </span></div><div>Benchmark numbers are the KEY to UNDERSTANDING rounding numbers. </div><div>In the model below, I know 44 thousand (plus) live in Palm Springs. So the value is more than 44 thousand but less than the next higher thousand (45 thousand). These values become my bookends. The benchmark value that falls exactly halfway between the two values is 44,500. </div><div><br /></div><div>Next I consider if my number is approaching 44,500 (making it closer in value to 44,000 rather than 45,000), or has my value of 44,612 already passed my halfway benchmark of 44,500 and is now closer to 45,000?</div><div><br /></div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQEd33gybN3xSBQdKIpCIHQb3OiGx4EFQtZ6N9EzDoZPXuJ62VBu5p0H0QJQFGwSWhb28Lf23uyTQHZ1gMZGWdNmxgjf6W_0vyVyL8HZI8l5sRkKipayP_xFaO9DqchQobCnbnI6Ukt8e8-gMn0zG2wpHR4-zy5-clbZlBdXTOilAiJO66XCZeieG-jQ/s2070/Screen%20Shot%202022-11-02%20at%2011.56.40%20AM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="878" data-original-width="2070" height="211" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQEd33gybN3xSBQdKIpCIHQb3OiGx4EFQtZ6N9EzDoZPXuJ62VBu5p0H0QJQFGwSWhb28Lf23uyTQHZ1gMZGWdNmxgjf6W_0vyVyL8HZI8l5sRkKipayP_xFaO9DqchQobCnbnI6Ukt8e8-gMn0zG2wpHR4-zy5-clbZlBdXTOilAiJO66XCZeieG-jQ/w497-h211/Screen%20Shot%202022-11-02%20at%2011.56.40%20AM.png" width="497" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div>Think about how <b><span style="font-size: medium;">this method builds a conceptual understanding</span></b> rather than relying on procedural memory, or worse, a catchy rhyme that requires no understanding of the math that drives the math. </div><div><br /></div></div><br /></div></div><div style="text-align: left;"><br /></div><div style="text-align: left;"><div class="separator" style="clear: both; text-align: center;"><h1>CONVERSIONS</h1><div style="text-align: left;"><div class="separator" style="clear: both; text-align: center;"><br /></div><div>I love using a double number line for conversions. I first started using this model when I learned that 24K jewelry is made of 100% gold, and being the mathcurious person I am, I wanted to figure out the percentage of gold in my 14K gold wedding ring. </div></div><div style="text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjU84g0RW1PQ4zQ6Bni1yLzvjqxqHiPwjY2EvcQpPGRnS363cAC-0KfPIkDUJxV1yU54tif4UPJNl7xG-sYM81OcAIyOUCOunYDGZWh8a6Xj334sQsJAzZSr2fva8bnQAvhH2GMjc37FJH09MvCuHnA33zg7lwlwxek9Semq1_5cvbDt2lv-AMfXxvltw/s912/Screen%20Shot%202022-11-02%20at%2010.37.24%20AM.png" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="912" data-original-width="562" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjU84g0RW1PQ4zQ6Bni1yLzvjqxqHiPwjY2EvcQpPGRnS363cAC-0KfPIkDUJxV1yU54tif4UPJNl7xG-sYM81OcAIyOUCOunYDGZWh8a6Xj334sQsJAzZSr2fva8bnQAvhH2GMjc37FJH09MvCuHnA33zg7lwlwxek9Semq1_5cvbDt2lv-AMfXxvltw/w184-h300/Screen%20Shot%202022-11-02%20at%2010.37.24%20AM.png" width="184" /></a></div></div><div style="text-align: left;"><br />Recently, a group of learners used the number line model for a conversion related to a Washington DC landmark: The Washington Monument. </div><div style="text-align: left;"><br /></div><div style="text-align: left;">Let's begin with a bit of background for the problem: The Washington Monument was built in two phases. The first phase was 152 feet tall, but they ran out of money to complete it, so the monument stayed incomplete for two decades until Congress decided to pass a joint resolution in 1876 to complete the project. The completed monument is 555 feet tall - at the time, it was the tallest structure in the world. </div><div style="text-align: left;"><br /></div><div style="text-align: left;">Back to the math.... As you study the progression of the model, you will notice they reflect the progression of thinking. </div><div style="text-align: left;"><br /></div><div style="text-align: left;">How does this number line model for unit conversions scaffold thinking better than the algorithm method of solving the problem? </div><div style="text-align: left;"><br /></div><div style="text-align: left;"><br /></div><div style="text-align: left;"><br /></div><div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSJ_NUDMXdDtzzdyYhq7Katu_WiKEvqfgOhw9hrBc3it62_PquqptpsnhMXNF1IrQJNqm7my0j3KCQ4OFWcKrH0693_aLSQtg2ggEJQmLJximjTfkkqkkuFB6MaB8ibAXUBo-216Kg_KYqaqX1B5_ORB9pMC5ObbU3sMKdQY3AGDWaQJ4uKRf4n134Iw/s3886/Screen%20Shot%202022-11-02%20at%2010.39.02%20AM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1644" data-original-width="3886" height="222" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSJ_NUDMXdDtzzdyYhq7Katu_WiKEvqfgOhw9hrBc3it62_PquqptpsnhMXNF1IrQJNqm7my0j3KCQ4OFWcKrH0693_aLSQtg2ggEJQmLJximjTfkkqkkuFB6MaB8ibAXUBo-216Kg_KYqaqX1B5_ORB9pMC5ObbU3sMKdQY3AGDWaQJ4uKRf4n134Iw/w526-h222/Screen%20Shot%202022-11-02%20at%2010.39.02%20AM.png" width="526" /></a></div><div class="separator" style="clear: both;"><br /></div><b>How can we use 1 foot = 12 inches to determine how many inches are in 100 feet?</b></div><div class="separator" style="clear: both; text-align: center;"> <br /><div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEioQUXDs4aFS5WU_jD18y79fkWiuYkx0Dc0HpPbNCpmkBnICkdyixPo0QmaQr8iBIiUELNz9MOzDJnuEmMSpJnBX1KOvll7JEuhBB_HZcwSrUqEtlB2qZ5LevZgva88EanuSR6MO8zYrkN5TtoFvJWEUEiXAx3f00mIO2tTXCJQkUTfeiwKHbAyyyG9UQ/s3874/Screen%20Shot%202022-11-02%20at%2010.39.16%20AM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="924" data-original-width="3874" height="125" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEioQUXDs4aFS5WU_jD18y79fkWiuYkx0Dc0HpPbNCpmkBnICkdyixPo0QmaQr8iBIiUELNz9MOzDJnuEmMSpJnBX1KOvll7JEuhBB_HZcwSrUqEtlB2qZ5LevZgva88EanuSR6MO8zYrkN5TtoFvJWEUEiXAx3f00mIO2tTXCJQkUTfeiwKHbAyyyG9UQ/w529-h125/Screen%20Shot%202022-11-02%20at%2010.39.16%20AM.png" width="529" /></a></div><div class="separator" style="clear: both;"><br /></div><b>How does knowing 100 feet, help us quickly know the number of inches in 50 feet? </b></div><div class="separator" style="clear: both; text-align: center;"><br /><div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi56pEpRo9cIw-NdL8tnCZ3qBZrY0m3EG7lwcTdclhXZdtKquaZNfXiSrYOAjQWMRCWrPvzTo55FDoaqN9832zhg5umCZE91nKZGcR_jWgetmgP5Vare5OPbG-_5z2q2oA1wg2WOTrmCH7VGxXI2S9fMenfjHNhcC-EOELE7e5txPxPTSAQhB0nxDLv8w/s3860/Screen%20Shot%202022-11-02%20at%2010.39.26%20AM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="900" data-original-width="3860" height="124" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi56pEpRo9cIw-NdL8tnCZ3qBZrY0m3EG7lwcTdclhXZdtKquaZNfXiSrYOAjQWMRCWrPvzTo55FDoaqN9832zhg5umCZE91nKZGcR_jWgetmgP5Vare5OPbG-_5z2q2oA1wg2WOTrmCH7VGxXI2S9fMenfjHNhcC-EOELE7e5txPxPTSAQhB0nxDLv8w/w532-h124/Screen%20Shot%202022-11-02%20at%2010.39.26%20AM.png" width="532" /></a></div><div class="separator" style="clear: both;"><br /></div><b>We have the conversion for 100 and for 50, that's 150 of the 152 feet. </b></div><div class="separator" style="clear: both; text-align: center;"><b>We just need 2 more feet.</b></div><div class="separator" style="clear: both; text-align: center;"><br /><div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLeMldF-YMVlcnJlRT8k-eCRF5CpooajbRImAXniCIJRx3jom9Seyo8GO4kL3QjLegq1RW-bD95RaYmJeAGFZPJOGqsBoDXpbQfmFo2beodmmEPTKEHy2c8tgUcJjQ0FLuLSg0LLNWW4TvVFFm1jYJMfEHbjqFH4QUGDuZ_5R-pMaAIjRVYvSfZhhHZw/s3854/Screen%20Shot%202022-11-02%20at%2010.39.38%20AM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="906" data-original-width="3854" height="124" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLeMldF-YMVlcnJlRT8k-eCRF5CpooajbRImAXniCIJRx3jom9Seyo8GO4kL3QjLegq1RW-bD95RaYmJeAGFZPJOGqsBoDXpbQfmFo2beodmmEPTKEHy2c8tgUcJjQ0FLuLSg0LLNWW4TvVFFm1jYJMfEHbjqFH4QUGDuZ_5R-pMaAIjRVYvSfZhhHZw/w532-h124/Screen%20Shot%202022-11-02%20at%2010.39.38%20AM.png" width="532" /></a></div><div class="separator" style="clear: both;"><br /></div><b>How did we determine that 152 x 12 = 1824 without actually multiplying 152 and 12?</b></div><div class="separator" style="clear: both; text-align: center;"><b><br /></b><div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbe_fEtwqLh7Xxz6DAa97ALv_zpDCXzeqKRXrLnjDj26-AgeNWJDdATuMNpohqfi3cq5jDho5bB0mdcE7l61Pfw4RSHKEojhTS7QgGi_mqvMbT4u5Jus8EkBlzdfe6DQU2Jtti5dNSU5-_rV-Ix00nq_mj3Kwm1_dABrcxz3c9AhiQ2dlKQG-szljzdQ/s3866/Screen%20Shot%202022-11-02%20at%2010.39.52%20AM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1392" data-original-width="3866" height="192" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbe_fEtwqLh7Xxz6DAa97ALv_zpDCXzeqKRXrLnjDj26-AgeNWJDdATuMNpohqfi3cq5jDho5bB0mdcE7l61Pfw4RSHKEojhTS7QgGi_mqvMbT4u5Jus8EkBlzdfe6DQU2Jtti5dNSU5-_rV-Ix00nq_mj3Kwm1_dABrcxz3c9AhiQ2dlKQG-szljzdQ/w534-h192/Screen%20Shot%202022-11-02%20at%2010.39.52%20AM.png" width="534" /></a></div><br /><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div></div></div><br /><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; font-size: x-large; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnfaF21i16sJyxN-3pbNz-D-m0dPKh-exJNEXFot2kegN6hATAFlz4tDilfiCZcYcIfFi356Fa3nVd2XbCElKERh1olGLoSsFdZH--xWYVnIkaTJitV2oACz6Mh5QvUGtv9womhTfUOeEyEA1ZVHBnihwrcswPWBKPv4t4uVAsQdv3wiU7eESCxFM_-w/s300/Picture1.png" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="210" data-original-width="300" height="143" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnfaF21i16sJyxN-3pbNz-D-m0dPKh-exJNEXFot2kegN6hATAFlz4tDilfiCZcYcIfFi356Fa3nVd2XbCElKERh1olGLoSsFdZH--xWYVnIkaTJitV2oACz6Mh5QvUGtv9womhTfUOeEyEA1ZVHBnihwrcswPWBKPv4t4uVAsQdv3wiU7eESCxFM_-w/w204-h143/Picture1.png" width="204" /></a></div><span style="font-size: large;">What math concepts can you teach using the <b>Number Line Model</b> to <b>build students' conceptual understanding of the relationship that numbers share</b>?</span></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div></div></div><br /><p></p></div>:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comtag:blogger.com,1999:blog-543907520077188162.post-84025602872384048312022-03-26T12:40:00.004-07:002022-03-27T08:44:20.137-07:00Effective Questioning in the Classroom<h1 style="text-align: left;">PUSH or PAUSE</h1><div>I recently had the pleasure of joining district supervisors and building administrators on some instructional walk-throughs in each of the elementary schools in my district – it was wonderful to see all the good instruction and relationship-building happening in the learning environments across the district. In one particular classroom, I was acutely aware of just how skilled the teacher was at facilitating student thinking by making in-the-moment-decisions about when to PUSH and when to PAUSE. </div><div><br /></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgiZgZnuxUSoLe7pBMNeX2lcLVMquPwbmSe2HDuWxpi6ZRM9rjnuBVdO0PTH0HRcZtXRiVKwFUcu5eDi6CsHSx-0NKwspWdtwS9GqW1sD6aJKBDLLez9RZUDSZKEw-LKdjVJ_uS5el0h90KULEG5YKGBxDq3cor8_ialxT5XOOIZRZi6tEUg-E3gSzYqA/s850/da40j7k-48025f59-493b-4667-9c9e-fe66611ae64c.png" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="850" data-original-width="650" height="225" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgiZgZnuxUSoLe7pBMNeX2lcLVMquPwbmSe2HDuWxpi6ZRM9rjnuBVdO0PTH0HRcZtXRiVKwFUcu5eDi6CsHSx-0NKwspWdtwS9GqW1sD6aJKBDLLez9RZUDSZKEw-LKdjVJ_uS5el0h90KULEG5YKGBxDq3cor8_ialxT5XOOIZRZi6tEUg-E3gSzYqA/w172-h225/da40j7k-48025f59-493b-4667-9c9e-fe66611ae64c.png" width="172" /></a></div><br />Teaching is often (and accurately) described as both a science and an art – and when the two work together seamlessly, well, that is when the magic happens! But it's not really magic, is it? It's a skilled teacher who understands the important balance between effective Questioning and effective <a href="http://mathsnack.blogspot.com/search?q=wait+time" target="_blank">Wait Time</a>. It doesn't matter if the teacher has 3 years or 30 years behind them – this is something we can all learn to do when we work to be purposeful about our craft. As I spent time in this classroom, I couldn't help but notice how this teacher had found that perfect balance. I found myself trying to figure out how to bottle it and share it with others, knowing then that it would be the topic of my next post – this post.<br /><div class="separator" style="clear: both; text-align: center;"><br /></div></div><div>So what does it mean to strike a balance between PUSH and PAUSE? And what does this balance look like in the classroom? We should probably begin by defining the terms <i>PUSH</i> and <i>PAUSE</i>, so we have a shared understanding of what those words mean as it relates to this post. </div><div><br /></div><div><blockquote style="border: none; margin: 0px 0px 0px 40px; padding: 0px;"><div style="text-align: left;"><b><span style="color: #800180;">PUSH</span></b> is when you question students and push them beyond their initial answers. Through effective questioning, you encourage them to analyze their own thinking and then push them to say more, explain more clearly, provide more detail, and articulate their thinking clearly for others to understand those thoughts they have swimming around in their heads. A <a href="http://mathsnack.blogspot.com/2019/11/how-do-you-know.html" target="_blank">previous MathSnack post</a> highlights specific <i>push</i> moves to encourage deeper student-thinking. </div></blockquote></div><blockquote style="border: none; margin: 0px 0px 0px 40px; padding: 0px;"><div><p style="text-align: left;"><b><span style="color: #800180;">PAUSE</span></b> happens when you simply give students a bit more time and space to analyze their own thinking and find the ideas and words to articulate that thinking. They don't need another question – they don't need a push – they just need time to process the ideas already firing the synapses in their brains and trying to find their way out into the room. </p></div></blockquote><p><br /></p><p>Though I can't do justice to the actual lesson, perhaps a short snippet from the lesson will help explain PUSH and PAUSE a bit more clearly:</p><p>During this class period, these young 2nd graders were learning about line plots. This was their introduction to seeing data represented on a line plot. The students discussed measurement the week prior and were now learning how to graph measurement data on a line plot. The teacher asked, "Why does this line plot end at 52?" She then provided PAUSE for students to consider her question. She was not expecting an immediate response, nor did she want one. After a few seconds, she prompted students to talk about their ideas with their Turn-n-Talk partner – clearly an established routine in her classroom. Students began talking about why the line plot ended at 52 with their partners; they even went further to discuss why it began at 48 instead of zero.</p><p>As students talked to each other, the teacher circulated the room just to listen to conversations and gauge her students' initial understanding of line plots. She waited just long enough for the conversations to generate ideas, but not enough time for the conversations to lag or wane. She then directed students' attention back to the data on the screen, calling on a few students she had noted had meaningful contributions to add to the discussion. The first student she called on replied, "It's the greatest." The teacher PUSHED and asked the student, "What do you mean by that?" How easy it would have been to just affirm the student's response by saying, "Yes, 52 is the greatest value of length in inches from the data we have." Many teachers would have given the student credit for words he did not actually say, but this teacher PUSHED, required the student to find his own words, and expected him to articulate his own ideas so others would also understand. The student thought briefly and then responded with a deeper, more thoughtful response that enriched the discussion. </p><p>The teacher's flow was natural, comfortable, and produced great results. She asked her students to consider a question (e.g., "What do you notice about the line plot?"). After she posed each question, her students knew she would leave room for PAUSE so they could consider the question and their initial ideas about it. She then asked them to talk through their ideas with their Turn-n-Talk partner, giving everyone in the room an opportunity to develop and share their thoughts rather than just one or two students who would have typically been called upon to answer (see more about the critical importance of <a href="http://mathsnack.blogspot.com/2019/04/lets-talk-practice-turns-feedback.html" target="_blank">Practice Turns and Feedback here</a>). Once students had an opportunity to talk with a peer, she opened the discussion to the whole class and encouraged students to compare their ideas to others being presented in the room. Many students used silent hand signals to indicate that they had a similar idea to the one being shared. When needed, the teacher PUSHED students' responses with questions that challenged them to connect the mathematics and fully articulate their ideas. The conversations were meaningful, the questions promoted deeper thinking, and the students rose to each challenge given to them. It would have been easy to forget that this was a class of 7- and 8-year-olds in a 2nd grade classroom. But instead, I left wondering how I would be able to explain this beautiful balance of PUSH and PAUSE – I am still wondering how I can bottle it up and share the experience with others. </p><p><br /></p><p><br /></p>:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comtag:blogger.com,1999:blog-543907520077188162.post-13894190812906812832022-02-01T23:22:00.019-08:002022-02-22T04:18:04.422-08:0022 Ideas to Celebrate Super TWOsDay<div class="separator"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjrPeRA11nGLsB0zKUZDvzhhAeM97keA3fSDBJyVcafRJKsqezjiqwshquCYxqGmYOStyLYaY69osJ4dsFzpksBcfcZ1JTRZpdMSlp5CjJVQ7qO09LMWGNkAAp5cYSWAsDaj4yu7_w28LZbTttJ4mXrWtX59pme6kB9bpW7OdSGmztr_-awrHLgXd5UGQ=s2620" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1626" data-original-width="2620" height="406" src="https://blogger.googleusercontent.com/img/a/AVvXsEjrPeRA11nGLsB0zKUZDvzhhAeM97keA3fSDBJyVcafRJKsqezjiqwshquCYxqGmYOStyLYaY69osJ4dsFzpksBcfcZ1JTRZpdMSlp5CjJVQ7qO09LMWGNkAAp5cYSWAsDaj4yu7_w28LZbTttJ4mXrWtX59pme6kB9bpW7OdSGmztr_-awrHLgXd5UGQ=w652-h406" width="652" /></a></div><br /><div class="separator" style="clear: both; text-align: left;"><span>For my school district, the 100th day of school falls on February 11th this year – perhaps you have or are planning to celebrate the 100th day of school with your students, too... </span></div><div class="separator" style="clear: both; text-align: left;"><span><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span>FUN FACT: The 100th Day of school is actually the<b> <u>1000</u>th day of school for 5th graders </b>- check the math: Kindergarten + 1st + 2nd + 3rd + 4th = 5 x 180 days = 900. Now add the first 100 days of 5th grade (900 + 100) and <b>that equals 1000 days! </b> </span></div><div class="separator" style="clear: both; text-align: left;"><span><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span>This year, less than two weeks after the 100th day of school, we will have an opportunity to celebrate a day that is TWICE as exciting: <span style="font-size: large;"><b>Super TWOsDay! </b></span></span></div><div class="separator" style="clear: both; text-align: left;"><span><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span>Super TWOsDay is February 22, 2022 and it falls on a <u>Tues</u>day! The next time that February 22 falls on a Tuesday will be in 2028, then 2033, 2039, 2050, and 2056 (none of those are nearly as exciting as 2/22/22 since the years are not also 2s).</span></div><div class="separator" style="clear: both; text-align: left;"><span><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span>I DOUBLE dog dare you to try out a COUPLE of the ideas on this page with your students – Perhaps, you'll want to set a goal of doing at least TWO Super TWOsDay activities. Keep scrolling to c</span><span>heck out these 22 ideas to celebrate Super TWOsDay with your students in ways that are t(w)otally awesome! (ugh! that last attempt at "two humor" was bad, wasn't it?)</span></div><div class="separator" style="clear: both; text-align: left;"><span><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span><span style="color: red;"><br /></span></span></div><div class="separator" style="clear: both; text-align: left;"><span><span style="color: red; font-size: large;"><span style="background-color: #fff2cc;"><b>IDEA #1</b></span><span style="background-color: white;"> </span></span><span style="background-color: white; color: #666666;">(for grades 3+)</span></span></div><p></p><p></p><div class="separator" style="clear: both; text-align: center;"><b><span>Here's a fun challenge for your class to try on this very special TWOsday.</span></b></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjx_ebG6QR0O9hqIF62d-l41H6auFRdG4tXjL7dfWxYrV_1NXBJSFeoAOUkZOVpLW62b93UcYw-kPHvgohNlbAf0c0PZKolWfXlf-uw2tGAuXLwdkD5iyB7B9YyTHr-vmBijkjwWH_-87EeWIMJMCs2SlA0EN7UQPhSBDCu3fAf1qzYsA7adv0uCscTjQ=s1774" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1632" data-original-width="1774" height="436" src="https://blogger.googleusercontent.com/img/a/AVvXsEjx_ebG6QR0O9hqIF62d-l41H6auFRdG4tXjL7dfWxYrV_1NXBJSFeoAOUkZOVpLW62b93UcYw-kPHvgohNlbAf0c0PZKolWfXlf-uw2tGAuXLwdkD5iyB7B9YyTHr-vmBijkjwWH_-87EeWIMJMCs2SlA0EN7UQPhSBDCu3fAf1qzYsA7adv0uCscTjQ=w475-h436" width="475" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><span style="color: #cc0000;"><b>DOUBLY DIFFICULT:</b> Try to create values up to 10 using the 2 sets of 2s</span></div><div class="separator" style="clear: both; text-align: center;"><span style="color: #cc0000;"><b>I wonder if there is more than one way to make each value?</b></span></div><div class="separator" style="clear: both; text-align: center;"><span style="color: #cc0000;"><b><br /></b></span></div><div class="separator" style="clear: both; text-align: center;"><span style="color: #38761d;">Making 9 was tricky for me, but I figured out a clever way to do it 😉</span><span style="color: #cc0000;"> </span></div><div class="separator" style="clear: both; text-align: center;"><span style="color: #2b00fe;">HELP! Now I'm struggling to make a value of 7</span></div><div class="separator" style="clear: both; text-align: center;"><span style="color: #cc0000;">I'd 💖 to see your students' solutions to this TWOsday challenge</span></div><p></p><p></p><p><br /></p><p><b><span style="background-color: #fff2cc; color: red; font-size: medium;">IDEA #2</span><span style="color: #38761d;"> </span></b><span><span style="color: #666666;">(for everyone!)</span></span></p><p><span><b>TWOsDay-INSPIRED WARDROBE:</b> Encourage your students to dress up in "2-themed" outfits: Tutus (get it?), wear 2 bows, dress like a twin with a classmate. I plan to wear my new TWOsday inspired t-shirt. If you want your own TWOsday tee, you can find dozens of super cute designs with simple Google search. My fact-based brain couldn't resist buying a design that offered a list of additional number facts about this day and year - found this one on <a href="https://www.redbubble.com/shop/?query=twosday%20tee&ref=search_box" target="_blank">RedBubble</a>. </span></p><p style="text-align: center;"></p><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjfhCkX9x7NTOGg6d4rcuQ5kj6JcPZYcDuh1pGJA9sO3pkzblO3ho6JJX225sO4d65mKY1h1mtFBnOiz6Qb7HubedGKvsmJUaMO_qBJxkENX9PsmeVa15y0XftftwHHdxrBYPyIErlheP-8cZ0L-6Ea_WZdQ2GK8fOugulB_UImeMl8G9zDZdjB7ihlGg=s3088" style="margin-left: auto; margin-right: auto; text-align: center;"><span style="font-size: x-small;"><img border="0" data-original-height="3088" data-original-width="2316" height="320" src="https://blogger.googleusercontent.com/img/a/AVvXsEjfhCkX9x7NTOGg6d4rcuQ5kj6JcPZYcDuh1pGJA9sO3pkzblO3ho6JJX225sO4d65mKY1h1mtFBnOiz6Qb7HubedGKvsmJUaMO_qBJxkENX9PsmeVa15y0XftftwHHdxrBYPyIErlheP-8cZ0L-6Ea_WZdQ2GK8fOugulB_UImeMl8G9zDZdjB7ihlGg=s320" width="240" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-size: x-small;">Got my long sleeve TWOSDAY tee today!</span></td></tr></tbody></table><p><span style="background-color: #fff2cc; color: red; font-size: medium;"></span></p><p><span style="background-color: #fff2cc; color: red; font-size: medium;"><b><br /></b></span></p><p><span style="background-color: #fff2cc; color: red; font-size: medium;"><b>IDEA #3</b></span><span style="color: #38761d;"> </span><span><span style="color: #666666;">(for grade K-2)</span></span></p><p><b>HUNDREDS CHART HUNT for 2s</b> – Give each of your students a hundreds chart (or 120s chart). Challenge students to find and color in all of the numbers that have the number 2 as a digit. THEN discuss any patterns that they notice [the second column is colored in because there is a 2 in the ones place for all of them, 20 and 120 are both highlighted, the 20's row is highlighted except for the last number 30]. Be sure to discuss why these patterns occur as it relates to place value. Then ask them, "If this chart went on, what would be the next number that we would color in?"</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjJLxYK6q3V-h35f_zsbTgImiv93sDn_hE5RHhEF5-36cmYAXLCMpMuM2a8-Yp2It-0r-ZkzGhy1BmbKelFHffKsKxcJE0M6KhRWDtz_S6oQhRmNdsa9-srmLSzP_yHck9zCIVsFThBN4CfZlDKsr7xKSF_aUExRcAgKcYngsP-VT39h6-a28QJoi-AoQ=s1716" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1716" data-original-width="1462" height="320" src="https://blogger.googleusercontent.com/img/a/AVvXsEjJLxYK6q3V-h35f_zsbTgImiv93sDn_hE5RHhEF5-36cmYAXLCMpMuM2a8-Yp2It-0r-ZkzGhy1BmbKelFHffKsKxcJE0M6KhRWDtz_S6oQhRmNdsa9-srmLSzP_yHck9zCIVsFThBN4CfZlDKsr7xKSF_aUExRcAgKcYngsP-VT39h6-a28QJoi-AoQ=s320" width="273" /></a></div><br /><p><br /></p><p><span style="color: red;"><span style="background-color: #fff2cc; font-size: medium;"><b>IDEA #4</b></span> </span><span style="color: #666666;">(this one is likely best to use with upper grades)</span></p><p>Same 120 chart as shown above, but for this one, challenge students to use the digits of each number to find a value equal to 2. Here are a COUPLE of examples (yep, I'm going to squeeze every "two"-related reference I can think of into this post!): </p><p></p><ul style="text-align: left;"><li>13 - using the digits of 13, we can subtract the digits 3 – 1<b> = 2</b></li><li>97 - using the digits of 97, we can multiply 9 x 7 = 63 and then use those digits 6 ÷ 3 <b>= 2</b></li></ul><p></p><p>I wonder how many of the numbers could be eliminated in this challenge?? Could we figure out a way to eliminate ALL of them? Or perhaps the challenge is to find a "2" calculation with 22 of them - ahhh, that we could probably do with just a bit of collective effort!</p><p><br /></p><p><span style="background-color: #fff2cc; color: red; font-size: medium;"><b>IDEA #5</b></span><span><span style="color: #666666;"> (can be adapted for any grade)</span></span></p><p style="text-align: center;"><span></span></p><p><span><b>MEASUREMENT ACTIVITY:</b> Ask students to find items that are exactly 2 units long. The units could be inches, feet, paperclips, shoes, ... be creative! Keep a record of your items. Compare measurements with other students. Allow time for students to discuss their observations. </span></p><div class="separator" style="clear: both; text-align: center;"><span><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjOrdZD29qeKjovZb3vOu3yzftUmHFVo-1DIcPY3mXU9d4Fm0DV8PjNVEwnSF3JswUNL_-rVG1wdvBC3qMJwNHuXITEs5SOwQizbCxVEtr7Ktqn-6pbAhtVGVXjtpM2qBHgmPEJyKCpH-ivgC1mNytqQAGn-HAHF6DGfP117_KVg8DV2XFw7xH-4pT8uQ=s630" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="344" data-original-width="630" height="174" src="https://blogger.googleusercontent.com/img/a/AVvXsEjOrdZD29qeKjovZb3vOu3yzftUmHFVo-1DIcPY3mXU9d4Fm0DV8PjNVEwnSF3JswUNL_-rVG1wdvBC3qMJwNHuXITEs5SOwQizbCxVEtr7Ktqn-6pbAhtVGVXjtpM2qBHgmPEJyKCpH-ivgC1mNytqQAGn-HAHF6DGfP117_KVg8DV2XFw7xH-4pT8uQ=w320-h174" width="320" /></a></span></div><p></p><p>ASK: How can all of these things have a measurement of 2 units if they are different sizes? This is a great activity to explore how the size of the unit impacts the relative length. </p><p>Could we create a new unit of measure where 2 of the larger unit equals 22 of the smaller unit? What would that look like? [D<i>id you just think about how each unit would be partitioned into elevenths -- see how a simple, purposeful question can generate so much mathematical reasoning and discussion?!!]</i></p><p><span style="color: red;"><br /></span></p><p><span style="color: red;"><span style="background-color: #fff2cc; font-size: medium;"><b>IDEA #6</b></span> </span><span><span style="color: #666666;">(pick and choose the questions that will challenge your students appropriately)</span></span></p><p><span><b>QUICK IDEAS: </b>22 quick cross-curricular ideas to do in the moment (click <b><a href="https://drive.google.com/file/d/1XC4wqdA6tmiXdeMjU506NEekkfnx7pBA/view?usp=sharing" target="_blank">HERE</a> </b>for a printable version of these 22 quick tasks)</span></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhvtSw8psHNMRTHCNDDNOgUkk6Mx9sT-TM6LIJ3gklT85Ljb6OpnaXex9vV9ZMBY96R2omQbNsWeGH8LFOl2ALLPxxNW-0kyb556aRXTSKs_xY3vvB_s0T27Ho1CTgwNiO84FOxAhhUWzJKnULDkvyekn0GXxfiXxbsPk_0mDlXUvtvQ7jKUN5zXQRXdw=s1880" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1880" data-original-width="1508" height="640" src="https://blogger.googleusercontent.com/img/a/AVvXsEhvtSw8psHNMRTHCNDDNOgUkk6Mx9sT-TM6LIJ3gklT85Ljb6OpnaXex9vV9ZMBY96R2omQbNsWeGH8LFOl2ALLPxxNW-0kyb556aRXTSKs_xY3vvB_s0T27Ho1CTgwNiO84FOxAhhUWzJKnULDkvyekn0GXxfiXxbsPk_0mDlXUvtvQ7jKUN5zXQRXdw=w514-h640" width="514" /></a></div><p><span style="color: red;"><br /></span></p><p><span style="background-color: #fff2cc; color: red; font-size: medium;"><b>IDEA #7</b></span><span><span style="color: #666666;"> </span></span></p><div style="text-align: left;"><span style="font-size: small;"><b>VIDEO FUN:</b></span><span style="font-size: small; font-weight: normal;"> Show a video celebrating the number 2 during your TWOsday celebration</span></div><p></p><p></p><span style="color: #666666;">(grades PK-2)</span><br /><ul style="text-align: left;"><li><a href="https://youtu.be/8jOzhiACB68" target="_blank">Doubles! Doubles!</a></li><li><a href="https://youtu.be/D32JZKKgjJg" target="_blank">The Number 2 Song</a><br /></li><li><a href="https://youtu.be/OCxvNtrcDIs" target="_blank">Jack Hartmann's Dancing 2s</a><br /></li><li><a href="https://youtu.be/-fAmAWQ_TTM" target="_blank">Jack Hartmann's I Can Show the Number 2</a><br /></li></ul><span style="color: #666666;">(grade 3)</span><br /><ul style="text-align: left;"><li><a href="https://youtu.be/iiR8hqJeQsw" target="_blank">Jack Hartmann's Multiply by 2</a><br /></li><li><a href="https://youtu.be/Li3aPcMEwHs" target="_blank">Catchy Multiply by 2 Song</a></li><li><a href="https://youtu.be/9C4EN7mFHCk" target="_blank">2 Times Table Song</a></li></ul><p><span style="color: red;"><br /></span></p><p><span style="background-color: #fff2cc; color: red; font-size: medium;"><b>IDEA #8</b></span><span style="color: #38761d;"> </span><span><span style="color: #666666;">(for everyone!)</span></span></p><p><span><b>BREAK TIME:</b> Take several brain breaks that also DOUBLE as exercise breaks. With each break, try to do 22 of the named exercise. Need a few ideas? Try these:</span></p><p></p><ul style="text-align: left;"><li><span>arm circles (22 forward circles / 22 backward circles)</span></li><li><span>hop on one foot (22 hops on each foot)</span></li><li><span>jumping jacks</span></li><li><span>toe touches</span></li><li><span>high knee marching</span></li><li><span>run in place for 22 seconds</span></li></ul><p></p><p><span style="color: red;"><br /></span></p><p><span style="background-color: #fff2cc; color: red; font-size: medium;"><b>IDEA #9</b></span><span style="color: #38761d;"> </span><span><span style="color: #666666;">(for grades 3+)</span></span></p><p><span><b>A 2-INSPIRED MATH GAME – </b></span>This game builds number sense: Roll two dice to get the digits for your starting number (for example a 4 and 5 would be 45 or 54). Students write the number and then DECIDE if they should ADD 22 or MULTIPLY by 2 to get the greater value. Keep a chart of the trials. Roll/record/calculate/repeat for at least ten numbers. Challenge your students to discover if there is a <i><b>pattern</b></i> of which operation is better to yield the greater value <i>[SPOILER ALERT: If the number is less than 22, it is better to +22. If the number is greater than 22, it is better to x2. If the number is exactly 22, the result is the same with either operation. Once students discover the pattern, be sure to discuss WHY it's true - the reflection discussion is where the power of just about any activity is found!]. </i></p><p></p><p style="text-align: center;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEj6nnUfFk4Uvkisqa0PQCesImV4aKfy4YdFLVmUbasfSEDysZKYdYmd0pxxRKrFGJ8XsYJCM3_dhdR1AAXA1ADtcDXkXZyH0Khl21_APtmqnA1kOyiDallJanfoD884oXwI8tzIqSk6yzcYRBc4n2iLyXP4lD-iFQVEmt5-Effd9sc5kWpxtH-wWa4aIQ=s946" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="676" data-original-width="946" height="143" src="https://blogger.googleusercontent.com/img/a/AVvXsEj6nnUfFk4Uvkisqa0PQCesImV4aKfy4YdFLVmUbasfSEDysZKYdYmd0pxxRKrFGJ8XsYJCM3_dhdR1AAXA1ADtcDXkXZyH0Khl21_APtmqnA1kOyiDallJanfoD884oXwI8tzIqSk6yzcYRBc4n2iLyXP4lD-iFQVEmt5-Effd9sc5kWpxtH-wWa4aIQ=w200-h143" width="200" /></a></div><br /><span style="color: red;"><br /></span><p></p><p><span style="color: red; font-size: medium;"><b style="background-color: #fff2cc;">IDEA #10</b></span><span style="color: #38761d;"> </span><span><span style="color: #666666;">(for grades PK-2)</span></span></p><p><span><b>READ ALOUDS:</b> Why not have a TWOsDay Read Aloud event? There are a lot of books that fit the TWOsDay theme – check your library or click on one of the links below for a video real aloud:</span></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhstNpYMGd0SNAs32ovO6eAk12-0kTDGzggKRZpPfy3UrI3-5c6_XucbrvQT4ABGkqh8LV-t8DC5pNBwMtcac8Tu45HScxWw-r1483OGSVU_B4gyEYEYDjl-u_KIO2800TvR9OsDlfNZli4wdZC2BbAhdnKeQXDcSiuQYycXFBebQILgGS_ioI9Y3GbaQ=s1716" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="416" data-original-width="1716" height="157" src="https://blogger.googleusercontent.com/img/a/AVvXsEhstNpYMGd0SNAs32ovO6eAk12-0kTDGzggKRZpPfy3UrI3-5c6_XucbrvQT4ABGkqh8LV-t8DC5pNBwMtcac8Tu45HScxWw-r1483OGSVU_B4gyEYEYDjl-u_KIO2800TvR9OsDlfNZli4wdZC2BbAhdnKeQXDcSiuQYycXFBebQILgGS_ioI9Y3GbaQ=w640-h157" width="640" /></a></div><p></p><ul style="text-align: left;"><li><b><a href="https://youtu.be/Tzd6uU-QR8Q" target="_blank">Just Right for Two</a></b> by Tracey Corderoy and Rosalind Beardshaw – a story about needing friends – click the title for a video reading of this book</li><li><a href="https://youtu.be/cutROw_NJvE" target="_blank"><b>A Tale of Two Beasts</b></a> by Fiona Roberton – a fun book about two perspectives</li><li><a href="https://youtu.be/ozDsg78miNs" target="_blank"><b>Double the Ducks</b></a> (PK-K) by Stuart J. Murphy – a story for PreK and Kindergarten students about the important math skill of doubling</li><li><b><a href="https://youtu.be/JML_7tsqlmU" target="_blank">Two of Everything</a></b> by Lily Toy Hong - A Chinese folk tale that also teaches a lesson about multiplying by 2s</li></ul><p style="text-align: center;"></p><br /><p></p><p><span style="background-color: #fff2cc; color: red; font-size: medium;"><b>IDEA #11</b></span><span style="color: #38761d;"> </span><span><span style="color: #666666;">(for everyone!)</span></span></p><p><span><b>TWOsDay GIFT: </b>Give each of your students a #2 pencil as a Super TWOsDay gift - look for brands that have the "2" clearly visible but don't waste your money on those horrible pencils that have terrible graphite inside - Ticonderoga pencils really do rule! and I hear the Amazon Basics are pretty good, too. </span></p><p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-left: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiDj4iax6Lnro2XHxP7IqoRYjAsMoF5J6ZfmsGoJahBmagthjfwV5obovH4p3MBiXKqJI7bENkhpr2ukfodeBItpupD_-XkRXhYetu8mWd1hMPmQ1YrybzW1gjG5IvH64mJKDzQNEzzmLPYzLBuRrPlb85aqWv0u52dtg9uq0p5RBONSrnIEWZBLmi_1A=s1128" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="852" data-original-width="1128" height="370" src="https://blogger.googleusercontent.com/img/a/AVvXsEiDj4iax6Lnro2XHxP7IqoRYjAsMoF5J6ZfmsGoJahBmagthjfwV5obovH4p3MBiXKqJI7bENkhpr2ukfodeBItpupD_-XkRXhYetu8mWd1hMPmQ1YrybzW1gjG5IvH64mJKDzQNEzzmLPYzLBuRrPlb85aqWv0u52dtg9uq0p5RBONSrnIEWZBLmi_1A=w488-h370" width="488" /></a></td></tr><tr><td class="tr-caption" style="text-align: right;"><span>Image Source: https://lifehacker.com</span></td></tr></tbody></table><span><br /></span><p></p><p><span style="color: #38761d;"><br /></span></p><p><span style="color: #38761d;"><br /></span></p><p><span style="color: #38761d;"><br /></span></p><p><span style="color: #38761d;"><br /></span></p><p><span style="color: #38761d;"><br /></span></p><p><span style="color: #38761d;"><br /></span></p><p><span style="color: #38761d;"><br /></span></p><p><span style="color: #38761d;"><br /></span></p><p><span style="color: #38761d;"><br /></span></p><p><span style="color: #38761d;"><br /></span></p><p><br /></p><p><span style="color: red;"><br /></span></p><p><span style="color: red; font-size: medium;"><b style="background-color: #fff2cc;">IDEA #12</b></span><span style="color: #38761d;"> </span><span><span style="color: #666666;">(best for grade 5 - you'll likely have to stretch their knowledge base by explaining squares and roots) </span></span></p><b><div style="text-align: center;"><b>MATH PUZZLE:</b> Click <b><a href="https://static1.squarespace.com/static/54905286e4b050812345644c/t/61f40f230bdc3b055459c391/1643384614282/Twosday-678.pdf" target="_blank">HERE</a></b> to get this challenging TWOsDay math puzzle from <a href="https://static1.squarespace.com/static/54905286e4b050812345644c/t/61f40f230bdc3b055459c391/1643384614282/Twosday-678.pdf" target="_blank">Mashup Math</a><a href="https://blogger.googleusercontent.com/img/a/AVvXsEggft8Qrw8u2BAHSeavmT9ZtmeUEySx8hTVceUk_IasHHoF6emFtwTK2uXdLPHku8-xJxMV3shBfMKt1HF4S10XaJa6dSDH6WczgJOZi5MfSIZWHp5otoOd4fFjFcufKG4qARUA-XJoIba3hJ8X5PyEifjnM2Y5El-bU9tiV3JIH-FaqXDH9dFiTWDKxQ=s1748" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="1748" data-original-width="1354" height="400" src="https://blogger.googleusercontent.com/img/a/AVvXsEggft8Qrw8u2BAHSeavmT9ZtmeUEySx8hTVceUk_IasHHoF6emFtwTK2uXdLPHku8-xJxMV3shBfMKt1HF4S10XaJa6dSDH6WczgJOZi5MfSIZWHp5otoOd4fFjFcufKG4qARUA-XJoIba3hJ8X5PyEifjnM2Y5El-bU9tiV3JIH-FaqXDH9dFiTWDKxQ=w310-h400" width="310" /></a></div></b><p></p><p><span style="color: red;"><br /></span></p><p><span style="color: red; font-size: medium;"><b style="background-color: #fff2cc;">IDEA #13</b></span><span style="color: red;"> </span><span><span style="color: #666666;">(can be adapted for most grades)</span></span></p><p><span><b>WRITING IDEA:</b> Just for fun, I'll throw in 2 ideas that are not math-related but still make great TWOsDay activities for your class. Perhaps a WRITING idea for this special TWOsDay:</span></p><p></p><ul style="text-align: left;"><li><span>Write about TWO people who have had a positive influence in your life </span></li><li><span>Complete a pictorial graphic for the theme "When I'm 22". Where will you live? What is your job? What do you like to do? </span></li><li><span>If I had $22 to buy someone a gift, I'd....</span></li></ul><p></p><p style="text-align: center;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhEiKzzbg_MxXbXcP9kn8zaim0pw6qKApgzsPR_SKN6tulu8FiXiJBVMEryHp-IzkMVOXmvd6qX9lt5dywECNVJFzQxLl0V8R5z0ay2TII2MUKyAHvY3IoUe1T0aV2Rq8qrdmVA4lzN-FKCZP_Sb9iby2uuot-CFNEIn7yRGl5asYusVW5bm2pmlpM5zA=s3857" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="3857" data-original-width="3336" height="200" src="https://blogger.googleusercontent.com/img/a/AVvXsEhEiKzzbg_MxXbXcP9kn8zaim0pw6qKApgzsPR_SKN6tulu8FiXiJBVMEryHp-IzkMVOXmvd6qX9lt5dywECNVJFzQxLl0V8R5z0ay2TII2MUKyAHvY3IoUe1T0aV2Rq8qrdmVA4lzN-FKCZP_Sb9iby2uuot-CFNEIn7yRGl5asYusVW5bm2pmlpM5zA=w173-h200" width="173" /></a></div><br /><span style="color: red;"><br /></span><p></p><p><span style="background-color: #fff2cc; color: red; font-size: medium;"><b>IDEA #14</b></span></p><p><span><b>READING IDEA:</b> Here is the SECOND not-so-mathy idea: Challenge your students to read TWO books in the TWO weeks prior to 2/22/22. When Super TWOsDay arrives, invite your students to bring their books for a partner book talk (that's TWO people). Ask each of your students to tell their partner what their book was about, what was their favorite part of the story, etc. </span></p><p style="text-align: center;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEigFA_nFCtAsQK8BtJxZB9-KdImiLuUECidRVbP5eSTY7ghOj0KL9g7YsD7kahRcv4yKoO9gNZPYZLRZMrxvtew-erpy1nUtcxR9QjNcxqm5I7P0fl_jtAP3xK3BpLg9yil9y6y9hvLx0JkrMg8tOUSI67G6t0U-mOsV8yZZrJL5xOC1m5z8SvUDGp_AQ=s1024" style="margin-left: auto; margin-right: auto;"><span style="font-size: xx-small;"><img border="0" data-original-height="616" data-original-width="1024" height="193" src="https://blogger.googleusercontent.com/img/a/AVvXsEigFA_nFCtAsQK8BtJxZB9-KdImiLuUECidRVbP5eSTY7ghOj0KL9g7YsD7kahRcv4yKoO9gNZPYZLRZMrxvtew-erpy1nUtcxR9QjNcxqm5I7P0fl_jtAP3xK3BpLg9yil9y6y9hvLx0JkrMg8tOUSI67G6t0U-mOsV8yZZrJL5xOC1m5z8SvUDGp_AQ=s320" width="320" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: right;"><br /></td></tr></tbody></table><br /><span style="color: red;"><br /></span><p></p><p><span style="background-color: #fff2cc; color: red; font-size: medium;"><b>IDEA #15</b></span><span style="color: #38761d;"> </span><span><span style="color: #666666;">(for everyone!)</span></span></p><p><span><b>I SPY 2: </b>Why not play "I Spy" while walking through the halls to lunch, recess, PE, etc. As students walk through the halls, ask them to look for the number 2. When they see one, they should raise their hand holding up 2 fingers, of course! Pause to notice all the 2s around your building. Be sure to include conversations about how that two is being used and talk about the place value of each 2 you find - after all, the 2 that you may find on room 211 is very different than the 2 you'll find on room 112 or on a clock or in a phone number.... </span></p><p style="text-align: center;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiZOJr7IMZODS5D1mJEYAVRwQpH9d2G1kOjJ1UXkwQ3BU7G-phighzh_OuJF-JHCBfFEp4WmEphYfQsvdxu3OwlXAjVo3UVC9zxZ0B3FJ4rYpHA98vNvYE4c-LGsLIuUc82DEZ0S5hwnRDu6ECJfxZSeeWzzPpprwZkGXQfBER48I6a_NXl2m3vtGBkoQ=s1024" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="819" data-original-width="1024" height="256" src="https://blogger.googleusercontent.com/img/a/AVvXsEiZOJr7IMZODS5D1mJEYAVRwQpH9d2G1kOjJ1UXkwQ3BU7G-phighzh_OuJF-JHCBfFEp4WmEphYfQsvdxu3OwlXAjVo3UVC9zxZ0B3FJ4rYpHA98vNvYE4c-LGsLIuUc82DEZ0S5hwnRDu6ECJfxZSeeWzzPpprwZkGXQfBER48I6a_NXl2m3vtGBkoQ=s320" width="320" /></a></div><br /><span style="color: red;"><br /><br /></span><p></p><p><span style="background-color: #fff2cc;"><b><span style="font-size: medium;"><span style="color: red;">IDEA #16</span><span style="color: #38761d;"> </span></span></b></span><span><span style="color: #666666;">(geometry for all!)</span></span></p><p><span><b>2-D DESIGN:</b> Design a picture using 2D shapes: circles, squares, triangles, rectangles, trapezoids.</span></p><p style="text-align: center;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjp2RwZQ-8XFUlfrenL4y3CLHV2P6Qj2qjgBU7o6DT3vqiEc93fmWpeZUp94sSr1Yd2OZiOr7B4w3VsJjieRnkeBBqzWP0KmiKjMPNGYiTpsYr9QnOijt4KPdjWEu6MU5LTZ5_WIYf3a4NzSxtQFeWVoTQeG3Cx4W-6D1h42ASl8dDGrtA5lInB6fA3Ug=s2042" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="2042" data-original-width="1366" height="640" src="https://blogger.googleusercontent.com/img/a/AVvXsEjp2RwZQ-8XFUlfrenL4y3CLHV2P6Qj2qjgBU7o6DT3vqiEc93fmWpeZUp94sSr1Yd2OZiOr7B4w3VsJjieRnkeBBqzWP0KmiKjMPNGYiTpsYr9QnOijt4KPdjWEu6MU5LTZ5_WIYf3a4NzSxtQFeWVoTQeG3Cx4W-6D1h42ASl8dDGrtA5lInB6fA3Ug=w429-h640" width="429" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-size: x-small;">Idea Source: https://kidsactivitiesblog.com/50959/art-math-inspired-klee/</span></td></tr></tbody></table><p></p><div class="separator" style="clear: both; text-align: center;"><br /></div><span style="color: red;"><br /></span><p></p><p><span><b style="background-color: #fff2cc; color: red; font-size: large;">IDEA #17</b><span style="color: #666666;"><span style="background-color: white;"> (grade 5 standard 5.OA.B.3)</span></span></span></p><p>Ask students to (1) generate a pattern that is related to the number two, (2) create ordered pairs using their "2-rule", and then (3) graph the pattern. Post all of the graphed patterns and discuss how using each 2-rule impacted the graphed lines. Students might, for example, DOUBLE the x-value to get the y-value. Or perhaps the y-value is equal to x + 2. Encourage students to be creative with their 2-rule. The power of this activity will be in comparing the graphs to see how the various 2-rules impacted the graphs. </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEi2J8u4gU7ztQQ2S_4_qKSLrox1HE8I3OSE-jbwAESF4RRm2iYQUS4zbzU2NamzkZJEFDUqMXb1YRTCIVZgP6OjZKvO-1x81v9WTqH_AtVXHc_Nmv-fZCY9-5dmpm4-afVEqedXVCIw74-iQcgX-PKudU7nmqMjhRglPvCumiOaarIb4cJVMITI9QVcuw=s3243" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="3243" data-original-width="2774" height="320" src="https://blogger.googleusercontent.com/img/a/AVvXsEi2J8u4gU7ztQQ2S_4_qKSLrox1HE8I3OSE-jbwAESF4RRm2iYQUS4zbzU2NamzkZJEFDUqMXb1YRTCIVZgP6OjZKvO-1x81v9WTqH_AtVXHc_Nmv-fZCY9-5dmpm4-afVEqedXVCIw74-iQcgX-PKudU7nmqMjhRglPvCumiOaarIb4cJVMITI9QVcuw=s320" width="274" /></a></div><br /><p><br /></p><p></p><p><span style="background-color: #fff2cc; color: red; font-size: medium;"><b>IDEA #18</b></span><span style="background-color: white; color: #666666;"> </span><span style="background-color: white; color: #666666;">(grade 5 standard 5.MD.A.1)</span></p><p><span style="background-color: white;">In grade 5, students are asked to convert units of measure, such as yards to feet and centimeters to meters to centimeters. On this very special TWOsDay, present students with various measurements that are "2-something" (i.e. 2 feet, 2 pounds, 2 miles) and ask students to convert the measurements into equivalent values. Don't think worksheet, think engagement.... Perhaps begin by creating a <b>student-generated list</b> like the one below:</span></p><p></p><ul style="text-align: left;"><li><span style="background-color: white;">My house is 2 MILES away from the school</span></li><li><span style="background-color: white;">My cell phone is about 2 INCHES wide</span></li><li><span style="background-color: white;">My guinea pig weighs about 2 POUNDS</span></li></ul><div>Once they have a class list, challenge them to convert the "2" measures into equivalent values either by providing them a reference sheet or encouraging them to look up various measurement conversions (I favor the latter if students have access to do a few in-the-moment searches on the internet). </div><div><ul style="text-align: left;"><li>My house is 10,560 feet away from school because 1 mile is 5,280 feet so 2 x 5,280</li><li>My cell phone is about 0.16 feet wide because 1 foot is 12 inches so 2 ÷ 12 (if you're wondering, yes, absolutely permit calculator use – we are digging deeper into unit conversions, not assessing their ability to divide fractional values)</li><li>My guinea pigs weighs about 32 ounces because 1 pound is 16 ounces so 2 x 16</li></ul></div><p></p><p style="text-align: center;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEj6SznnWWwzaYjmPL-sBiT0zbRFg5-V2XeQzHSFBZXaI5hya4uzBg7pHRrA6QRvRjb0nXzyapEpFZi9J74LsjnaNQNV_-2HEZXxbrwv1GQ8vDxx9bxKWtX2WGPs-gjCLNp4Lr437ZAaqSjMtlvbnpzQAijMM_jA1nKdznevIRVqUrOtMIFkEHn-0zdHCQ=s636" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="636" data-original-width="636" height="200" src="https://blogger.googleusercontent.com/img/a/AVvXsEj6SznnWWwzaYjmPL-sBiT0zbRFg5-V2XeQzHSFBZXaI5hya4uzBg7pHRrA6QRvRjb0nXzyapEpFZi9J74LsjnaNQNV_-2HEZXxbrwv1GQ8vDxx9bxKWtX2WGPs-gjCLNp4Lr437ZAaqSjMtlvbnpzQAijMM_jA1nKdznevIRVqUrOtMIFkEHn-0zdHCQ=w200-h200" width="200" /></a></div><br /><span style="background-color: white; color: #666666;"><br /></span><p></p><p><span style="background-color: #fff2cc; color: red; font-size: medium;"><b>IDEA #19</b></span><span style="background-color: white; color: #666666;"> </span><span style="background-color: white; color: #666666;">(grade 4 standard 4.NF.A.2)</span></p><p><span>Ask students to generate 2 different fractions that each contain the number 2 [i.e. 1/2 and 2/3]. Then ask students to create models of these two fractions </span>[definitely plan to use hands-on fraction models or try out these virtual fraction tools – I love the ones found on <a href="https://toytheater.com/fraction-bars/" target="_blank">Toy Theater</a> and <a href="https://apps.mathlearningcenter.org/fractions/" target="_blank">Math Learning Center</a>]. Encourage students to discuss the comparisons. </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgzgTOtGOKXQuZbzGHIWpvkS0DGuUBQlAlM9Gs_gWDav1J3cLwLnmFqZaiAaSM3LmDp5_xk7qCKxwzyx644cgmk9z8Cpx9ptaicDYXCaPQZ86zcBnFzLre3iIxB1UO3102BhCCBh1RxAn9-k4cHtFZsnfVfHevMycOU8BrOEowOawZ6KV0YOKpl43rjgg=s1004" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="624" data-original-width="1004" height="199" src="https://blogger.googleusercontent.com/img/a/AVvXsEgzgTOtGOKXQuZbzGHIWpvkS0DGuUBQlAlM9Gs_gWDav1J3cLwLnmFqZaiAaSM3LmDp5_xk7qCKxwzyx644cgmk9z8Cpx9ptaicDYXCaPQZ86zcBnFzLre3iIxB1UO3102BhCCBh1RxAn9-k4cHtFZsnfVfHevMycOU8BrOEowOawZ6KV0YOKpl43rjgg=s320" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: left;"> </span></div><p><br /></p><p><span style="color: red;"></span></p><p><span style="background-color: #fff2cc; color: red; font-size: medium;"><b>IDEA #20 </b></span><span style="background-color: white; color: #666666;">(grade 4 standard 4.NBT.B.6)</span></p><p><span>When students can write their own word problems, this demonstrates a higher level of understanding and thinking. Challenge students to write multiplication/division word problems with one of the values in the problem being 22, 222, or 2222. Ask them to draw a model of their problem to solve it. Display all of the amazing word problems that students created. </span></p><p><span>Here's how one <b>4th grader</b> approached this task:</span></p><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><br /></div><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgXcF4k_wCFPe7xDSmTBRsstmkI2o_n5iLVGYOQrHT939UCkdGEgJ228leu957_zCAFnd7zpG3KNn5JV7-oRl-XZXtHxJU4Nu1FE22K-tj93-I8npB5n0xKZoZ8E4c90JUjcBRixttxsElW1FdC-n_lpG6M7dApXHXge0HsMVmwpTVjrjWZDgHLW4OFfw=s3618" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="3618" data-original-width="2612" height="400" src="https://blogger.googleusercontent.com/img/a/AVvXsEgXcF4k_wCFPe7xDSmTBRsstmkI2o_n5iLVGYOQrHT939UCkdGEgJ228leu957_zCAFnd7zpG3KNn5JV7-oRl-XZXtHxJU4Nu1FE22K-tj93-I8npB5n0xKZoZ8E4c90JUjcBRixttxsElW1FdC-n_lpG6M7dApXHXge0HsMVmwpTVjrjWZDgHLW4OFfw=w289-h400" width="289" /></a></div><br /><span><br /><br /></span><p></p><p><span><span style="background-color: #fff2cc; color: red; font-size: medium;"><b>IDEA #21 </b></span><span style="background-color: white; color: #666666;">(grade 3 standard 3.MD.C area and perimeter)</span></span></p><p><span><span style="background-color: white;">Give students 22 one-inch tile blocks. Guide them through this area/perimeter activity through questioning and discussion: </span></span></p><p></p><ul style="text-align: left;"><li><span><span style="background-color: white;">Can you arrange these blocks so they make a rectangle? (give plenty of time to explore - students may likely attempt arrays that are more square-like and discover that they cannot use all, so will need time to discover and rethink their ideas - try not to rush this important part of the learning) <br />NOTE: Students will be able to make an 11 by 2 or a 22 by 1 rectangle.</span></span></li></ul><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiRd7detkyXD9Kq3RE_1Bb5xq8xhDZowDZlI1fBacgBegedeG8JpXN5hqfVmcgzMHF1hWoGdyo0PPgL8agn9eCA2WDKYCWMlTEdjCRvhkByMyQnhYMHGUFj7jtGC7R-oWV9C4Sk6C-sqzmQxRwKToMjECUY0rTAVx6k00tiUiCo1ag14iENVGq3LRtIaw=s1728" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="630" data-original-width="1728" height="117" src="https://blogger.googleusercontent.com/img/a/AVvXsEiRd7detkyXD9Kq3RE_1Bb5xq8xhDZowDZlI1fBacgBegedeG8JpXN5hqfVmcgzMHF1hWoGdyo0PPgL8agn9eCA2WDKYCWMlTEdjCRvhkByMyQnhYMHGUFj7jtGC7R-oWV9C4Sk6C-sqzmQxRwKToMjECUY0rTAVx6k00tiUiCo1ag14iENVGq3LRtIaw=s320" width="320" /></a></div><ul style="text-align: left;"><li><span>Discuss the various configurations that students created. </span></li><li><span>Chart the various models as you discuss them. </span></li><li><span>Ask, "What is the area of the rectangle?" (add the information to the chart)</span></li><li><span><span style="background-color: white;">Ask, "What is the perimeter of your rectangle?" (add to the chart)</span></span></li><li><span><span style="background-color: white;">Challenge students to make composite figures using the 22 unit squares.</span></span></li><li><span style="background-color: white;">Sketch and chart the information. </span></li><li><span style="background-color: white;">Ask what generalizations can be made about the area and perimeter relationship? Below are some sample ideas that your students may name:</span></li><ul><li><span style="background-color: white;">The area is always 22 not matter how the units are configured</span></li><li><span style="background-color: white;">The more the shape looks like a square, the smaller the perimeter</span></li><li><span style="background-color: white;">The area is measured in "square units"</span></li><li><span style="background-color: white;">The perimeter is measured in "units" (not squared since we are measuring the one dimension of length)</span></li></ul></ul><p></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjJeILmpzatx_B6h9m3iHgljZ81oHSeUuaaRe057a9bSmK2Nr_G7zTZS22JyWr_3_jvnVQURjdZBZQZxuJgnOjRpy6rzFWWD-7ysoFT1r3NhFakgWBDYfRnbPRr6mGBKm1ydwVJzrOu8sStnHezu6IqUVjZKFIOczN4mhqFrG876AyTN49ca3Q8uW9BHg=s2878" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2203" data-original-width="2878" height="306" src="https://blogger.googleusercontent.com/img/a/AVvXsEjJeILmpzatx_B6h9m3iHgljZ81oHSeUuaaRe057a9bSmK2Nr_G7zTZS22JyWr_3_jvnVQURjdZBZQZxuJgnOjRpy6rzFWWD-7ysoFT1r3NhFakgWBDYfRnbPRr6mGBKm1ydwVJzrOu8sStnHezu6IqUVjZKFIOczN4mhqFrG876AyTN49ca3Q8uW9BHg=w400-h306" width="400" /></a></div><br /><span><br /><span style="color: #38761d;"><br /></span></span><p></p><p><span><span style="color: #38761d;">...and finally... <br /></span></span><span style="color: red; font-size: medium;"><b style="background-color: #fff2cc;">IDEA #22</b> <span style="background-color: white;">is, of course, targeted to <b>2nd</b> GRADE content</span><b style="background-color: white;"> </b></span><span style="background-color: white; color: #666666;">(</span><span style="background-color: white; color: #666666;">grade 2 standard 2.NBT.A.4)</span></p><p><span style="background-color: white;">Students in second grade and beyond are expected to be able to compare any 3-digit number based on place value. Show students the comparison statement 11=11 (eleven equals eleven). Tell them that since today is a very special TWOsDay, you have two 2s that you are going to squeeze in as digits with each of the numbers shown. Challenge them to not only tell which number is now greater, but to explain how the location of the 2 impacted each number. </span></p><p><span style="background-color: white;">11 = 11 after inserting a 2 digit into each number, show students 211 ? 121. Notice that both 3-digit numbers have two ones and one two. But which one has the greater value? Give your students time to discuss their ideas with a partner then select and discuss some of their ideas with the whole class. Use inequality symbols to show the correct number sentence </span></p><p style="text-align: center;"><span style="background-color: white; color: #0b5394; font-size: x-large;"><b>211 > 121 </b></span></p><p><span style="background-color: white;">Now move the 2s to different locations (112 ? 211). Discuss the new inequality. Perhaps change the 1s to 9s and repeat the process. </span></p><p><br /></p><div class="separator" style="clear: both; text-align: left;"><b><span style="color: #b45f06; font-size: medium;">Just for fun, I set this post to publish on 2/2/22 at 2:22 am</span></b></div><div class="separator" style="clear: both; text-align: left;"><i><br /></i></div><div class="separator" style="clear: both; text-align: left;"><i>THANK YOU, <b>Steve O</b>. for encouraging me to get this resource out there - it was on my mind but may have fallen to wayside had you not given me that little push last week :) </i></div><br /><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br />:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comtag:blogger.com,1999:blog-543907520077188162.post-43701530242559544172021-05-04T17:46:00.037-07:002021-08-05T20:47:50.474-07:00Accelerate vs. Remediate<p></p><div style="text-align: right;"><div style="text-align: left;"><div class="separator" style="clear: both; text-align: center;"><span style="color: #274e13;"><br /></span></div><span style="color: #274e13;"><span style="font-family: arial;">I had a conversation the other day that is likely a common one, but why it’s common (or even an acceptable practice) is a mystery to me – I’ve accepted it as “normal” for so many years – recently, however, <b><span style="font-size: medium;">a very bright lightbulb lit up in my brain</span></b> </span></span><b style="color: #274e13; font-family: arial; text-align: right;"><span style="font-size: medium;">💡</span></b><span style="color: #274e13; font-family: arial;">, and I finally have enough light to see a better path....</span></div><div style="text-align: left;"><span style="color: #274e13;"><span style="font-family: arial;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJn78N6L-pr0Bozii9y5xYfNnoImWZT2ZrxfiB4Yq6-yIZar1r09Wf6m9mCXp8R4DKYWDEbnN_EHjUNzjE-fc2hStd4fj3jnfR3zF8GxQrdYbere-3me8f590RGI_hYalorTnkHQiKI77L/s512/lightswitch.jpeg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="512" data-original-width="349" height="159" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJn78N6L-pr0Bozii9y5xYfNnoImWZT2ZrxfiB4Yq6-yIZar1r09Wf6m9mCXp8R4DKYWDEbnN_EHjUNzjE-fc2hStd4fj3jnfR3zF8GxQrdYbere-3me8f590RGI_hYalorTnkHQiKI77L/w108-h159/lightswitch.jpeg" width="108" /></a></div></span><span style="font-family: arial; text-align: left;"><div style="text-align: left;"><span style="font-family: arial; text-align: left;"><br /></span></div>I’m not sure that there was a specific “thing” that flipped the switch to light the path, but here’s an interaction that was the driving event behind this month’s post.</span></span></div><div style="text-align: left;"><span style="color: #274e13; font-family: arial;"><br /></span></div><div style="text-align: left;"><span style="color: #274e13; font-family: arial;">I saw the special education teacher in the hall and inquired about the progress of a student we had previously discussed. </span></div><div style="text-align: left;"><b style="font-family: arial;"><span style="color: #990000;"><br /></span></b></div></div><blockquote style="border: none; margin: 0px 0px 0px 40px; padding: 0px;"><div style="text-align: right;"><div style="text-align: left;"><b style="font-family: arial;"><span style="color: #990000;">Me:</span> </b><span style="color: #274e13; font-family: arial;">Hi, Mr. Soenso. How did Jenny do trying the compensation strategy? Did it help her wrap her head around subtraction a bit better? </span></div></div></blockquote><blockquote style="border: none; margin: 0px 0px 0px 40px; padding: 0px; text-align: left;"><p><span style="font-family: arial;"><b><span style="color: #990000;">Special Education Teacher: </span></b><span style="color: #274e13;">Yeah, it was a good start. Today I’m working with Jenny on rounding because she struggled with it during math class yesterday. She has always struggled with place value concepts, so I’m on my way to pull her for some remedial support now.</span></span></p></blockquote><p></p><p><span style="color: #274e13; font-family: arial;"><b><br /></b></span></p><p><span style="color: #274e13; font-family: arial;"><b>I'm willing to bet that conversations like this one take place in your school, too. </b>They are so common, in fact, that you may be scratching your head trying to figure out what I'm trying to highlight by sharing this interaction. </span></p><p><span style="color: #274e13; font-family: arial;">Often when we provide instructional support to students, we “put the car in reverse” and back up to the things the student was unable to do during regular instruction while the rest of the class continues to drive forward.</span></p><p></p><span style="color: #274e13; font-family: arial;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPKfToizwKZMSDGCln9NpsYIPLMjSpP98P3vAGHMUQ5inROJWm1GoLDs46mvyTou1w65dtvvoI3rGPBIUF9HxTFHEyfxq18A_-RpNK8S1z5gQoXjau4vVj7kUFRqsIVWLYT4dt1YHAP8RJ/s251/download.jpeg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="251" data-original-width="201" height="220" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPKfToizwKZMSDGCln9NpsYIPLMjSpP98P3vAGHMUQ5inROJWm1GoLDs46mvyTou1w65dtvvoI3rGPBIUF9HxTFHEyfxq18A_-RpNK8S1z5gQoXjau4vVj7kUFRqsIVWLYT4dt1YHAP8RJ/w175-h220/download.jpeg" width="175" /></a></div>I was talking about this observation with a colleague, and she said, “This reminds me of a book I’m reading, <i>Learning in the Fast Lane</i>. I think you'd like it. The beginning part of the book aligns exactly with what you are saying.” So, I, of course, got a copy of the book, and, sure enough, the author put many of my thoughts right in the opening chapters of her book. </span><div><p></p><p><span style="color: #274e13; font-family: arial;">My conversation with the special education teacher was not unique to the role of special educators or to students with IEPs; we do the exact same thing in our general education classes during small group instruction, too. We plan our small groups based on who was or was not successful on the lesson that we taught to the whole group – I know this is pretty typical because I planned the small groups in my own classroom using this exact same model for many years.</span></p><p><b style="font-family: arial;"><span style="color: #6aa84f; font-size: medium;">It looked something like this:</span></b><span style="color: #274e13; font-family: arial;"> I knew that some of my students did not have the foundational knowledge that would be needed for the next lesson, and it was unlikely that they would "get it" during whole group instruction, so, in my plans, I included small group instruction that would follow the whole-group instruction. I would group these students together with the plan of going over the material with them<b> again </b>while their classmates completed independent practice work or played partner games to reinforce the concepts. </span></p><p><span style="font-family: arial;"><span style="color: #6aa84f;"><span style="font-size: medium;"><b>Now let’s consider an alternate </b>(yes, better!)<b> plan:</b></span> </span></span><span style="color: #274e13; font-family: arial;">I knew that some of my students did not have the foundational knowledge that would be needed for the next lesson, and it was unlikely that they would "get it" during whole group instruction, so, in my plans, I included small group instruction that would be taught <b>the week BEFORE</b></span><span style="font-family: arial;"><b style="color: #274e13;"> the whole-group lesson</b><span style="color: #274e13;">. During this small group instructional time, I could work with the students who I already knew needed more support learning the specific foundational skills required to fully participate in next week's whole-group lesson. And </span><span style="color: #6aa84f;">because they arrive in the whole-group lesson armed with new, relevant foundational knowledge,</span><span style="color: #674ea7;"> </span><b><span style="color: #b45f06;">they participate more,</span> <span style="color: #0b5394;">they connect ideas more,</span> <span style="color: #741b47;">they learn more. </span></b><span style="color: #6aa84f;">They are not trying to catch up to their classmates during whole group instruction; they are working alongside of them. </span></span></p><p><span style="color: #274e13; font-family: arial;">This way of planning instruction is referred to as <i><b>acceleration</b></i>. It takes a pro-active approach to small group instruction and is designed with the expectation that the <b>whole </b>group will be able to engage in the whole-group lesson during core instruction. Acceleration enhances many skills: (1) Students gain increased ability with the skill; (2) they have a broader understanding of one or more strategies; and, most importantly, (3) student confidence increases during the on-grade level whole group lesson because the student had an opportunity to PREview the skills and strengthen foundational skills before that whole-group lesson occurred -- and student confidence probably has the greatest effect of all when it comes to learning and achievement. </span></p><div class="OutlineElement Ltr SCXP38857241 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: #edebe9; clear: both; color: #444444; cursor: text; direction: ltr; font-size: 14.6667px; margin: 0px; overflow: visible; padding: 0px; position: relative; touch-action: pan-x pan-y; user-select: text;"><p class="Paragraph SCXP38857241 BCX0" data-ccp-props="{"335551550":1,"335551620":1,"335559683":0,"335559685":0,"335559731":0,"335559737":0,"335562764":2,"335562765":1,"335562766":4,"335562767":0,"335562768":4,"335562769":0}" lang="EN-US" paraeid="{6175ef79-5e99-4673-82b5-16036b055f02}{176}" paraid="0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; margin: 0px; overflow-wrap: break-word; padding: 0px; touch-action: pan-x pan-y; user-select: text; vertical-align: baseline;" xml:lang="EN-US"><span style="font-family: arial;"><span class="TextRun SCXP38857241 BCX0" data-contrast="none" lang="EN-US" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-kerning: normal; font-size: 12pt; font-variant-ligatures: none; letter-spacing: 0px; line-height: 1.2; margin: 0px; padding: 0px; touch-action: pan-x pan-y; user-select: text;" xml:lang="EN-US"><span class="NormalTextRun SCXP38857241 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; position: relative; touch-action: pan-x pan-y; user-select: text;"><br /></span></span></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6a5dsCOwXRBYMxddRsa__y7T_VvHSfnw6l0xk9ESoCCXswvjMj3cOY2nqzwe5s9lHCgK4OUOF9Iq5MYOwKmPuXGyHd3591VA8AzNK80P9z-L0Lf-6wOA3gBh1FG5kBcHhKbdkFNV1DhVZ/s694/acceleration+lane.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="295" data-original-width="694" height="272" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6a5dsCOwXRBYMxddRsa__y7T_VvHSfnw6l0xk9ESoCCXswvjMj3cOY2nqzwe5s9lHCgK4OUOF9Iq5MYOwKmPuXGyHd3591VA8AzNK80P9z-L0Lf-6wOA3gBh1FG5kBcHhKbdkFNV1DhVZ/w640-h272/acceleration+lane.png" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><p></p></div><p><span style="color: #274e13; font-family: arial;">Think about the structure and purpose of the acceleration lane on the highway.... The acceleration lane is designed to help drivers "get up to speed" so they can merge smoothly into the flow of traffic. Similar to the acceleration lane on the highway, the purpose behind using acceleration practices/strategies in the classroom is to help our students "get up to speed" on the specific foundational skills required to engage in the upcoming lesson WITH their peers (in the flow of traffic), not after their peers have zoomed past them on the highway of learning.</span></p><p><span style="color: #274e13; font-family: arial;"><span style="font-size: medium;"><b><br /></b></span></span></p><p><span style="color: #274e13; font-family: arial;"><span style="font-size: medium;"><b>Let’s talk ACCELERATION vs. REMEDIATION</b></span></span></p><p><span style="color: #274e13; font-family: arial;">The term “acceleration” is one that has been around for a while. If you’re like me, you haven’t used it the way it is currently being used in educational circles. So for the purpose of this post, let’s establish a common definition: </span></p><p><span style="color: #274e13; font-family: arial;">For me, acceleration previously brought images of students doing work that is beyond the scope or depth of what is considered typical for their grade level peers. My school district’s Accelerated Math 8 class, for example, allows students to work on their high school Algebra content while still in middle school. We will, however, be using the term<i> acceleration</i> differently today – and we’ll mention the term <i>remediation</i>, too. Here is how remediation and acceleration are described in Suzy Pepper Rollins' book <i>Learning in the Fast Lane</i>:</span></p><p><span style="font-family: arial;"><span style="color: #073763;">The primary focus of <i>remediation </i>is mastering concepts of the past. <i>Acceleration</i>, on the other hand, <b>strategically prepares students for success in the present</b>—this week, on this content. Rather than concentrating on a litany of items that students have failed to master, <b><i>acceleration</i> readies students for new learning</b>. Past concepts and skills are addressed, but always in the <b>purposeful context </b>of future learning</span><span style="color: #274e13;"> (p.6).</span></span></p><p><span style="font-family: arial;"><span style="color: #073763;">Remediation is based on the misconception that for students to learn new information, they must go back and master everything they missed<i> </i></span><span style="color: #274e13;">(p.5). By backing students up to reteach “everything”, we are not closing the gap at all, in fact, we are widening it! As the gap gets wider and wider and students fall farther behind, motivation decreases and we now have a student who not only struggles in math, but actually hates it.</span></span></p><p><span style="color: #351c75; font-family: arial; font-size: medium;"><b><br /></b></span></p><p><span style="color: #351c75; font-family: arial; font-size: medium;"><b>Let’s be PRO-active rather than RE-active</b></span></p><p><span style="font-family: arial;"><span style="color: #274e13;">If we </span><span style="color: #274e13; font-size: medium;"><b>anticipate</b></span><span style="color: #274e13;"> which students will need support with the foundational skills that are necessary to actively engage in the whole-group lesson, we can (and should!) use our small group time helping these students gain those </span><b style="color: #274e13; font-size: large;">“just in time” skills </b><span style="color: #274e13;">in the days </span><span style="color: #990000; font-size: medium;"><b>prior </b></span><span style="color: #274e13;">to the whole-group lesson.</span><b style="color: #274e13; font-size: large;"> </b><span style="color: #274e13;">Rather than allowing these students to sit through an entire lesson, gain nothing, and then have to repeat (not only that lesson but also provide instruction to address foundational gaps), why don't we spend our time more effectively by anticipating the needs and </span><b style="color: #274e13;">meeting those needs before the grade-level lesson.</b></span></p><p><span style="color: #660000; font-family: arial; font-size: medium;"><b><br /></b></span></p><p><span style="color: #660000; font-family: arial; font-size: medium;"><b>So HOW do we get started?</b></span></p><p><span style="color: #660000; font-family: arial; font-size: medium;"><b>Step 1</b></span><span style="color: #274e13; font-family: arial;">: <b>Shift our mindset about small group instruction</b>. I believe small group instruction is important, but I don’t think that every student needs it every day for the exact same amount of time. For some of my students, small group time is the optimal time to work on just-in-time foundational skills that will enable them to participate (<b>with their peers!</b>) in next week’s whole group lesson.</span></p><p><span style="font-family: arial;"><b><span style="color: #660000; font-size: medium;">Step 2</span></b><span style="color: #274e13;">: <b>Determine which skills are foundational to next week’s lesson. </b>You may be wondering how to do this? In math, I rely on <a href="https://achievethecore.org/coherence-map/" target="_blank">Achieve the Core’s Coherence Map</a> tool. First I select the standard that will be addressed next week during the whole-group lesson. Then I simply click on the linked standards that are foundational to the selected standard (look at the standards to the left when viewing the Coherence Map). And that brings us to Step Number 3. </span></span></p><p><span style="color: #660000; font-family: arial; font-size: medium;"><b>Step 3</b></span><span style="color: #274e13; font-family: arial;">: <b>Assess which students will need additional support</b> with foundational skills necessary to access the upcoming lesson. This can be a formal or informal process. I prefer quick formative assessments and the wealth of teacher data I collect just from being observant and listening to my students share their mathematical ideas.</span></p><p><span style="font-family: arial;"><span style="color: #660000; font-size: medium;"><b>Step 4</b></span><span style="color: #274e13;">: <b>Plan small group instruction</b> t<b>hat will occur PRIOR to whole-group instruction</b>. This time should be purposeful in its attempt to level the playing field </span></span><span style="color: #274e13; font-family: arial;">for your students so everyone can engage with the content and join the discussion during the upcoming whole-group lesson.</span></p><p><span style="font-family: arial;"><span style="color: #660000; font-size: medium;"><b>Step 5</b></span><span style="color: #274e13;">: Engage the targeted students in <b>activities that create BRIDGES that will CONNECT</b> the work done in small group to the grade level standard that will be taught in the coming days during whole group. And remember, the targeted group of students should not be a static list – during Step 3, consider which students need support with <i>these </i>specific skills. </span></span></p><p><span><span><span style="font-family: arial;"><b style="color: #b45f06;">IMPORTANT NOTE:</b><b style="color: #b45f06; font-size: large;"> </b><span style="color: #444444;">And if you have a co-teacher (special education teacher, Title I teacher, instructional assistant, etc.) who delivers some or all of your small group instruction to any of your students, be sure to communicate daily with that teacher so they, too, can plan small group instruction that is that is both pro-active and aligned to the upcoming core lesson.</span></span></span></span></p><p><b style="font-family: arial; font-size: large;"><span style="color: #783f04;">Drivers, start your engines and let's get in the "FAST LANE"!</span></b></p><p><b style="font-family: arial; font-size: large;"></b></p><div class="separator" style="clear: both; text-align: center;"><b style="font-family: arial; font-size: large;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0mREZrY7VcIO5eN_zmM6FJ2lWb7pmFEDapHTBo3jpJCMRGTjzYm03QQEASeo76c0eWmj-2SKH0f_zJhZrSTppB5baB9Pai_AQHC9M7cu-UfPSwikPAJwtnEk7U7KoGQACEFba5tKHR46j/s848/speedometer.jpeg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="848" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0mREZrY7VcIO5eN_zmM6FJ2lWb7pmFEDapHTBo3jpJCMRGTjzYm03QQEASeo76c0eWmj-2SKH0f_zJhZrSTppB5baB9Pai_AQHC9M7cu-UfPSwikPAJwtnEk7U7KoGQACEFba5tKHR46j/s320/speedometer.jpeg" width="320" /></a></b></div><b style="font-family: arial; font-size: large;"><br /><span style="color: #6aa84f;"><br /></span></b><p></p><p><b style="font-family: arial; font-size: large;"><span style="color: #6aa84f;"><br /></span></b></p><p><b style="font-family: arial; font-size: large;"><span style="color: #6aa84f;"><br /></span></b></p><p><b style="font-family: arial; font-size: large;"><span style="color: #6aa84f;"><br /></span></b></p><p><b style="font-family: arial; font-size: large;"><span style="color: #6aa84f;"><br /></span></b></p><p><b style="font-family: arial; font-size: large;"><span style="color: #6aa84f;"><br /></span></b></p></div>:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comtag:blogger.com,1999:blog-543907520077188162.post-71443266647831837652021-02-03T19:04:00.477-08:002021-02-24T13:34:46.574-08:00Think-Share-Compare<div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><h1 class="entry-title" style="background-color: white; border-bottom-color: rgb(231, 231, 231); border-bottom-style: solid; border-image: initial; border-left-color: initial; border-left-style: initial; border-right-color: initial; border-right-style: initial; border-top-color: initial; border-top-style: initial; border-width: 0px 0px 2px; box-sizing: inherit; color: #f05923; font-family: "Open Sans", Arial; font-size: 36px; font-stretch: inherit; font-variant-east-asian: inherit; font-variant-numeric: inherit; line-height: 43.2px; margin: 0px 0px 35px; padding: 0px 0px 15px; text-align: center; vertical-align: baseline;">Think-Pair-Share Gets an Upgrade</h1></div></div><span style="font-family: arial;"><div style="text-align: center;"><b><span style="color: #2b00fe; font-size: medium;">POP QUIZ</span></b></div></span><div><div style="text-align: center;"><b style="font-family: arial;"><span style="color: #6aa84f; font-size: medium;"><br /></span></b></div><div style="text-align: left;"><b style="font-family: arial;"><span style="color: #6aa84f; font-size: medium;">How many years have we used the <i>Think-Pair-Share</i> routine in our schools?</span></b></div><div style="text-align: left;"><b style="font-family: arial;"><span style="color: #6aa84f; font-size: medium;"><br /></span></b></div><div><ul style="text-align: left;"><li><span style="font-family: arial;"><span style="font-size: large;">4 years</span><span style="font-size: medium;"> </span><i><span style="color: #666666;">– c'mon, it was definitely in our classrooms prior to 2017, right?</span></i></span></li><li><span style="font-family: arial;"><span style="font-size: large;">14 years</span><span style="font-size: medium;"> </span><i><span style="color: #666666;">– Yes, I remember using this around 2007, so 14 years is possible</span></i></span></li><li><span style="font-family: arial;"><span style="font-size: large;">40 years</span> </span><span style="color: #666666; font-family: arial;"><i>– definitely didn't use it when I started 32 years ago, was that just my inexperience?</i></span></li><li><span style="font-family: arial;"><span style="font-size: large;">140 years </span></span><span style="font-family: arial;"><i style="color: #666666;">– surely, it hasn't been around since the late eighteen hundreds</i></span><i style="font-family: arial;"><span style="color: #666666;">, has it? </span></i></li></ul><div><span style="font-family: arial;"><br /></span></div><div><span style="font-family: arial;"><br /></span></div><div><div class="separator" style="clear: both; text-align: center;"><br /></div><span style="font-family: arial;">The <i>Think-Pair-Share</i> </span><span style="font-family: arial;">collaborative teaching strategy</span><span style="font-family: arial;"> </span><span style="font-family: arial;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_vMs4llnn1jQTnTlGiQUxl8orH60cN7bz255ruODOIxuInhJniLCWMVl-s02oEUFP7zYd7w5zsGjJq_RQopffuJkRjmB_Gtw2RxVPirAspYeujGV_KeAkguHRblQWcuqvSpxD_ZDilrxc/s2048/univarch-027524_0000.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: left;"><img border="0" data-original-height="2048" data-original-width="1385" height="166" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_vMs4llnn1jQTnTlGiQUxl8orH60cN7bz255ruODOIxuInhJniLCWMVl-s02oEUFP7zYd7w5zsGjJq_RQopffuJkRjmB_Gtw2RxVPirAspYeujGV_KeAkguHRblQWcuqvSpxD_ZDilrxc/w112-h166/univarch-027524_0000.jpg" width="112" /></a>is credited to a professor from the University of Maryland named Frank Lyman, PhD (<i>go UMD Terps!</i>). He was formerly an elementary teacher and was one of the first in the U.S. to use cognitive mapping with students. His research investigated how the Think-Pair-Share routine could improve oral communication and motivation for students, and his research results first appeared publicly in the University of Maryland publication <i>Mainstreaming Digest in 1981. <span style="color: #666666;"> [Click on the book and you'll notice an inscription on the cover of that university publication] </span></i></span></div></div><div><span style="font-family: arial;"><i><br /></i></span></div><div><span style="font-family: arial;"><i><br /></i></span></div><div><span style="font-family: arial;"><i><br /></i></span></div><div><span style="font-family: arial;"><br /></span></div><div><span style="font-family: arial;">There is no denying that the Think-Pair-Share routine transformed the way we thought about education. It encouraged collaboration and required <u>students</u> to do most of the talking during class times <span style="color: #666666;">(<i>scandalous, I know!</i>). </span>It has been a staple in the world of education for 40 years, and my own instruction was greatly enhanced once I began using this as one of my key instructional tools <i><span style="color: #666666;">(a full decade after the research results were published). </span></i> </span></div><div><br /></div><div style="text-align: center;"><span style="color: #2b00fe; font-family: arial;"><b><span style="font-size: large;">It's</span><span style="font-size: large;"> time </span><span style="font-size: medium;">for </span><span style="font-size: medium;">an</span><span style="font-size: large;"> UPGRADE!</span></b></span></div><div style="text-align: center;"><span style="color: #2b00fe; font-family: arial;"><b><span style="font-size: x-large;"><br /></span></b></span></div><div style="text-align: left;"><span style="font-family: arial;">Let me begin by confirming that I do not work for, nor is this blog endorsed by Curriculum Associates, the maker of iReady <i><span style="color: #666666;">(or any other company or agency, for that matter)</span></i>. I say that because I am going to talk about their version of the routine which has been <b>subtly, yet powerfully modified</b>. This upgraded version of the original routine has transformed <span style="color: #666666;"><i>(yes, transformed)</i></span> the way I think about student-to-student collaboration and discussions in the mathematics classroom. </span></div><div style="text-align: left;"><span style="font-family: arial;"><br /></span></div><div style="text-align: left;"><div><span style="font-family: arial;">Before I dive into the upgraded version of this instructional routine, let's do a 1-2-3 review of the original Think-Pair-Share routine</span><span style="font-family: arial;"> <span style="color: #666666; font-style: italic;">(or at least how it worked in MY classroom prior to my use of the upgraded version). </span>First, students were presented with a mathematical problem and asked to <b>THINK</b> about it. Next the students would <b>PAIR</b> off and discuss their ideas with a partner. Then I would ask a few students to <b>SHARE</b> their ideas during our class discussion. Sound about right?</span></div><div><span style="font-family: arial;"><br /></span></div><div><span style="font-family: arial;">Well, here are some of the <b>problems </b>my class<b> </b>consistently encountered with Think-Pair-Share:</span></div><div><ul><li><span style="font-family: arial;">during the <i>think</i> time, many students just waited quietly without doing too much thinking at all – they knew if they kept a low profile, others would carry the discussion</span></li><li><span style="font-family: arial;">once <i>paired</i>, students didn't always talk about the math - sometimes the discussion was about the new puppy one of them just got</span></li><li><span style="font-family: arial;">when they were talking about the math, some students didn't have much to say on the topic, so the discussion fell flat or most of the talking was done by just one student in the pair </span></li><li><span style="font-family: arial;">as I walked around monitoring conversations, it often <b><i>looked</i> </b>like good conversations, but really some students were not listening to their partners at all because they were so busy planning what they were going to say when it was their turn – <span>or still thinking about that puppy</span></span></li><li><span style="font-family: arial;">our <i>sharing</i> time was often just students repeating what <u>the</u>y had said earlier in their pairs without a single revision or consideration for what their partner had told them</span></li></ul></div></div><div style="text-align: left;"><span style="font-family: arial;"><br /></span></div><div style="text-align: center;"><span style="color: #cc0000; font-family: verdana; font-size: x-large;"><b>Think-Share-Compare</b></span></div><div style="text-align: left;"><span style="font-family: arial;"><br /></span></div><div style="text-align: left;"><span style="font-family: arial;">So all of <i>THAT</i> has led up to <i>THIS</i>: The <i style="font-weight: bold;">Think-Share-COMPARE </i><span>routine</span><i style="font-weight: bold;">.</i></span></div><div style="text-align: left;"><span style="font-family: arial;"><br /></span></div><div style="text-align: left;"><span style="font-family: arial;">The designers say that this routine helps students "achieve greater mathematical proficiency and rigor within a collaborative structure" – Want to hear how it's different? </span></div><div style="text-align: left;"><span style="font-family: arial;"><br /></span></div><div style="text-align: left;"><span style="font-family: arial;">Check out the chart below: I share my step-by-step instructional plan for facilitating the Think-Share-Compare routine with students </span><span style="color: #666666; font-family: arial;"><i>(and the adults I work with during professional development),</i></span><span style="font-family: arial;"> and I explain why I love this upgraded version so much.</span><span style="color: #666666; font-family: arial;"> </span></div><div style="text-align: left;"><span style="color: #666666; font-family: arial;"><br /></span></div><div style="text-align: left;"><span style="color: #666666; font-family: arial;"><br /></span></div><div style="text-align: left;"><span style="color: #38761d; font-family: arial;">*Unless you have <i>really</i> great vision, be sure to CLICK on the CHART for a</span><span style="color: #38761d; font-family: arial;"> </span><span style="color: #38761d; font-family: arial;">BETTER VIEW</span></div><div style="text-align: left;"><span style="color: #38761d; font-family: arial;"><br /></span></div><div style="text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVnigUC5Wy5C4T-UBo49498C-Xy7fdiA-uwYjYi5kKYyn1CPSbXEUEZvVKJHkQyPA2yMkv3aagu6UKLinr6dC8juXagqik29iqkCj-Z0zjYh0KWZ1JrxxqB1s4Yt_e6SbTv4t0xDfD4JbV/s2048/Screen+Shot+2021-02-04+at+2.15.47+AM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1343" data-original-width="2048" height="420" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVnigUC5Wy5C4T-UBo49498C-Xy7fdiA-uwYjYi5kKYyn1CPSbXEUEZvVKJHkQyPA2yMkv3aagu6UKLinr6dC8juXagqik29iqkCj-Z0zjYh0KWZ1JrxxqB1s4Yt_e6SbTv4t0xDfD4JbV/w640-h420/Screen+Shot+2021-02-04+at+2.15.47+AM.png" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div></div><div style="text-align: center;"><span style="color: #cc0000; font-family: verdana; font-size: x-large;"><b><br /></b></span></div></div>:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comtag:blogger.com,1999:blog-543907520077188162.post-11586958701401152492020-10-01T09:56:00.002-07:002020-10-26T10:22:07.388-07:00<p></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: helvetica; font-size: x-large;"><b>Best of MathSnack</b></span><br /><span style="font-size: large;"><i>...so far....</i></span></div><div class="separator" style="clear: both; text-align: center;"><span><i style="font-size: x-large;"><br /></i><span style="background-color: white; color: #38761d; font-family: verdana; font-size: medium;">Click <a href="http://mathsnack.blogspot.com/2020/10/best-of-mathsnack.html#more">here</a> for the menu of favorites!</span></span></div><span><a name='more'></a></span><div class="separator" style="clear: both; text-align: center;"><br /><div class="separator" style="clear: both; text-align: center;"><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://mathsnack.blogspot.com/2019/11/how-do-you-know.html" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="250" data-original-width="249" height="178" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9-3GXo6oPfyCWBdV-YwVwbnrMxJ-pl7f92Y8Enzme-0IN9LOvYhRJQONkBXcYg0NHnrnYvt-xqNx8WxDLX3XQd4Yk5w-BYLHC5StfAiVua8CnvpfCqRlui9_cYhBnzcRJ3ij3P7GPnrTE/w177-h178/Screen+Shot+2020-10-26+at+12.04.47+PM.png" width="177" /></a><a href="http://mathsnack.blogspot.com/2020/04/learning-unplugged-screen-time.html" style="margin-left: 1em; 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text-align: center;"><a href="http://mathsnack.blogspot.com/2019/08/mathematical-discourse.html" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="277" data-original-width="278" height="177" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgznbBE0FoNh_Lm-PQnkBgwzIRLlVhkzodewp9qdvJFr9NfQ54idFBAvFOltvIjYi0fK4vjR-8-wb6-a0pLyLaySQwOFIPgbVFnPpD60fQBEJoVDc9R94ZUXUKHdlco-cR0bYL-ZqdvMK9d/w178-h177/Screen+Shot+2020-10-26+at+12.10.34+PM.png" width="178" /></a><a href="http://mathsnack.blogspot.com/2020/03/closing-learning-gaps-and-increasing.html" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="254" data-original-width="253" height="181" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiK_dQVHkEpT65gxo7OatmeuBsCRoOjLzIFkaOQSjRJ-j1l34po34FfH3P4inWOcgGhGhGf9skE8bE7LXCKx6KpUOXkFchwUxzXBsYpVBt3nTFQ3FngWBgLD7eppkEi229Jq67nRvWdDJAP/w181-h181/Screen+Shot+2020-10-26+at+11.54.25+AM.png" width="181" /></a><a href="http://mathsnack.blogspot.com/2020/02/if-youve-met-me-in-person-you-know-that.html" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="251" data-original-width="250" height="179" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCPbeuYYiUqc4t7hYKNZdiDz3hjIAlucSJLTbEv_NMdK5j1mkdP9Xhg0MVPwRzyH_Amc_O-sawYhx8w06Z1Nw7QMsqRXnb_-AVhPYeLGAItPB3sg2iuic70LmlxBWYlkmPZJCfnIedG6j9/w178-h179/Screen+Shot+2020-10-26+at+12.02.18+PM.png" width="178" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://mathsnack.blogspot.com/2019/10/the-progression-of-place-value.html" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="278" data-original-width="273" height="179" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1ROPzu54uA6And4Se_vr8aNK9laTb9_APIrLxRbDbfORsQp2u-6vARIA7tXeBTvEVCXYRuXTKsQN4dmpifUIdL5K8LA9tNaO_mZjzAOdeafqO9fcvPhms9kFA_exePoEyVpbLgCC-RXOh/w176-h179/Screen+Shot+2020-10-26+at+12.07.37+PM.png" width="176" /></a><a href="http://mathsnack.blogspot.com/2017/12/using-open-number-line-to-develop.html" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="211" data-original-width="212" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2QpsuuyU5nSo0U0uekJvAGofxGixNINY-zgQuhLb51nFD5jP8mBt3eczLR7TuY8jbq4IDsXX-B2SJQ5bs0PjiagLJVsTn9IyO5nNyKczm9803Uo4xT0cFmdKXiy1gRLdWyXMoNoE8_HE-/w181-h180/Screen+Shot+2020-10-26+at+12.33.10+PM.png" width="181" /></a> <a href="http://mathsnack.blogspot.com/2019/05/using-playing-cards-to-practice.html" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="278" data-original-width="278" height="178" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEve-pxcpv43In8Uc7kDqqGGpNFjRalzLMydYtCs90DemYMsV069J9Km-GqNCZ0vpTFUEW9mwgeZe5oYJko-zTiTvxiaZ3Dynqj3mGp-QnKzOWXQptM24mzjOF2WWlJEgnF_sb8Jf5_D14/w178-h178/Screen+Shot+2020-10-26+at+12.13.23+PM.png" width="178" /></a> </div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://mathsnack.blogspot.com/2018/11/cuisenaire-rods.html" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="209" data-original-width="211" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_kJXYpqOmzSYXYvETM7UCIqhTGf8PAYUAJrOINknbsDIy0rEY_sgjwoFZu6JzsM6S7QiFwBpCZNwY3Doe3bSR1ipkE_de3mjcHlhPxJ7RsZ3GcwxrdmlVlZFwnJniIKHBeS67ezZbtPmR/w181-h180/Screen+Shot+2020-10-26+at+12.26.24+PM.png" width="181" /></a><a href="http://mathsnack.blogspot.com/2019/02/estimation.html" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="278" data-original-width="277" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpLOshAxXfRRB4Kq9KNeYAYA5VIOrI-xQIPPmC5NXoRtdVrZIjRJIwpB35JhgnmiKemADr9ZfwN-5twVbCT6Bz-esLTzQv4EIiDCmFSEKNVnuF0kRDDZ3fKGrSx0uQ8hAqY_aoV9IC2llG/w179-h180/Screen+Shot+2020-10-26+at+12.20.23+PM.png" width="179" /></a> <a href="http://mathsnack.blogspot.com/2019/02/anchor-charts.html" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="211" data-original-width="210" height="181" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgU9sH24-XbSW_3VwV8PXLTyYa9Bq4NyYxJEQDzXW2wseOjaXfk_EVRDkS1Y_hGNnO8We5S5Aib23cf9Eoj-n4D3GsNvDKlsVYGHO3EZbCZj9GnQK5cF54x_y2HZ5NYOTy_K8p53ticq0pm/w180-h181/Screen+Shot+2020-10-26+at+12.23.00+PM.png" width="180" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://mathsnack.blogspot.com/2017/10/number-talks-part-ii.html" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="212" data-original-width="211" height="181" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8N3rzZbTRIEttyhaOJmUalYhLKnWmbb-Ah5deQrfyzEGWt3lyutyrpq8cPH63VLMp0MCHJmL_5uEIK67icJHXAn-3dFw_lv0dcIoVZPP4rU0VxF18mWsDjAd8hK-1ssPe6WO9aEZPHv7W/w180-h181/Screen+Shot+2020-10-26+at+12.37.19+PM.png" width="180" /></a><a href="http://mathsnack.blogspot.com/2018/03/rich-tasks-culture-of-engagement.html" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="212" data-original-width="212" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwIUqmYz2N75zap6Djb__6d4Q3GqeaC_fT6EPgT3Kg3UDthgbhw8Mabj-ncp3Ve519IAO6rwjy93etRQnJzgb9qGKOJ7BsuvC6gf8Ij45-APiC44792MhRNNL-tzZNRa9e8okK1Bb2mP0i/w180-h180/Screen+Shot+2020-10-26+at+12.30.25+PM.png" width="180" /></a><a href="http://mathsnack.blogspot.com/2020/09/make-space-for-grace.html" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="250" data-original-width="253" height="181" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgA3p4xXQkKPZcrkdeXMGsU2u1ZGvQoQZ00k1m0fIH9peiDPjTO3P0u__4vVnX9jzbe7cb63dw4jI-YRQQLBU6wE_dgVRWB9NIL_MS9qlq4-B_aWWXy8PmauobBTrIlFyjYF-il_XypMvy2/w182-h181/Screen+Shot+2020-10-26+at+11.58.29+AM.png" width="182" /></a> <br /><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://mathsnack.blogspot.com/2017/10/cra-concrete-representational-abstract.html" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="211" data-original-width="212" height="179" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7uAMg6ZpRSh3DQ5NDwipz8usziUSxPYIlhCjY6vZ46XL5ZPh1EvCj3vp17zjihiQ4YpmSU96-TrgmGk-sK9JNezSABcl2Af4R9oY98T1xHJKzGtdvOXqhwhbYbayBO32aVaCcHYO_4_5U/w180-h179/Screen+Shot+2020-10-26+at+12.48.02+PM.png" width="180" /></a> <a href="http://mathsnack.blogspot.com/2017/08/close-reading-in-mathematics.html" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="249" data-original-width="249" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTryGMIrK7HqcIlSVirJEFE7KIxLaBQng30gDaTzjk3aeGtBJksVR4yv1Do1PwtWWHQXdWSkas7edrAvremficWWkDPKVx4aWx5p6lBGlvRZLLeIWl1W6hPHwhMX_U1hGJFSSfEpsjl-Ck/w180-h180/Screen+Shot+2020-10-26+at+12.52.04+PM.png" width="180" /></a> <a href="http://mathsnack.blogspot.com/2018/01/my-3-act-task-obsession.html" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="248" data-original-width="250" height="179" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnEsF93bJha0NpKFYm1YWteevN5y145QEaurrfgvWycL5jR2fT9rnLKoo0OX3QWTQM_YZorUZbBG3J7nTlfQRt0Km_i7B2BIxfRlS2nobmID0yckaI67Ox2rYXbJRSaXyMp52-j91KEB1r/w181-h179/Screen+Shot+2020-10-26+at+12.55.15+PM.png" width="181" /></a><br /><br /><br /><br /></div><br /><br /><div class="separator" style="clear: both; text-align: center;"><br /><br /><br /><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /><br /><br /><br /></div><br /><div class="separator" style="clear: both; text-align: center;"><br /><br /><br /><br /></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div></div><br /><br /><br /></div><br /> <p></p>:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comtag:blogger.com,1999:blog-543907520077188162.post-20945272904946047972020-09-09T18:40:00.014-07:002020-10-26T09:43:07.182-07:00Make Space for Grace<p> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjy6zMlpNdcrWGSppjq_nRm4aTUuI4x99eo12856Q7iEZO80TC0lV9udMf9TDG768WiNtb5kRoWcFPkIAudKay778xA7AP6JYHnEHmasRf2LCrsVTGWWqa1SBL6RTKD0VwkyAsNlFsqWNTH/s640/napkin+note.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="font-family: inherit; font-size: medium;"><img border="0" data-original-height="640" data-original-width="480" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjy6zMlpNdcrWGSppjq_nRm4aTUuI4x99eo12856Q7iEZO80TC0lV9udMf9TDG768WiNtb5kRoWcFPkIAudKay778xA7AP6JYHnEHmasRf2LCrsVTGWWqa1SBL6RTKD0VwkyAsNlFsqWNTH/w300-h400/napkin+note.jpg" width="300" /></span></a></div><span style="font-family: inherit; font-size: medium;">The new school year is now in full swing!<br /><b>Why do I feel both exhausted and exhilarated? </b><br />These two seemingly opposite emotions have been my norm in recent weeks. </span><div><span style="font-family: inherit; font-size: medium;"><br /></span></div><div><span style="font-family: inherit; font-size: medium;">The increased screen time required to do my job (and connect with my grown children, brothers, and parents during our Sunday night Zoom meeting) is, most definitely, more draining since I spend hours each day staring at a screen. </span><div><span style="font-family: inherit; font-size: medium;"><br /></span></div><div><span style="font-family: inherit; font-size: medium;"><span>On the other hand, the new opportunities for collaboration with colleagues (and my weekly family check-ins) has been an exciting addition. The amount I've learned about using digital tools is mind-blowing, and now that travel time between schools isn't part of the equation, </span>I'm able to meet with more people each day. </span></div><div><span style="font-family: inherit; font-size: medium;"><br /></span></div><div><span style="font-family: inherit; font-size: medium;">See what I mean - it's exhausting, yet exhilarating!</span></div><div><span style="font-family: inherit; font-size: medium;"><br /></span></div><div><span style="font-family: inherit; font-size: medium;">And, it seems, that I am not the only one feeling both overwhelmed and excited at the same time. We are all still getting comfortable with the new teaching models in place across the country --- some of us are using a new online platform, some a hybrid model, and some are trying to teach with social distance rules in place --- I don't have to tell you that it ain't always easy! If that's not enough, in my district, we are using a brand new math curriculum because we needed one that would transition to remote learning more smoothly. Couple that with the fact that most of us simply prefer in-person teaching and learning where we can assess the subtleties of the whole learning process --- you know, reading student body language, building a community of learners through all of the little things we do during the school day, and providing emotional support to individuals with a simple smile, nod, or kind word. </span></div><div><span style="font-family: inherit; font-size: medium;"><br /></span></div><div><span style="font-family: inherit; font-size: medium;">Recently, a colleague reminded me that I need to give myself <b><i>SPACE for GRACE</i></b>. I was stressed because I didn't feel prepared to support my fellow teachers as they ventured into this strange start to the school year with a brand new curriculum (the instructional standards weren't changing, so that was a relief!). She reminded me that I needed to give myself SPACE and time to learn what I needed to know and GRACE when I overburdened myself with a feeling that I should have known it "yesterday". I then found myself having the same conversation with dozens of colleagues who, like me, were experiencing moments of stress and panic because they are fantastic teachers who don't (yet!) know how to do their best job under their new circumstances. I found myself offering the same advice: <b><i>Make Space for Grace</i></b></span></div><div><span style="font-family: inherit; font-size: medium;"><b><i><br /></i></b></span></div><div><span style="font-family: inherit; font-size: medium;"><b><i><br /></i></b></span></div><div><span style="color: #38761d; font-size: medium;"><b>Here are a few ideas that got me started making that Space and giving myself Grace:</b></span></div><div><ol style="text-align: left;"><li><b><span style="color: #cc0000; font-size: medium;">Recognize that I do not have all of the answers </span><span style="font-size: medium;">- </span></b><span style="font-size: medium;">heck, I don't even have all of the questions!</span></li><li><span style="font-size: medium;"><b style="color: #351c75;">Be open to new ideas, new learning, and new ways of doing things </b>- this openness will likely get me many of those answers that I do not yet have.</span></li><li><span style="font-size: medium;"><b><span style="color: #b45f06;">Collaborate </span>- </b>Let's not be alone during this time of "social isolation". I will ask for help when I need it, and I will extend my hand when others need help.</span></li><li><span style="font-size: medium;"><span style="color: #2b00fe;"><b>Assess the content more critically</b> </span>- Which topics can students not learn on their own and will need greater support? Which topics allow for simple exposure, which need to be further explored, and which ones require full mastery? I can't do it all in a remote or hybrid model, so I need to make better decisions to ensure effective instruction. After all, maintaining high standards is not achieved by cramming the same work load into a smaller space at a faster pace. I must look for ways to ensure engaging levels of rigor without making students and teachers feel like they were run over by a 100-car train going 150 mph!</span></li><li><span style="font-size: medium;">And finally, <b><span style="color: #800180;">embrace the silver linings of the situation</span> - </b>sure, our current teaching model is not ideal for many reasons, but, I have started to notice so many things that are (surprisingly) even better than they were previously. What silver linings have you noticed? <b><span style="color: #38761d;">Embrace them!</span></b></span></li></ol></div><div><span style="font-size: medium;"><div class="separator" style="clear: both; font-size: medium; text-align: center;"><br /><br /></div></span></div><div><div><br /></div></div></div>:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comtag:blogger.com,1999:blog-543907520077188162.post-40400441148778163152020-06-06T10:32:00.037-07:002020-06-09T06:20:37.240-07:00Learn Something New This SummerIf you've ever received an email from me, you might have noticed that my signature tagline is <div><br /><div style="text-align: center;"><font color="#0b8043"><b>"<i><font size="4">Learn Something New Every Day</font></i>" </b></font></div><div style="text-align: center;"><br /></div><div>I truly do live by that motto. I started using that tagline wa-a-ay back in 1993 (oh my! that's 27 years ago!). I was teaching a 3rd/4th grade combination class; my class joined me on a year-long endeavor to document something we had each learned every single day (including the weekends!). At the end of each school day, we would take time to journal what we learned that was new (usually students wrote about school-related learnings, but not always). On days that I couldn't recall a new learning for myself, I would literally open the dictionary and find a word that I did not already know. I wrote the word and its definition on an index card and then tried to use it in context at least three times on the following day. I've come a long way from the dictionary with the invention of Google, Alexa, and Siri – but I STILL "look up" something new Every. Single. Day.<div><br /></div><div><br /><div>Summer is a fantastic time to learn something new. I hope to get the wheels in your brain churning by offering this starter list of ideas for you to consider – but please, don't limit yourself to just the items on this list – there are so many other learning opportunities that may be just the thing that'll spark your interest for <b>YOUR</b> <i>Learn Something New</i> endeavor this summer. </div><div><br /></div><div><br /></div><div><br /></div><div><b><i><font size="4">EXPLORE</font></i></b></div><div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRzpOR0oN8n4eVTyISkk3ml2h65PQKIW-ZXleibj9QF8h-FR-aMPPlvI-KHzGtmevPRbcDRuUdkkoRz0tVi3-r5yVrJPRM_PPTz9Ih8GgyMhkJBNIa6c2bjbHfpVb49KRcBnXevVelkCV1/s833/Mallows.jpg" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="601" data-original-width="833" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRzpOR0oN8n4eVTyISkk3ml2h65PQKIW-ZXleibj9QF8h-FR-aMPPlvI-KHzGtmevPRbcDRuUdkkoRz0tVi3-r5yVrJPRM_PPTz9Ih8GgyMhkJBNIa6c2bjbHfpVb49KRcBnXevVelkCV1/s320/Mallows.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Mallows Bay in Charles County, Maryland<br /></td></tr></tbody></table>My husband is a great fan of history, so we often combine our vacation with learning something new about old things and past events. Don't judge... but when we visit an old historic town, one of the places we often end up is in the local cemetery where we look for the oldest headstone or we Google the names we find on an interesting headstone to see if we can find that person's history as it relates to the town we are visiting. If you're not into cemeteries, there are plenty of ways to explore and learn. Last summer, for example, we kayaked in <a href="https://www.worldwar1centennial.org/index.php/maryland-wwi-centennial-home/900-mallows-bay-the-ghost-fleet.html" target="_blank">Mallows Bay</a> to get a look at the old sunken fleet of WWI wooden ships – I definitely learned a whole lot of "something new" that day. <div class="separator" style="clear: both; text-align: center;"><br /></div></div></div><div><div><br /></div><div><div><font size="4"><b><i>BUILD SOMETHING / FIX SOMETHING</i></b></font></div><div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhf5iitfMgneZBGtHP11S_35edZbsC20uHJmy9DwZBwTjE7uWOcl2bXhjc6mTXcYfDBr1wtYLY5JA-fM3ERa8LNn1l3yhBOZ5O-MI_R5aMGT-ehXFgJsllYkOipRzj2P6AUePIFg_2a8Ctj/s320/thumbnail_IMG_1140.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="320" data-original-width="240" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhf5iitfMgneZBGtHP11S_35edZbsC20uHJmy9DwZBwTjE7uWOcl2bXhjc6mTXcYfDBr1wtYLY5JA-fM3ERa8LNn1l3yhBOZ5O-MI_R5aMGT-ehXFgJsllYkOipRzj2P6AUePIFg_2a8Ctj/w150-h200/thumbnail_IMG_1140.jpg" width="150" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">model of my next project</td></tr></tbody></table>The truth of this story is I'm a little bit cheap and always up for a challenge. Two summers ago, our freezer was making terrible noises and we KNEW it was about a day away from just completely shutting down and leaving us with a freezer full of frozen goods that would eventually end up in the trash, so after the repairman quoted us a price tag of $80 to walk in the door and then any needed parts and labor would be on top of that, I went to the ever-informative YouTube and looked up "how to fix a noisy freezer". I discovered a whole lot about the inner workings of freezer fans and condensation and how the two do not always get along nicely. The punch line of the story is my freezer has been working perfectly ever since and I knew just what to do last week when the freezer started making those same sounds again. </div><div><br /></div><div><ul style="text-align: left;"><li>Repair bill: $0 </li><li>Value of learning something new: Priceless (or at least 80 bucks plus parts and labor!)</li><li>Next build it/fix it adventure: Learn to build an axe throwing target - yep, just for the fun and sport of it</li></ul></div></div><div><font size="4"><b><i><br /></i></b></font></div><div><font size="4"><b><i><br /></i></b></font></div><div><font size="4"><b><i>READ</i></b></font></div><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTmy0cJpHEXQHQ9lGCSThqWQfrpSqT2ELr9HSwr4HzyMGBBkO0ZIA2GRiGyKOFnbGrFr6u96Hs0IHe5lUMDfspWVWFEQ2C1ayTaTXzGMV7r0OtGoEBguImtDgmdhnfJoxqoKemNOhwmkWP/s322/Screen+Shot+2020-06-08+at+12.04.56+PM.png" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: left;"><img border="0" data-original-height="322" data-original-width="214" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTmy0cJpHEXQHQ9lGCSThqWQfrpSqT2ELr9HSwr4HzyMGBBkO0ZIA2GRiGyKOFnbGrFr6u96Hs0IHe5lUMDfspWVWFEQ2C1ayTaTXzGMV7r0OtGoEBguImtDgmdhnfJoxqoKemNOhwmkWP/w133-h200/Screen+Shot+2020-06-08+at+12.04.56+PM.png" width="133" /></a>Whether it's fiction or non-fiction, reading is a great way to learn something new. It requires no suitcases to pack, no planes to catch, and you can travel around the world without even taking a day off of work. I learned a tremendous amount about the lives of elephants (which has been surprisingly impactful to my own life) by reading a work of fiction by Jodi Picoult called <i>Leaving Time</i>. I learned about the terrible wars of the 1980's and 90's in Sierra Leone in West Africa while reading <i>Long Way Gone: Memoirs of a Boy Soldier</i> by Ishmael Beah. Prior to reading either of these books, I never once thought about the powerful bonds within the elephant community or even knew about the terrible civil wars that impacted so many people in Sierra Leone (including young children). Learn something new this summer by reading a book of your choice.</div><div><div class="separator" style="clear: both; text-align: center;"><br /></div></div><div><br /></div><div><b><i><font size="4">JOURNAL</font></i></b></div><div style="text-align: left;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqVBy6xvPCEZJTk4rxL8piuaTMuKqcmWiWbD_VAQTLJXuU5U1Wh67fpPXeHVuIIxaGc25xpSOjnbe7gO104iXKfY1161ghfginEBAVN2eoOM0jSWMDEiEuH1i709PsCpnIcpByt5tLiLwY/s669/Screen+Shot+2020-06-08+at+12.01.02+PM.png" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="182" data-original-width="669" height="109" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqVBy6xvPCEZJTk4rxL8piuaTMuKqcmWiWbD_VAQTLJXuU5U1Wh67fpPXeHVuIIxaGc25xpSOjnbe7gO104iXKfY1161ghfginEBAVN2eoOM0jSWMDEiEuH1i709PsCpnIcpByt5tLiLwY/w400-h109/Screen+Shot+2020-06-08+at+12.01.02+PM.png" width="400" /></a></div><div>How about learning something new this summer by journaling. In truth, I am not much of a journal keeper myself, but I do know that writing in a journal on a regular basis is a way that many of my friends and family learn more about their own thinking and feelings. My daughter (the writer) loves to quote one of her favorite authors, Flannery O'Connor, and I think the quote sums up the power of journaling nicely: <i>I write because I don't know what I think until I read what I say.</i></div><div><font size="4"><b><i><br /></i></b></font></div><div><br /></div><div><br /></div><div><div><div><font size="4"><b><i>PHYSICAL ACTIVITY</i></b></font></div><div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4_IqWrWdMruxEHP__nnyrARG2mDWcKWSEikax7S1QOPnHwJGM36TvON73nBmdhyRolgNgZu6OjDCyIbIkFy2BWnNHAdLF1Q2QWnxQ9x2MD-mNwIjenh1VTwtDUBnTRfQ2_jd0am5011In/s1024/zublu_bali-3.jpg" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="768" data-original-width="1024" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4_IqWrWdMruxEHP__nnyrARG2mDWcKWSEikax7S1QOPnHwJGM36TvON73nBmdhyRolgNgZu6OjDCyIbIkFy2BWnNHAdLF1Q2QWnxQ9x2MD-mNwIjenh1VTwtDUBnTRfQ2_jd0am5011In/w400-h300/zublu_bali-3.jpg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Photo by ZuBlu shared on GreenQueen.com<br /></td></tr></tbody></table>True confession: I have always wanted to learn how to climb and rappel - you know, going up mountains (or mole hills) with ropes and such and then using those ropes to bounce my way down the side of the mountain. Here's another truth: My husband is not fond of heights, so we never attempted this bit of learning. We always seem to gravitate to the water. We truly love all things water! We learned to kayak many years back and have been addicted ever since. We also love to snorkel, so we often take vacations that lend themselves to those types of events. This year, my husband is interested in learning how to scuba dive. Perhaps that will be my "something new" this summer – or maybe I'll stay home and finally learn how to make a proper crepe.</div></div><div><div><br /></div></div><div><br /></div><div><br /></div><div><font size="4"><b><i>TAKE A CLASS – LEARN A NEW SKILL</i></b></font></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipaTJsYuZerDZV0YR6Pin33h29SGnSUEYltO2vxVFWYS45dIN1dT66SOypMif6mS2U8LuwT9S3M62ZR-UjSyImxEyAO53A4MFx9yywVePloKdL1We2vnKAs8BCo7RVguUmGHcSAMjMOuUY/s700/Sands-eye-view-CC-olly_o-1.jpg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="427" data-original-width="700" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipaTJsYuZerDZV0YR6Pin33h29SGnSUEYltO2vxVFWYS45dIN1dT66SOypMif6mS2U8LuwT9S3M62ZR-UjSyImxEyAO53A4MFx9yywVePloKdL1We2vnKAs8BCo7RVguUmGHcSAMjMOuUY/s320/Sands-eye-view-CC-olly_o-1.jpg" width="320" /></a></div>Taking a class is an obvious way to learn something new this summer, but have you ever stopped to think about just how varied an experience taking a class can be? Sure, you can start working on your next degree by registering at a college, but you can also check your local Parks & Rec calendar for community classes in pottery, sign language, swimming, jewelry making, and so much more. Yes, social distancing may put a damper on those community-based classes, but you can also learn something new right from your smartphone like my brother who has been using <a href="https://www.duolingo.com" target="_blank">Duolingo</a> to learn Spanish for the past six months. You can learn to cook from Gordon Ramsay or join Chris Hadfield as he teaches you about space exploration on <a href="https://www.masterclass.com/" target="_blank">MasterClass</a>. I recently learned how to create a <a href="http://mathsnack.blogspot.com/p/kid-sized-snacks.html" target="_blank">virtual classroom</a> by watching a <a href="https://www.youtube.com/watch?v=Y3ZiClcIYJs&feature=youtu.be&app=desktop" target="_blank">YouTube video</a> (Thanks, Thomas Blakemore of Dubai). There really is no limit to what you can learn or how you can learn it. In my house, for example, my trio of 22-year olds will be learning about financial literacy with the help of the book <i>Personal Finance for Dummies</i> by Eric Tyson; they'll also learn how to sew a button (with master instructor Mom!)</div></div><div><br /></div><div><font color="#0b8043" size="4"><br /></font></div><div><font size="4"><b><font color="#0b8043">Whatever you decide to do this summer, </font><font color="#4285f4">be healthy,</font><font color="#0b8043"> </font><font color="#f57c00">be kind</font><font color="#0b8043">, and </font><font color="#9c27b0">be on the lookout for opportunities</font><font color="#0b8043"> to </font><i><font color="#0b8043">Learn Something New Every Day</font></i><i style="color: #0b8043;">. </i></b></font></div><div><br /></div><div><br /></div></div></div></div>:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comtag:blogger.com,1999:blog-543907520077188162.post-28740815604873336852020-05-01T03:00:00.001-07:002022-11-02T10:11:30.800-07:00Learning UNplugged (screen time alternatives)<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPGMUGanLwLQKVMIv8BTfDMADZhuPnGVBfhzJLg_xQPbfn5wJOBxR8S7XSiGvDAA2EGz55qL4Fk2QpEJnlaZ0blIwuYqPbOTWM3sWVsMZDq0dF2ucvZkk8Ch3RuuXl4I2DOS5L6Fay8rTd/s1600/Screen+Shot+2020-04-30+at+6.02.07+PM.png" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: "georgia" , "times new roman" , serif;"></span></a></div>
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<span style="font-family: "georgia" , "times new roman" , serif;">These are just a handful of the headlines I came across when I searched for articles related to screen time and our current pandemic situation. My district, like nearly every other district in the nation, relies on an online platform to deliver instruction and instructional materials during this learn-from-home emergency. We are producing some great activities that is helping to maintain continuity of learning, but I do worry that students are being asked to spend too much time in front of a computer – which comes with its own laundry list of concerns: eye strain, inactivity, passive engagement, etc.... In these uncharted times, let's embrace opportunities for whole families to engage in mathematical discussions and "thinking outside the (internet-connected) box". </span></div>
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<b><span style="color: #38761d; font-family: "georgia" , "times new roman" , serif; font-size: large;">REFRIGERATOR DRY ERASE CHALLENGE</span></b><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">When I started this activity with my kids, all three of them said something to the effect of "Really, mom, you're not serious?" But you wanna know what happened before I even left the kitchen? – they stopped rolling their eyes, slowly gravitated toward the numbers written on the refrigerator door, and became fully engaged in finding solutions. Getting started is as easy as 1-2-3!</span></div>
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<li><span style="font-family: "georgia" , "times new roman" , serif;">Post 3 number cards on the refrigerator (I used randomly selected cards from our Phase 10 deck)</span></li>
<li><span style="font-family: "georgia" , "times new roman" , serif;">Write the numbers 1-20 with an equal sign and line following each one.</span></li>
<li><span style="font-family: "georgia" , "times new roman" , serif;">Put some dry erase markers nearby and watch the magic happen!</span></li>
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<span style="font-family: "georgia" , "times new roman" , serif;">RULES for PLAY: You can only use each of the three numbers once per equation. You do not have to use all three numbers. All mathematical symbols are permitted. Proper notation for Order of Operations is, of course, required when needed. </span></div>
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: "times" , "times new roman" , serif;"><i style="text-align: start;"><span style="font-family: "georgia" , "times new roman" , serif; font-size: small;">If your refrigerator is textured or filled with artwork, </span></i><i style="font-size: 12.8px;"><span style="font-family: "georgia" , "times new roman" , serif; font-size: small;">try the front of the washing machine!</span></i></span></td></tr>
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<span style="font-family: "georgia" , "times new roman" , serif;">Do you notice how this activity is well-suited to many readiness levels working together at the same time? I have played this with 7 year olds and 7th graders. For this home version, my college-aged son contributed to the board with square roots and factorial notation. I love that this activity has no time limits and isn't a competitive event (unless you want it to be). It reminds me of doing jigsaw puzzles with my auntie at the beach. Each summer, one of my aunts rents a beach cottage for several weeks where members of our family come and go throughout the week. She always has a jigsaw puzzle set up on the coffee table that we add pieces to as the week goes on. These refrigerator problems have the same sense of relaxed collaboration. When I put problems like this one on my refrigerator, my kids add answers as they think of them throughout the day/week until the puzzle is completed – and the refrigerator is the perfect spot with all the snacking happening these days. The first few equations are added very quickly, but as we get to the tougher numbers (like 19!), we find ourselves gathering around the refrigerator contemplating possibilities together – sometimes leaving it and coming back later, often times discovering the final solution together. Today I found my son (one of the original eye rollers), camped out in front of the refrigerator – he pulled a stool over and was all in. He is determined to find the last two solutions, 16 and 19, before the end of the day<i> [update: It's 9pm and still no solution for these two remaining values]. </i></span></div>
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<span style="color: #6aa84f; font-family: "georgia" , "times new roman" , serif;"><b>Maybe you know a solution for 16 & 19</b>. Frankly, we're stuck.... Tweet your solution and tag me <b>@HelloMrsCaine</b>. We'd love to see what you discovered. </span><br />
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<b><span style="color: #351c75; font-family: "georgia" , "times new roman" , serif; font-size: large;">23 STEPS</span></b><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">A simple concept. Try to guess which things are 23 steps away.</span></div>
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<span style="font-family: "georgia" , "times new roman" , serif;">The steps can be of any size, but all 23 steps must be the same size. So if you take "tiny mouse steps", all 23 steps must be "tiny mouse steps". </span><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">This activity builds the mathematical understanding that when we change the size of the measurement unit (tiny steps vs. giant steps), the number of units needed changes (</span><a class="identifier" href="http://www.corestandards.org/Math/Content/2/MD/A/2/" name="CCSS.Math.Content.2.MD.A.2" style="box-sizing: border-box; color: #108ebc; font-family: georgia, "times new roman", serif; font-size: 11.76px; outline: 0px; text-transform: uppercase;" target="_blank">2.MD.A.2</a><span style="font-family: "georgia" , "times new roman" , serif;">).</span><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">Once you've mastered this version of the game, try a modification. You might change it to a "how many steps" activity. Players guess how many steps it will take to get to the end of the driveway using regular-sized steps. Whoever gets the closest to the actual value wins! </span></div>
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<b><span style="color: magenta; font-family: "georgia" , "times new roman" , serif; font-size: large;">SIDEWALK MATH</span></b><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">Take your math play outside! Each week, I look forward to the Twitter posts of <b><span style="color: magenta;">@traciteacher</span></b>. Traci Jackson has been engaging her neighbors with some sidewalk math since mid-March when most of the country's school buildings closed and we were advised to practice social distancing. When her neighbors emerge from their homes to get a bit of exercise, they are greeted with her sidewalk art as they pass her home. What fun it must be to live in Traci's neighborhood! To see the whole collection from @traciteacher, visit <a href="http://bit.ly/mathwalks2020" target="_blank">bit.ly/mathwalks2020</a>.</span></div>
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<b><span style="color: #3d85c6; font-family: "georgia" , "times new roman" , serif; font-size: large;">EGG CARTON 10-FRAME</span></b><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">Another simple idea (this time focused on our youngest mathematicians) involves unitizing. </span><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">Unitizing is an essential skill that extends well beyond primary school – beyond all formal schooling, actually. Think about the retail giant Amazon. Do you think they count items one by one? No. They unitize them on pallets and efficiently count the inventory in groups of 10, 120, 1000.... Learning how to unitize begins at a very young age and, like any other skill, it needs to be taught and practiced. </span></div>
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<span style="font-family: "georgia" , "times new roman" , serif;">Here's a simple idea for building skill in unitizing:</span><br />
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<li><span style="font-family: "georgia" , "times new roman" , serif;">Get an empty egg carton and cut off two of the sections to make a 10-Frame.<br />I like to leave the lid on the egg carton when I cut off the last section allowing me to close the lid and hide the contents inside.</span></li>
<li><span style="font-family: "georgia" , "times new roman" , serif;">Place objects in some of the spots - the items should be large enough to be seen easily (blocks, pom pons, etc.)</span></li>
<li><span style="font-family: "georgia" , "times new roman" , serif;">Open the lid for 2 seconds. Close the lid. Ask "How many did you see?"</span></li>
<li><span style="font-family: "georgia" , "times new roman" , serif;">After an answer is given, follow up with "How do you know there are (7)?"</span></li>
<li><span style="font-family: "georgia" , "times new roman" , serif;">Child explains how they saw the seven (perhaps they used subitizing skills and saw 4 and 3 or 5 and 2 or maybe they saw that 3 spaces were empty and since 3 + 7 = 10, there must be 7 objects). </span></li>
<li><span style="font-family: "georgia" , "times new roman" , serif;">Reveal how many are in the carton. </span></li>
<li><span style="font-family: "georgia" , "times new roman" , serif;">Discuss.</span></li>
<li><span style="font-family: "georgia" , "times new roman" , serif;">Play another round.</span></li>
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What variations could you make to expand this activity? </div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKIxxM1tYGdPeqW2Jt4fLCQ7k62jmt6HjXBOC1zd25wkelyDcUVHFe7yzBnUGmDqAChsN5zqoXbLBu6Z2yDk2BIaDHXu7J-hRvQjtmSZUHIa_tbrOtqaXsWOJTJALsOX4v5AnoH4NBUzXM/s1600/making-10-foam-blocks-math.jpg" style="margin-left: auto; margin-right: auto;"><span style="font-family: "georgia" , "times new roman" , serif;"><img border="0" data-original-height="450" data-original-width="675" height="213" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKIxxM1tYGdPeqW2Jt4fLCQ7k62jmt6HjXBOC1zd25wkelyDcUVHFe7yzBnUGmDqAChsN5zqoXbLBu6Z2yDk2BIaDHXu7J-hRvQjtmSZUHIa_tbrOtqaXsWOJTJALsOX4v5AnoH4NBUzXM/s320/making-10-foam-blocks-math.jpg" width="320" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: "georgia" , "times new roman" , serif;">Image Source: <a href="https://www.schooltimesnippets.com/" target="_blank">https://www.schooltimesnippets.com/</a></span></td></tr>
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<b><span style="color: #bf9000; font-family: "georgia" , "times new roman" , serif; font-size: large;">BEDTIME STORIES</span></b><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">Bedtime stories (or "anytime stories" for that matter!) are not reserved for building literary knowledge. The next time you read a storybook, think about what mathematical ideas could be supported by the story or the pictures? There are many ways to incorporate mathematical thinking into story time. One approach would be to read the story all the way through, THEN go back to the beginning of the story and have a mathematical scavenger hunt. As you peruse the pages a second time, ask questions that support mathematical thinking, like "how many" and "which is more". When my children were small, they always begged to have books read again (and again and again). By approaching the second reading of the book from a mathematical standpoint, we interact with the book in a different way. </span></div>
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<span style="font-family: "georgia" , "times new roman" , serif;">Another way to bring math into the discussion during story time is to stop along the way. As you are reading, stop on interesting pages and ask a mathematical question about the story or the picture. These questions can be easily tailored to the child's readiness level – even when reading to a multi-age audience. </span></div>
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<span style="font-family: "georgia" , "times new roman" , serif;"><span style="font-family: "georgia" , "times new roman" , serif;">Let's imagine that we are reading the book</span><i style="font-family: georgia, "times new roman", serif;"> Where the Wild Things Are</i><span style="font-family: "georgia" , "times new roman" , serif;"> by Maurice Sendak. As you may know, this book was not written for the purpose of supporting mathematical thinking (like </span><i style="font-family: georgia, "times new roman", serif;">Even Steven and Odd Todd</i><span style="font-family: "georgia" , "times new roman" , serif;"> by Kathryn Cristald used in many 2nd grade math classrooms), but that shouldn't stop us from using </span><i style="font-family: georgia, "times new roman", serif;">Where the Wild Things Are</i><span style="font-family: "georgia" , "times new roman" , serif;"> to focus on numbers and patterns. Consider how these questions support mathematical thinking: </span></span></div>
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<li><span style="font-family: "georgia" , "times new roman" , serif;">How many teeth does this Wild Thing have? Let's count.</span></li>
<li><span style="font-family: "georgia" , "times new roman" , serif;">How many claws does this Wild Thing have on each hand? </span></li>
<li><span style="font-family: "georgia" , "times new roman" , serif;">Is that more or less than the number of fingers that you have on your hand? </span></li>
<li><span style="font-family: "georgia" , "times new roman" , serif;">Let's skip count to see how many claws the Wild Thing has in all: 4, 8, 12, 16.</span></li>
<li><span style="font-family: "georgia" , "times new roman" , serif;">Which is more? The number of teeth the Wild Thing has or the number of claws? How do you know?</span></li>
<li><span style="font-family: "georgia" , "times new roman" , serif;">What shape are the Wild Thing's teeth? </span></li>
<li><span style="font-family: "georgia" , "times new roman" , serif;">How many more buttons does Max need on his pajamas to have ten buttons? </span></li>
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<span style="font-family: "georgia" , "times new roman" , serif;">...So many possibilities - Have fun with it!</span></div>
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<b><span style="color: #ea9999; font-family: "georgia" , "times new roman" , serif; font-size: large;">DAILY CALENDAR</span></b><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">One of the best things about <i>the whole world</i> moving to a </span><span style="font-family: "georgia" , "times new roman" , serif;">learn-from-home</span><span style="font-family: "georgia" , "times new roman" , serif;"> instructional model during our current pandemic situation is that many educators and educational company's are sharing resources like never before! Most of them are free. I recently came across Zorbit's Math daily calendar. Honestly, I had never heard of Zorbit's Math before learn-from-home teaching forced me to seek alternative resources, and one of the things I found was this daily math calendar of simple things that families can do at home to support mathematical thinking. </span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXmoHP06oldueDBnPCAS6OTxvOze9-iI_nhCRTQ4p8Dj9OOuoHNSKa9JTFUmn_7415raAAf-xS4hz8ji0XdOK0ddF_6DNMfPVjkntT-n4jGl_BS9JIkNw_ww52nG-FiI1lxuoDVshnsiyJ/s1600/Screen+Shot+2020-04-30+at+11.26.19+AM.png" style="clear: left; display: inline; float: left; margin-bottom: 1em; margin-right: 1em; text-align: center;"><span style="clear: left; float: left; font-family: "georgia" , "times new roman" , serif; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="849" data-original-width="871" height="387" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXmoHP06oldueDBnPCAS6OTxvOze9-iI_nhCRTQ4p8Dj9OOuoHNSKa9JTFUmn_7415raAAf-xS4hz8ji0XdOK0ddF_6DNMfPVjkntT-n4jGl_BS9JIkNw_ww52nG-FiI1lxuoDVshnsiyJ/s400/Screen+Shot+2020-04-30+at+11.26.19+AM.png" width="400" /></span></a><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">Click </span><a href="https://go.zorbitsmath.com/home-learning?utm_source=twitter&utm_medium=social&utm_content=overview&utm_campaign=athomelearning" style="font-family: georgia, "times new roman", serif;" target="_blank">HERE</a><span style="font-family: "georgia" , "times new roman" , serif;"> to see the full May calendar of daily mathematical activities from </span><a href="https://go.zorbitsmath.com/home-learning?utm_source=twitter&utm_medium=social&utm_content=overview&utm_campaign=athomelearning" style="font-family: georgia, "times new roman", serif;" target="_blank">Zorbit's Math Home-Learning Kit</a><br />
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<b><span style="background-color: white; color: #674ea7; font-family: "georgia" , "times new roman" , serif; font-size: large;">GAMES THAT REINFORCE MATH CONCEPTS</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGyqxM59qe5aLlIkDb31TiEpkKniFqLefl5mZ_kO6nebU81xQKX7LES6QiJ6t6z9kMOnIIn5t8cB8B7uRi99YJFqUd6WzS0wHp_zaBshc3gmlNEjkhYasbFRNrHq7iI9frgU-JgnO8J8ZY/s1600/Screen+Shot+2020-05-01+at+12.41.14+AM.png" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="477" data-original-width="680" height="224" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGyqxM59qe5aLlIkDb31TiEpkKniFqLefl5mZ_kO6nebU81xQKX7LES6QiJ6t6z9kMOnIIn5t8cB8B7uRi99YJFqUd6WzS0wHp_zaBshc3gmlNEjkhYasbFRNrHq7iI9frgU-JgnO8J8ZY/s320/Screen+Shot+2020-05-01+at+12.41.14+AM.png" width="320" /></a></div>
<span style="font-family: "georgia" , "times new roman" , serif; text-align: justify;">On March 23rd, Mick Minas and his sweet child Nash started posting daily math games. The father-child duo demonstrate how to play each game. The games are great for building essential basic math skills. I look forward to the new game each day! You'll love his collection of videos; check them out on </span><a href="https://www.youtube.com/channel/UC-F-4IIfKSd3mZCjs1zwukA" style="font-family: georgia, "times new roman", serif;">YouTube</a><span style="font-family: "georgia" , "times new roman" , serif;"> and follow him on Twitter @mminas8 or look for his Facebook page.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEUvd9t4AXbQc4rGtTcoEkTnsKU3373buLsbPI_HeUi4yH78HNmUWsHhm_UFuurR4nOrHtO6p29xs8_blrfNogMn6AO0NGBjYk3rYZ8_695y4Yjt5BNPhyHS8IGbi4YwwOsH65JRjLdY38/s1600/Screen+Shot+2020-05-01+at+1.16.59+AM.png" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="48" data-original-width="50" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEUvd9t4AXbQc4rGtTcoEkTnsKU3373buLsbPI_HeUi4yH78HNmUWsHhm_UFuurR4nOrHtO6p29xs8_blrfNogMn6AO0NGBjYk3rYZ8_695y4Yjt5BNPhyHS8IGbi4YwwOsH65JRjLdY38/s1600/Screen+Shot+2020-05-01+at+1.16.59+AM.png" /></a>I just love the math practice that young Nash is getting every day playing games with dad. What an amazing opportunity this is for Nash!<br />
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<li><a href="https://youtu.be/aSeB_0hJuhg" target="_blank">Go Fish! (Near Doubles)</a><br />I have played Go Fish Make Ten and Go Fish Doubles, this version focuses on near doubles, too</li>
<li><a href="https://youtu.be/nqu1BY9oExk" target="_blank">Combo Dominoes</a><br />I just love this creative version - even played it with my nearly-grown children!</li>
<li><a href="https://youtu.be/UnPNpIm8ZMw" target="_blank">100 Laughs</a><br />This one is delightfully challenging and requires participants to laugh once they make a sum of 100</li>
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<b><span style="background-color: white; color: blue; font-family: "georgia" , "times new roman" , serif; font-size: large;">NOW GO AWAY and PLAY!</span></b><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">I hope you found several great ideas that you want to try at home or share with others, but even more, I am hoping that you were inspired to look around and to find ways to incorporate math and math discussions in places that may, at first, seem unlikely. And yes... I get the irony of you reading a blog post on your online device that encourages you to get off your device to do more live-action math – so get offline and go find some <span style="color: blue;"><b>UNPLUGGED opportunities</b>! </span></span></div>
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:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comtag:blogger.com,1999:blog-543907520077188162.post-46156837796702422212020-04-06T13:37:00.004-07:002022-11-02T10:15:47.521-07:00So You've Just Become a Math Teacher<div style="text-align: right;">
<span style="font-size: x-large;"><b>...or perhaps you’ve been one for years!</b></span></div>
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<span face=""arial" , "helvetica" , sans-serif">With nearly every child across the globe working from home during the COVID-19 pandemic crisis of 2020, <span style="background-color: white;">many parents are now working more closely than ever with their children in an effort to maintain a continuity of learning as best we can under the current circumstances</span>. </span><br />
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<span face=""arial" , "helvetica" , sans-serif">Whether you are a teacher in the classroom or a parent who is reading this during our current reality of learning-from-home, it is important to know that <b><span style="color: red;">the way we respond to the math answers given by children plays a critical role in how they think about their own reasoning</span></b>.</span><br />
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<span face=""arial" , "helvetica" , sans-serif">When learners make mistakes, it's almost a reflex to say, "<i>No, that's not correct</i>" – not because we are trying to shut down thinking, but because <b>it's efficient</b>. It saves time and energy and we do it as a way to prevent the learner from going down the wrong pathway of thinking. </span><span face=""arial" , "helvetica" , sans-serif">Saying "NO" is a great strategy when we need to prevent someone from touching something hot or walking across a busy road without checking for traffic, but... <b><span style="color: purple;">when it comes to learning</span></b>, it is important to<b style="color: purple;"> invest a few more moments of time</b> encouraging learners to <span style="color: purple;"><b>evaluate and justify their ideas.</b></span></span><br />
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<span face=""arial" , "helvetica" , sans-serif">Here's the interesting part: </span><br />
<span face=""arial" , "helvetica" , sans-serif"><b style="background-color: white;"><span style="color: #38761d;">We can assess learning by asking the exact same questions whether the given answer is right or wrong. </span></b></span><br />
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<span face=""arial" , "helvetica" , sans-serif">By asking questions that are reflective, learners <b><span style="color: #b45f06;">engage more deeply </span></b>with the problem and will often self-correct their own thinking when it's needed (this is powerful!).</span><br />
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<span face=""arial" , "helvetica" , sans-serif">Perhaps you're thinking, <i><b>"Well, that's not very efficient at all – isn't it faster to just tell them that the answer is wrong and ask them to try again?" </b></i> Well, yes, that IS faster – asking reflective questions is not the most efficient path to let a child know that the answer given was wrong, but it is the <b><span style="color: blue;">ONLY path </span></b>for helping to <b><span style="color: blue;">develop a true understanding of the math </span></b>that is in front of them. </span><br />
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<span face=""arial" , "helvetica" , sans-serif">The next time your child/student makes a math mistake, rather than saying, "No, that is not correct", try out one of these replies to <b><span style="color: red;">promote deeper thinking and greater problem solving </span></b>– We may be surprised at how much we can learn from a wrong answer.</span><br /><br />
<span face=""arial" , "helvetica" , sans-serif"><br /></span><span face=""arial" , "helvetica" , sans-serif" style="font-size: large;">Some reflective questions to try when discussing math with a child:</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1m9h4ZKYZrfY1VeqFhv5eaYitiy_71-ACLRA4pJJXyfNSxM7EBjKUpedOZ1CK4yug4JUyE-tK-utFTRJdVn_7PlDEIFIAzylBqBWlzLmdM2_9wE4S48__ye0zMDwOkYMwhf9ZhQr5nMs9/s1600/Screen+Shot+2020-04-06+at+5.25.45+PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1286" data-original-width="1153" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1m9h4ZKYZrfY1VeqFhv5eaYitiy_71-ACLRA4pJJXyfNSxM7EBjKUpedOZ1CK4yug4JUyE-tK-utFTRJdVn_7PlDEIFIAzylBqBWlzLmdM2_9wE4S48__ye0zMDwOkYMwhf9ZhQr5nMs9/s640/Screen+Shot+2020-04-06+at+5.25.45+PM.png" width="572" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><span face=""arial" , "helvetica" , sans-serif"><br /></span><i><span style="color: #8e7cc3;"><span face=""arial" , "helvetica" , sans-serif">Exciting sidenote:</span> <span face=""arial" , "helvetica" , sans-serif">I talked to a parent this week who couldn't wait to share that she tried this strategy of asking reflective questions instead of saying, “wrong”. She told me that she was nervous because she didn’t really understand the work her child was doing and wasn’t sure how she would be able to help. By the time mom and child were done, the child had a full understanding (and so did mom!). So... you don’t actually have to know the correct answer or understand the strategy that was used before asking reflective questions to gauge your child’s level of understanding (and that is just another brilliant feature of reflective questions</span><span face=""arial" , "helvetica" , sans-serif">!)</span></span></i></div>
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:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comtag:blogger.com,1999:blog-543907520077188162.post-202695288129516972020-03-07T19:16:00.002-08:002020-03-16T10:00:36.196-07:00Closing Learning Gaps and Increasing Rigor Through Reasoning<div class="separator" style="clear: both; text-align: center;">
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If you've been following this blog, then you already know that I'm likely to tell a little story before jumping into <i>the good stuff</i> – I promise, I'll take you to the practical, usable stuff just as soon as I can.</div>
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THE STORY – The way my math teachers taught me (back in the day) as compared to the way I teach young students today are <i>very</i> different models of instruction. One of the primary differences with the way we teach today is the <b><span style="color: #134f5c;">emphasis on reasoning</span></b> and not just focusing on correct answers. As I think back, I remember so many of my math teachers grading papers by simply laying a template over our papers and looking for the penciled in shading peeking through the punched out holes to determine if our answers were right or wrong – I also remember my very clever friend Mary sometimes marking two answers if she was unsure which was correct; she knew one of the two circles she shaded was bound to turn up in the grading hole on the teacher's template.</div>
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The problem with the method of instruction I experienced as a young learner of mathematics was – well actually, there are many problems with it – but two that come to mind immediately are (1) how could my teacher possibly use the powerful instructional strategy of <b><span style="color: #134f5c;">error analysis</span></b> to help me refine my thinking if all he was doing was looking for shaded dots and (2) how could he possibly know why I thought the answer was "C" if he didn't ask me to <b><span style="color: #134f5c;">justify</span> </b>any of <b><span style="color: #134f5c;">my responses</span></b>? If you're thinking, "he couldn't", you're right!</div>
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By emphasizing increased instructional rigor through activities that require students to reason, we do a better job of closing learning gaps and can better prepare our students for the type of math they will do throughout their lives – after all, <b><span style="color: #990000;">math in the real world is rarely multiple choice! </span></b></div>
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The Department of Education in my state has recently refined the expectations for student-reasoning in mathematics. These newly designed reasoning standards do a nice job of reminding us to use a variety of task types to help students develop their mathematical reasoning skills. As I continue my own journey of learning how to better teach students to reason, I came across a quote from Michael Battista (<i>Reasoning and Sense Making</i>, 2017) that reminds me why helping our students to make sense of the math is so important to their mathematical development:</div>
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<i><span style="color: #3d85c6; font-size: large;">Students who achieve understanding and sense making of mathematics are likely to stay engaged in learning it. Students who fail to understand and make sense of mathematical ideas and rely on rote learning will eventually experience continued failure and withdraw from mathematics learning. </span></i></div>
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<i><span style="color: #b45f06;">Okay, so here comes the practical, usable ideas I promised you when you started reading....</span></i></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjw9tb1wGbzAS_hlhXaAM9Vt9kYXq9SiPfS2hZecOqaR5rjM5XkNMb-b1ey33aqcsMxh0hf1SkKbDBLOpEArcBJe_KV9O3av2s-chhiIlgA47dx3nU14X8CoUbN562thaGcQgcQAlrk9Diz/s1600/math-icon-60.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="72" data-original-width="72" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjw9tb1wGbzAS_hlhXaAM9Vt9kYXq9SiPfS2hZecOqaR5rjM5XkNMb-b1ey33aqcsMxh0hf1SkKbDBLOpEArcBJe_KV9O3av2s-chhiIlgA47dx3nU14X8CoUbN562thaGcQgcQAlrk9Diz/s1600/math-icon-60.png" /></a></div>
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<b><span style="font-size: large;">Transforming Basic Operations into Reasoning Opportunities!</span></b></div>
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<i><span style="text-align: center;">Below are specific examples of how we can transform a rote-type of mathematics question into one that requires students to use reasoning. For each of the four new MCAP reasoning standards, I have included one example of how to<span style="font-size: large;"><b> <u>change</u> "THIS" to "<span style="color: #cc0000;">THAT</span>"</b></span>. </span></i></div>
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:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comtag:blogger.com,1999:blog-543907520077188162.post-66039851340768173482020-02-07T07:38:00.002-08:002020-02-22T17:44:55.213-08:00Math Relies on Generalizations!<span style="color: #222222; font-family: "roboto" , "arial" , sans-serif;"><span style="background-color: white; font-family: "arial" , "helvetica" , sans-serif;">If you've met me in person, then you already know that I not only write about mathematics instruction, but I also love to talk about mathematics instruction (a lot!). With that said, it is very possible that you’ve heard me share this exemplum of my own experience before: </span></span><br />
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<span style="background-color: white; font-family: "arial" , "helvetica" , sans-serif;"><span style="background-color: transparent;"><span style="background-color: white;">When I was in 5th grade, I was asked to find the quotient of 8,024 </span></span><span style="background-color: white; font-family: "roboto" , "arial" , sans-serif; font-size: 16px;"><b>÷</b> 17. </span></span><br />
<span style="background-color: white; font-family: "arial" , "helvetica" , sans-serif;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="background-color: white;"><b>Would you be surprised to learn that I have never been asked to solve that same problem again -- not even once!</b> (Probably not surprised, are you?). Back when I was learning about multi-digit division, I could have practiced and rehearsed to memorize the solution, but that would have used up precious storage space in my brain that could have been available for something else.</span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="background-color: white;">The truth is, we do not ask students to solve, memorize, and store things like the quotient of 8,024 </span><b>÷</b><span style="background-color: white;"> 17 because good mathematics instruction focuses on the patterns and relationships of numbers, not just isolated specific elements. Good mathematics instruction is not about <i>specializing</i>, it is about <i><b>GENERALIZING</b></i>. </span></span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmFLKEirwwJwUXlqEL-pIULKnT6gpcuJ445NVs8nhmU5iYAujxtQkWGGPec8SAjccjt8a22JlQ3PWeSVbpWGNXYHmMe9jXT9WuMakV9ox2ms76F3p3vwdV6wCvYhCtvrJWPyShl4S6UY1h/s1600/small+door.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="color: black; font-family: "arial" , "helvetica" , sans-serif;"><img border="0" data-original-height="398" data-original-width="489" height="260" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmFLKEirwwJwUXlqEL-pIULKnT6gpcuJ445NVs8nhmU5iYAujxtQkWGGPec8SAjccjt8a22JlQ3PWeSVbpWGNXYHmMe9jXT9WuMakV9ox2ms76F3p3vwdV6wCvYhCtvrJWPyShl4S6UY1h/s320/small+door.jpg" width="320" /></span></a><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="background-color: white;">Let's connect this idea to something a bit more universal in nature to illustrate the importance of generalizing even more: Every day, we turn on lights and open doors without much thought or effort. Opening the front door to your home is much like opening the front door to your friend's home, or the door at your favorite bookstore, or even the refrigerator door. We recognize value in generalizing the process of opening a door in order to apply that information to other doors that we encounter. The doors do not have to be in the same location or even open in exactly the same way. If we had to learn, memorize, and store information about how to open each individual door we encountered each day, we would spend most of our time just figuring out how to get inside. </span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="background-color: white;">The importance of generalizing mathematical concepts is often an undervalued lesson. We either expect our students to automatically generalize information or we simply overlook the essential role that generalizations play in learning mathematics. We should introduce students to mathematical concepts beginning with things that are simple and then move toward the underlying generalizations</span><span style="background-color: white;"> in order to help our students better understand the patterns and relationships behind what they are learning. My own 5th grade teacher recognized (so many years ago) that the value of the lesson was not simply knowing that the quotient was 472, but rather, the value was in understanding the relationships of the numbers and generalizing both the process and my conceptual understandings so I could go on to divide<b> any</b> pair of values.</span></span><br />
<span style="background-color: #fdffff; font-family: "arial" , "helvetica" , sans-serif;"><br /></span><span style="background-color: #fdffff; font-family: "arial" , "helvetica" , sans-serif;">Before I share specific examples illustrating the importance of mathematical generalizations, I’d like to thank my wonderful thought partners and share a bit about our recent idea sharing session:</span><br />
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<span style="background-color: #fdffff; font-family: "arial" , "helvetica" , sans-serif;">Every now and then I hear people talking about how they had an idea and scribbled their thoughts on a bar napkin. Well, my notes for this month's post are scribbled on a cardboard coaster with mathematical models and notes weaving in and out among the water rings caused by the condensation of my drink -- actually from my colleague's ice tea. I am at an educational conference this week and was thrilled to be surrounded by like-minded colleagues who were willing to talk about instruction as we tossed around ideas over a three hour dinner. Ideas were flying and I didn't want to lose a single one of them -- the napkins were cloth, so I reached across and grabbed Julie's drink coaster 😊 Thank you for being thought partners with me. I am grateful for the specific examples that stemmed from the wonderful academic conversations I had with Julie, Jason, Candace, Kristin, and others at the table. </span><br />
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<span style="background-color: #fdffff; font-family: "arial" , "helvetica" , sans-serif;">So let’s call this next segment "<b>The Coaster Notes”</b></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="background-color: #fdffff;">Below are a few of the ideas we discussed as we shared each of our ideas about the critical importance of mathematical generalizations. </span></span><br />
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<span style="background-color: #fdffff;"><span style="font-family: "open sans" , sans-serif;">When we teach early skills in decomposing numbers, we are actually preparing students for subtraction with regrouping in later years. For example, students learn that 47 = 40 + 7 but 47 also equal 30 + 17. It is this second decomposition of 47 that will be essential when we are later asked to solve 47 – 28. The model shown below shows the progression of how 47 – 28 might be approached across various grade levels until students are simply using what we've come to know as the standard algorithm. Why didn't we just start with the standard algorithm? Well, it is important that student have a conceptual understanding of the process, so they can work more flexibly and fluently when using these types of calculations for real-world applications.</span></span></span><br />
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<span style="background-color: #fdffff;">The work we do at the elementary level has far-reaching implications as students enter higher levels of mathematics in middle school, high school, and beyond. </span></span><br />
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<span style="background-color: #fdffff;"><br /></span><span style="background-color: #fdffff;">With every lesson we teach, it is critical that we help our students discover the generalizations that create the patterns and relationships of the mathematics they are doing. When a student notices that the sum of an even and an odd integer always results in an odd integer, for example, that student is generalizing. Generalizations allow students to think about computations independently of the particular numbers that are used. Without this, and many other generalizations made in mathematics from the early grades, all work in mathematics would be cumbersome and inefficient<span style="font-size: x-small;"> [CA Digital Chalkboard].</span></span></span><br />
<span style="background-color: #fdffff; font-family: "arial" , "helvetica" , sans-serif;"><br /></span><span style="background-color: #fdffff; font-family: "arial" , "helvetica" , sans-serif;">Assess how much you talk with your students about the generalizations of their math work. If you are spending a large chunk of instructional time discussing specific solutions, you are most definitely missing the proverbial boat! Mathematics is about the patterns and relationships of numbers - to see these, we must look for the generalizations that create them. Set a goal to increase the amount of time you dedicate to discussing the generalizations and less time focused just on correct solutions. </span><br />
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:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comtag:blogger.com,1999:blog-543907520077188162.post-87002893430537329282019-12-06T08:50:00.001-08:002019-12-19T19:00:01.356-08:00Teachers are a Gift!<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWEomtgxZlbsNg_AtKM4KxiZKrpjVSTfigjUmDuWNDiWPViSQn-OLU6P0vDzAhZDjM2yzj2mnZCjsqRX5wb3JkJx9oktsUJLto9M_1HUSkIGHKDJdxK04VDvOu-moEUHUaxYYc_pmaXpS7/s1600/5eb9ee4eccfc5a292c44a75150a32b39.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWEomtgxZlbsNg_AtKM4KxiZKrpjVSTfigjUmDuWNDiWPViSQn-OLU6P0vDzAhZDjM2yzj2mnZCjsqRX5wb3JkJx9oktsUJLto9M_1HUSkIGHKDJdxK04VDvOu-moEUHUaxYYc_pmaXpS7/s200/5eb9ee4eccfc5a292c44a75150a32b39.jpg" width="150" /></a></div>
<span style="color: #38761d;">This past weekend, I went into the basement and pulled out my Christmas decorations from storage and began the annual transformation – my home was soon filled with twinkling lights and the the smells of the holiday season. As we were decorating our tree, I couldn't help but think about all of the students I have taught over the years – after all, many of my ornaments are ones I received from students – I found one of the first dated 1989! As I carefully unwrapped each one and hung it on the tree, I began thinking about not only the students I have known but the many amazing teachers with whom I've had the privilege to work alongside. </span><span style="color: #38761d;">This month's Snack is dedicated to YOU – to every teacher who has dedicated their life to making the lives of students richer through education. </span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtw7iGu6KLiF6Tfr4FyKvT9-Y1q2ylmjuzFqchBTncdLshvBwmL8-LqmoEn4Ld2V5ATAsXobpUSrD59KuPYrNToCqLZ2Ass44knPevFvNzgXUafDFaDoQeqUSnF8IODMarz-K_oRRaLf6x/s1600/51OvKrWEDPL._SX466_.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="366" data-original-width="466" height="244" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtw7iGu6KLiF6Tfr4FyKvT9-Y1q2ylmjuzFqchBTncdLshvBwmL8-LqmoEn4Ld2V5ATAsXobpUSrD59KuPYrNToCqLZ2Ass44knPevFvNzgXUafDFaDoQeqUSnF8IODMarz-K_oRRaLf6x/s320/51OvKrWEDPL._SX466_.jpg" width="320" /></a>Whether you celebrate the 12 Days of Christmas, the 8 Days of Hanukkah, the 7 Days of Kwanzaa, Three Kings Day, Pancha Ganapati, Winter Solstice, or the various other winter holidays celebrated around the world, this page is dedicated to celebrating the GIFTS that YOU bring to your classroom each and every day – Thank You!<br />
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Our school district has so many amazing educators who work with our students. I'd like to highlight a few to represent the many – the many amazing teachers who bring a wide array of gifts and talents to their classrooms every day.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoHPKikP1ooBVmQoA1-371yBgwxLiWd6-0PdiNaiZ1b4Q6CsKdV8TXV0wvjD30_0L9hAtcy0QvNKQP_v6yQ2xwrlpWPCDXQXCghvKbB_bJfcUOvBak2eGFzn6eedhwoAYVNq9w0WjP1gDe/s1600/Screen+Shot+2019-12-03+at+10.55.18+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="150" data-original-width="668" height="88" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoHPKikP1ooBVmQoA1-371yBgwxLiWd6-0PdiNaiZ1b4Q6CsKdV8TXV0wvjD30_0L9hAtcy0QvNKQP_v6yQ2xwrlpWPCDXQXCghvKbB_bJfcUOvBak2eGFzn6eedhwoAYVNq9w0WjP1gDe/s400/Screen+Shot+2019-12-03+at+10.55.18+AM.png" width="400" /></a></div>
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<tr><td class="tr-caption" style="text-align: center;">Ms. Puglisi, Ms. Baker, Mr. Freytag, Ms. Shores, Ms. Roland</td></tr>
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This team of teachers has a spirit of teamwork and collaboration that is truly inspiring. They meet with each other every morning to talk through their day and to encourage each other. When I am invited to meet with one member of the team, I am sure to find all of them at the meeting - including the special education teacher who provides services to the students in 2nd grade. I asked them to tell me the secret to such amazing collaboration – they sent me a group-composed email with permission to change whatever wording I needed – I didn't need to change a word! "We plan and meet together daily. This allows us to share what we are each doing, to talk about what is and is not working, and to discuss ideas for specific students to ensure appropriate instruction. Not only do we support each other instructionally, but we look out for each other's best interest and support each other in the personal aspects of life. We are there to lift each other up and rub each other's back as needed. We set aside time and commit to each other's well-being - personally and professionally." What an amazing gift to students – a whole team of teachers fully invested in each other and the learning of all of their students.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjt5c5Wm2Hvylkpm94IBTtfSwvBE0r5LkDJDzkEla19spapLhGDxvoVrEYd7hZRWYLddLU2qSqF_7CiWNbmxLDY3vQpJ4nNRoGCqHwLWGMrbhzwQKzf89u3t-T1Q9uiOFlmWvRMVyiOJrxr/s1600/IMG_0351.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjt5c5Wm2Hvylkpm94IBTtfSwvBE0r5LkDJDzkEla19spapLhGDxvoVrEYd7hZRWYLddLU2qSqF_7CiWNbmxLDY3vQpJ4nNRoGCqHwLWGMrbhzwQKzf89u3t-T1Q9uiOFlmWvRMVyiOJrxr/s320/IMG_0351.jpg" width="320" /></a></div>
If you visit Mr. Taylor's 3rd grade classroom, you will find that student voices have a prominent role in the classroom. Not only does he give them time and space to talk, but he amplifies their voices (literally!). During Number Sense routines, students share their ideas using a microphone - a real microphone! Student ideas can be heard throughout the room by everyone, and I couldn't help but notice how much more ownership the students had of their own ideas by having their voices highlighted and heard when using the mic. We have so many classrooms where student voices are encouraged and celebrated (even when it's not through the use of an amp!) – allowing students to be heard and celebrating their ideas are true gifts that we give to our students.<br />
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If you were a student in Mrs. Murphy's room, you would certainly know the <i>Golden Rule</i> to treat others as you hope to be treated and would definitely understand that your words should be used to lift others, not pull them down. Mrs. Murphy will be the first to tell you that, in her room, learning the content is important but it is secondary to learning how to be a good person and a community of kind humans. Mrs. Murphy helps her students develop a positive mindset each day by greeting every student who enters the classroom with a cheerful "good morning" as she calls them each by name. Of course, every minute of every day is not easy and the room is not devoid of behaviors that may make being kind a bit challenging, but Mrs. Murphy works purposefully to develop true relationships with each student so, when she does need to redirect student behaviors, she knows just the right approach to use with each student while maintaining an environment still rooted in kindness. The gift of kindness is one that all can offer and every one deserves.<br />
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Like so many teachers, Ms. Brown brings many gifts to her classroom. One of those gifts is the gift of structure. As a Kindergarten teacher, Ms. Brown teaches some of our youngest learners, and a room full of 5 year olds could easily feel like herding cats, as they say, but in Ms. Brown's classroom, there is a secure feeling of structure – of knowing exactly what to expect and what is expected. As I entered her room, her students were just returning from recess. They went straight to the carpet where a video was playing to help them to transition from the free range movement of playing outside to a more structured type of movement while they practiced counting and getting their minds ready for math time. After a few minutes of counting with Jack Hartmann, they helped each other get dry erase boards and markers to do a "before and after" number activity. The focal point changed several times as Ms. Brown changed her point of instruction with each planned activity. As she moved from place to place, she simply said, "swivel, swivel" and the students tracked her with both their eyes and body position. After a few brief directions about the day's groups, students headed off to four different learning stations throughout the room – there was a lot of movement but it all seemed like a choreographed dance, of sorts. Everyone knew what to expect – these were clearly established routines – and everyone knew what was expected of them allowing it to just flow. It is truly a gift to our students when we provide an environment that feels safe, where students have been taught the expectations, and a consistent structure is in place to help them feel confident and secure.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjay8BxTHLmqpNXmYSrCW06uuBwzBKgdthVSgrud4tgHNL7togJDBacQYP8noB_S-vdzZtDQyBNv1mggmDbZZIFIJTDkxDMzxoQN6x8rx_4Y82sciFTbJX8mnGzncwsgy8lIJ_JCTK8Yc_c/s1600/Jon.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjay8BxTHLmqpNXmYSrCW06uuBwzBKgdthVSgrud4tgHNL7togJDBacQYP8noB_S-vdzZtDQyBNv1mggmDbZZIFIJTDkxDMzxoQN6x8rx_4Y82sciFTbJX8mnGzncwsgy8lIJ_JCTK8Yc_c/s320/Jon.jpg" width="320" /></a>Want to come see a nice quiet classroom where students are sitting neatly in rows and listening intently to the lesson being delivered by the teacher? Then look somewhere else because that is not the type of learning community that Mr. Cox is striving to build among his students. In Mr. Cox's classroom, you will find a variety of flexible seating options that include some desks, some tables, and some hightop counters where students might even opt to stand instead of sit. Students are encouraged to talk to each other and Mr. Cox has been known to stir up a mathematical debate or two by posing questions that he knows will make some of his students analyze their own thinking. Last week, I found his students using cut up pieces of old overhead projector sheets (you know, the clear plastic sheets that have been long forgotten since the era of SmartBoards) to make "sliders" as they worked with decimals and multiplying by powers of ten. A few weeks prior to that, students were building rectangular prisms with Unifix cubes to create a structure that matched the details on their task cards in order to discover the missing dimension of the structure, and today I walked in to see his students moving throughout the room solving a variety of error analysis problems that centered around multi-digit multiplication. When we engage our students in their own learning, we give them the gift of ownership of that learning. It is well-documented that engaging students in the learning process increases attention and focus and motivates students to practice higher-level critical thinking – a gift that is certainly worth giving!</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTyndh-KruTlQZ4IeG7zCkwy4GN1NZWn0B0m8fpiHQsnZKrXRWZ9ogVF2403yNoxR93PrCwuoLgKynFJh-sPkE3Ao_0Ap9IRwWjubNf10Td5rodkAsaUSSr0OhyphenhyphenvhQ8Ws_WTC4jdjkhzNb/s1600/IMG_0413.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="220" data-original-width="402" height="175" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTyndh-KruTlQZ4IeG7zCkwy4GN1NZWn0B0m8fpiHQsnZKrXRWZ9ogVF2403yNoxR93PrCwuoLgKynFJh-sPkE3Ao_0Ap9IRwWjubNf10Td5rodkAsaUSSr0OhyphenhyphenvhQ8Ws_WTC4jdjkhzNb/s320/IMG_0413.png" width="320" /></a>I just love visiting Ms. Torres' 1st grade classroom. It is a place that is filled with hard work and high expectations – but it is also a room of smiles and positive language. In Ms. Torres' room, students are embraced each and every day with words of encouragement that makes them want to strive for higher goals and achieve more. I recently spent just 10 or so minutes with Ms. Torres' class – actually, I was just passing through the library and they were there. Ms. Torres was working with students one-on-one offering personal feedback and instruction before making her rounds to those who were on the computers fully engaged in Dreambox learning. As she stopped by every single student's work station, students clicked on their progress monitoring button as Ms. Torres helped them to self-check their progress – she offered just the right type of encouragement whether they were lagging behind or right on track. As she left each student's station, I couldn't help but notice two things: (1) every student seemed to work even harder to either meet the goal she set with them or to continue gaining her approval and (2) every student was smiling from the words of encouragement she had offered. When we encourage our students and help them to realize their own potential, we give them a gift that will last throughout their lives.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVB0SR8cuzC5LpfN5uxFntNJZkUjFbfDNHbC9jQewavB3JQXGDp6EhiMOWVn1e2GNLKy1G156vaktEf8O7jAuZY4e2IK-MLIbaZ3Us0zLIiNkBxhCy-AIuG_81iv5yGDpV4_m7vP19Y2_S/s1600/kelly.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVB0SR8cuzC5LpfN5uxFntNJZkUjFbfDNHbC9jQewavB3JQXGDp6EhiMOWVn1e2GNLKy1G156vaktEf8O7jAuZY4e2IK-MLIbaZ3Us0zLIiNkBxhCy-AIuG_81iv5yGDpV4_m7vP19Y2_S/s320/kelly.jpg" width="320" /></a>One of the most essential gifts that we can offer our students is the gift of patience. They are young – I mean, think about it... I have t-shirts that were born before most of our students. They are new to most things, and they really do want to do their best – but they may not always know how to do that, just yet. Patience is certainly a key ingredient when you work in education. So how do we give our students this important gift? I asked Ms. Brunner, a special education teacher working with several grade levels, because she always seems to take things in stride no matter how difficult the situation. Her approach is to begin by recognizing and celebrating all student growth because it allows her to focus on the positive and "when you are focused on the positive, you can't help but to be more patient." If focusing on the positive doesn't seem to do the trick, Ms. Brunner knows she just hasn't found the right fit (yet!) and it's time to start brainstorming for a new strategy or tool that will help her students learn and grow. And when all else fails, she says, "just take a few deep breaths and focus on moving forward."</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPWJ3g7emBCKWDbkvdQXxrEfa_Gjt7GDFmIYOIRous24M0u-6bLn_0w6qqv12FD9amA6xAMRE4pgsc3LSIze5hhvJ7KgilnyT03r6LPeyTzqw8s5UHYcBjNM7jK0UdGUqgFEld0Okpsl1G/s1600/IMG_0325.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPWJ3g7emBCKWDbkvdQXxrEfa_Gjt7GDFmIYOIRous24M0u-6bLn_0w6qqv12FD9amA6xAMRE4pgsc3LSIze5hhvJ7KgilnyT03r6LPeyTzqw8s5UHYcBjNM7jK0UdGUqgFEld0Okpsl1G/s320/IMG_0325.jpg" width="240" /></a>Ms. Broussard is most definitely one of those "lifelong learner" types (I say this with the utmost admiration and respect!). Ms. Broussard is a phenomenal teacher – just ask any of the students that she has taught over the past 18 years or colleagues who have had the pleasure of teaching alongside of her. Despite her years of experience and success, she is still (and always) on a mission to learn more. Like others, she regularly attends the Wednesday night planning sessions – not to share what she knows, although she shares her knowledge freely – but to learn from her colleagues. She is equally eager to talk about an amazing lesson she taught yesterday or to learn about another approach or activity that she might try tomorrow with her students. When she learns something new, it is difficult to contain her obvious excitement – but truthfully, why would anyone even try? An excitement for learning is contagious! When you think about it, lifelong learning is actually a double gift to our students: They "catch" our excitement for learning and because we now know more ourselves, we are even better teachers for them.<br />
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It is likely that as you read these vignettes, you recognized these gifts as ones that you and your colleagues bring to your students, too. You were, in fact, also a part of this story. Your photo may not have appeared in the article, but, as you are well-aware, it is simply not possible to teach without offering our students the gift of ourselves: our time, our talents, our hearts. As we head into the gift-giving season and then into the new year, let's unwrap all the gifts that we have to offer because <b>the best gift we can give our students is being a caring adult whose goal is to help each student in our care become their best self</b> 🎁<br />
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:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comtag:blogger.com,1999:blog-543907520077188162.post-27093514537462882552019-11-07T18:48:00.002-08:002020-03-29T15:34:38.473-07:00How Do You Know? <h2 style="text-align: center;">
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<span style="font-size: x-large;">The POWER of 4 Little Words!</span></h2>
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I am pretty sure that I am not the original author of this powerful saying, but I am absolutely positive that I say these words more than any other words during mathematical conversations with students.<br />
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Indulge me as I tell a little side story to offer some background information: When working with teachers, I regularly talk about my "Teacher Wall" because it is one of the things in my career that was very simple to implement, and yet, has had some of the greatest impact on my own instruction. My Teacher Wall held a simple 8-1/2 by 11 piece of paper with the words "How Do You Know?" for an entire school year and eventually these words fell out of my mouth before I even thought about it when I was teaching - especially during math time. </div>
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...so what is a Teacher Wall? </span></h3>
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Early in my career I realized that I often answered my own questions in class – who knows if my students knew the answers or not – it seems that I was just too impatient to find out. Somewhere around my fourth year of teaching, I had a principal who was amazing at using Wait Time (on students and with staff!). If you went to her with a problem, she would listen and let you talk it through and, by the time you left, you had a solution – she, however, had hardly said a word. I began to notice that I did not give my students the same kind of <i>time and space</i> that my principal gave me to work through things, so I went on a mission to become skilled at Wait Time. It seems, though, that the hardest part of a mission is <i>remembering</i> that you are on a mission. What to do?<br />
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I decided to make myself a simple sign to remind me to use Wait Time – it simply said, in big block letters (all CAPS) on a piece of white copy paper, WAIT TIME! And that was the start of my teacher wall – where a single sign hung every year after that year. The sign was not the same, but the intent was: <i>What do I want to do better this year? </i><br />
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WAIT TIME stayed on the wall for three years (!) until I finally felt like I had mastered the art of using it during instruction. For the fourth year of my Teacher Wall, I posted a sign that said, "ASK MORE THAN YOU TELL" which eventually gave way to the specific question of <b>"HOW DO YOU KNOW?"</b><br />
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Signs have followed, but "How Do You Know?" has become somewhat of an anthem for me.<br />
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Last week I was visiting a first grade classroom where one of the activities during Math Workshop was to place numbered cards in the correct place on a 100s chart. As I watched the student placing cards and then rearranging cards that had already been (mis)placed, those words just fell out of my mouth, "<b>How do you know that number goes there?</b>"<br />
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<b>Student:</b> I just know.<br />
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<b>Me: </b>(Undaunted and always intrigued to discover more about students' thinking, I pressed on)<br />
<i>How do you know </i>the 41 goes there and not in this pocket?" (I point to the spot where 42 would go).<br />
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<b>Student: </b>Because that isn't the right spot.<br />
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<b>Me: </b><i>How do you know </i>it would not be the right spot?<br />
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(Long pause.Very long)<b> </b><br />
<b><br />Student: </b>Because it's a pattern.<br />
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(I had to work hard to contain my excitement as I was hopeful that a conversation about mathematical patterns was beginning to emerge ... patience, Dawn, patience ... use what you know about Wait Time!)<br />
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<b>Me: (</b>I remain silent)<br />
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<b>Student:</b> See... all of these numbers have a 1 (he points to the ones place of each number in the first column). The numbers in this row (column) will have a 2, so 41 can't go in that pocket - that would be 42.<br />
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Our conversation continues for a few more sentences - I can tell <b>he is beginning to formulate new ideas in his mind about the patterns</b> he explained to me and the ones he was not (yet) able to explain. The classroom timer goes off and my new 100s chart friend moves on to his next workshop station where he will be building numbers with base ten blocks that he rolls on a pair of dice.<br />
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:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comtag:blogger.com,1999:blog-543907520077188162.post-3750195110067573732019-10-06T13:35:00.002-07:002021-02-19T11:57:12.569-08:00The Progression of Place Value <div class="separator" style="clear: both; text-align: center;">
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<u><b>ADDITIONAL RESOURCES</b></u><br />
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<li><a href="https://intensiveintervention.org/sites/default/files/Place-Value%20Concepts-Considerations.pdf" target="_blank">Teaching Place Value Concepts</a> by the National Center for Intensive Intervention</li>
<li><a href="https://commoncoretools.files.wordpress.com/2011/04/ccss_progression_nbt_2011_04_073.pdf" target="_blank">Progressions document for NBT</a> by the Common Core Standards Writing Team</li>
<li><a href="http://www.corestandards.org/Math/Content/NBT/" target="_blank">Number and Operations in Base Ten</a> by the Common Core State Standards Initiative</li>
<li><a href="https://mrelementarymath.com/teaching-place-value/" target="_blank">3 Super Tips for Teaching Place Value </a>a blog post by Greg Coleman at Mr. Elementary Math</li>
<li><a href="http://www.marilynburnsmathblog.com/place-value-how-to-assess-students-understanding/" target="_blank">Place Value: How to Assess Student Understanding </a>by Marilyn Burns</li>
<li><a href="https://www.youtube.com/watch?v=_CRKmH7DCVc" target="_blank">Subtraction with Place Value Disks</a> - mini-PD video by Heather Boschen</li>
<li><a href="https://www.youtube.com/watch?v=VXH2oxTnbQ8" target="_blank">Multiplying Decimals on a Place Value Chart </a>- a video by Worksheets and Walkthroughs</li>
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A special "snack" for PAC-1</div>
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<li style="text-align: left;"><a href="https://pambarnhill.com/eight-fun-munchy-math-activities/" target="_blank">Eight Munchy Math Activities</a></li>
<li style="text-align: left;"><a href="http://keepinglifecreative.com/creative-learning/goldfish-graphing-math-activity" target="_blank">Goldfish Graphing</a></li>
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:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comtag:blogger.com,1999:blog-543907520077188162.post-21567465839250543042019-09-01T07:06:00.000-07:002019-11-07T14:24:08.048-08:00Mathematical Discourse<div class="separator" style="clear: both; text-align: center;">
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<span style="font-family: "arial" , "helvetica" , sans-serif; font-size: x-large;">8 Moves to Harness the Power of </span></h2>
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<span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Which "teacher move" do you think is the most powerful <br />for generating mathematical thinking and discourse? </span></h3>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;">Below are 8 strategies </span><span style="font-size: large;">that you can use right away in your classroom to promote deeper thinking and richer discourse for ALL students – and </span><span style="font-size: large;">for my own entertainment, I thought it would be fun to use some well-known (and lesser known) sayings as a way to categorize and remember each of the eight strategies. </span></span></div>
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<li><span style="color: #0b5394; font-family: "arial" , "helvetica" , sans-serif; font-size: large;">A Goal Without a Plan is Just a Wish</span></li>
<li><span style="color: #0b5394; font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Be Careful What You Ask For Because You Just Might Get It </span></li>
<li><span style="color: #0b5394; font-family: "arial" , "helvetica" , sans-serif; font-size: large;">The More the Merrier</span></li>
<li><span style="color: #0b5394; font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Good Things Come to Those Who Wait</span></li>
<li><span style="color: #0b5394; font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><strike>RBF</strike> – No, Let's Call It "RMF": Resting Math Face</span></li>
<li><span style="color: #0b5394; font-family: "arial" , "helvetica" , sans-serif; font-size: large;">A Few Fries Short of a Happy Meal</span></li>
<li><span style="color: #0b5394; font-family: "arial" , "helvetica" , sans-serif; font-size: large;">The Mind Needs More Space Than the Body</span></li>
<li><span style="color: #0b5394; font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Keep the Home Fires Burning</span></li>
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<span style="color: #cc0000; font-family: "arial" , "helvetica" , sans-serif; font-size: large;">INTRIGUED? Keep Reading....</span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">1. A Goal Without a Plan is Just a Wish </span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_-In4ORCHRT3WdNtyYctl80U4RzVuIWKwIyxAygmXQPCWf-7xIQDDC-Sv4TFfDJT2VY-KxwwRfpdtuuQyVVK9X1eB4PUpbO4I-C6VK2soLFIVRKd6IOWpCV6Z3xM38V1aq-MkJb1ipBnj/s1600/Screen+Shot+2019-08-25+at+12.16.38+AM.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="101" data-original-width="99" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_-In4ORCHRT3WdNtyYctl80U4RzVuIWKwIyxAygmXQPCWf-7xIQDDC-Sv4TFfDJT2VY-KxwwRfpdtuuQyVVK9X1eB4PUpbO4I-C6VK2soLFIVRKd6IOWpCV6Z3xM38V1aq-MkJb1ipBnj/s1600/Screen+Shot+2019-08-25+at+12.16.38+AM.png" /></a><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: normal;">As you prepare your lessons, plan for a variety of possible paths and possible misconceptions that your students will have. Design the tasks so that rich student-to-student discourse and productive struggle are inevitable. P</span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: 400;">lan for specific questions ahead of time – before you are standing in front of students. Some of the questions that you plan will get used, others will not.</span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: 400;"> </span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">2. Be Careful What You Ask For Because You Just Might Get It</span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><span style="font-size: large; font-weight: normal;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span></span></span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><span style="font-size: large; font-weight: normal;"><span style="font-family: "arial" , "helvetica" , sans-serif;">As you plan those questions (see #1 above), </span><span style="font-family: "arial" , "helvetica" , sans-serif;">plan to use a lot of </span></span><a href="https://www.mathmammoth.com/lessons/from_closed_math_problems_to_open.php" style="font-weight: normal;" target="_blank"><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">open questions</span></a><span style="font-size: large; font-weight: normal;"><span style="font-family: "arial" , "helvetica" , sans-serif;">,</span><span style="font-family: "arial" , "helvetica" , sans-serif;"> rather than closed questions. If you ask a closed question, you will get a closed response. When you ask open questions, students have room to think and explain and expand their ideas. You will learn more about your students' thinking and they will make more mathematical connections and will develop their mathematical vocabulary. Win-Win! </span></span></span></div>
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<span style="font-size: small;"><a href="https://vimeo.com/76884124" style="font-family: arial, helvetica, sans-serif; font-weight: normal;" target="_blank">To learn more about creating/using open questions, check out this video from Jo Boaler</a></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">3. The More the Merrier</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif; font-weight: normal;">In our classrooms, we must become more intentional to include more student voices. Honestly, we (teachers) talk WAY too much in our classrooms. Our students should be doing much of the mathematical talking, not us. Our job is to facilitate their discussions by asking questions that focus them to ideas that they may not stumble upon without us. We need to encourage student-to-student mathematical discourse – a lot of it! We have to increase student voice in the classroom. Let's teach our students to rely on one another as sources of information rather than the teacher always being the only one with the answers and good ideas. We don't intentionally do it, but we steal students' opportunities to learn pretty regularly in a typical classroom. Want an easy first step for changing this pattern? Try this: Pose a question (an OPEN question as mentioned in #2 above). Have students think about their own ideas (we'll talk more about this one in #4). Then have students rehearse their ideas with a partner – I like to use </span><a href="https://betterlesson.com/lesson/reflection/20695/peanut-butter-and-jelly-partners" style="font-weight: normal;" target="_blank">Peanut Butter Jelly Partners</a><span style="font-family: "arial" , "helvetica" , sans-serif; font-weight: normal;">. </span></span><br />
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<span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif; font-weight: normal;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_BOV6MgKK7ZtExe0Q-LW_bd4ZWKC6qXQ5laAzr4VME96KQFK_guz3Knl_C4YHFpddFPSnHkKXhvvSXkrWvfYnMD842_YxskD0DfxR7AQh3UROlQ6XylZSWEdkwCJnvbnRMj9k6POnjMa_/s1600/Screen+Shot+2019-08-25+at+12.18.17+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="135" data-original-width="182" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_BOV6MgKK7ZtExe0Q-LW_bd4ZWKC6qXQ5laAzr4VME96KQFK_guz3Knl_C4YHFpddFPSnHkKXhvvSXkrWvfYnMD842_YxskD0DfxR7AQh3UROlQ6XylZSWEdkwCJnvbnRMj9k6POnjMa_/s1600/Screen+Shot+2019-08-25+at+12.18.17+AM.png" /></a></span></span></div>
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</span></span><span style="font-size: large; font-weight: normal;"><span style="font-family: "arial" , "helvetica" , sans-serif;">After a minute or so of partner discussion, ask the question again and ask a student to share his/her response out to the whole group. The student-to-student talk takes less than 2 minutes and the benefits are worth every 120 seconds of it! Think about it: Every student had a chance to share and listen to ideas as they talked with a partner. In a </span><span style="font-family: "arial" , "helvetica" , sans-serif;">traditional </span></span><i style="font-weight: normal;"><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">ask and respond</span></i><span style="font-size: large; font-weight: normal;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> classroom</span><span style="font-family: "arial" , "helvetica" , sans-serif;">, if 8 questions are asked, only 8 students talked about their ideas - which means most students in my class had zero opportunities to process the information, formulate a response, and talk about math. By adding a simple turn-n-talk teacher move, EVERY student interacts with EVERY question... AND... because students have rehearsed their ideas with a partner, student responses are more refined and classroom discussions are much richer and deeper. </span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif; font-weight: normal;">In 1986, an <a href="https://www.scoe.org/blog_files/Budd%20Rowe.pdf" target="_blank">article by Mary Budd Rowe</a> came out in </span><i style="font-family: arial, helvetica, sans-serif; font-weight: normal;">The Journal of Teacher Education</i><span style="font-family: "arial" , "helvetica" , sans-serif; font-weight: normal;"> on the topic of <a href="https://www.scoe.org/blog_files/Budd%20Rowe.pdf" target="_blank">Wait Time</a></span><i style="font-family: arial, helvetica, sans-serif; font-weight: normal;">. </i><span style="font-family: "arial" , "helvetica" , sans-serif; font-weight: normal;">I was in college at the time and o</span><span style="font-weight: normal;"><span style="font-family: "arial" , "helvetica" , sans-serif;">ne of my classes required us to subscribe to the Journal as our textbook. I have a clear memory of reading that article during the second year of my teacher prep program. I'm not sure why, but I saved that volume even after I graduated. In 1986, I didn't fully understand the power of Wait Time, but during my third year of teaching (after a disastrous second year), it would become one of the most powerful tools in my teaching arsenal. That year, I established my "teacher wall" which I have had in every classroom since that year. My teacher wall was a place on the back wall where I looked most often during instruction (it was not an out-of-sight/out-of-mind spot next to my desk). Each school year, I decided on a skill I wanted to professionally develop then I posted a sign to remind me to practice that skill every day. For three years straight, my sign said "WAIT TIME". In year three, I revised it to specifically include both Wait Time </span><span style="font-family: "times" , "times new roman" , serif;">I</span><span style="font-family: "arial" , "helvetica" , sans-serif;"> and Wait Time </span><span style="font-family: "times" , "times new roman" , serif;">II</span><span style="font-family: "arial" , "helvetica" , sans-serif;">.</span></span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: normal;">So what exactly is Wait Time </span><span style="font-family: "times" , "times new roman" , serif; font-size: large; font-weight: normal;">I</span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: normal;"> and </span><span style="font-family: "times" , "times new roman" , serif; font-size: large; font-weight: normal;">II</span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: normal;">? In short, it's one of the most powerful tools you'll possess as a teacher. It's an easy concept to explain – but honestly, it takes practice to perfect in the classroom. </span><br />
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<li><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">WAIT TIME </span><span style="font-family: "times" , "times new roman" , serif; font-size: large;">I</span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">: </span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: normal;">After asking a question, pause and expect students to think about the question before any discussion begins. I consistently remind students that I am not looking for hands or discussion in the first <u>5 seconds</u> after I ask a question. I remind them (and myself) by putting my finger to my head to signal 5 seconds of think time. I then cue them to discuss their ideas with a partner or to raise a hand to share. In my classroom, these 5 little seconds improved the quality of the answers that students gave ten-fold, and I noticed that I had a larger pool of student hands from which to call and a wider variety of students who were willing to share. Now that's a powerful 5 seconds! By my second year of practicing this teacher move, I was pretty good at it. As I was sharing the idea with some colleagues, I realized that I had completely ignored Wait Time </span><span style="font-family: "times" , "times new roman" , serif; font-size: large; font-weight: normal;">II</span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: normal;">, so during that third year of working to improve my use of Wait Time, I took steps to intentionally include Wait Time </span><span style="font-family: "times" , "times new roman" , serif; font-size: large; font-weight: normal;">II</span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: normal;">. </span></li>
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<li><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">WAIT TIME </span><span style="font-family: "times" , "times new roman" , serif; font-size: large;">II</span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">: </span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: normal;">Every time a student gives an answer, pause. You may want to silently count 1-2-3-4-5 to help you remember – I used to use my fingers hidden behind my back to count down. Do not nod in agreement or make one of those typical "teacher faces" that indicates the answer was not what you had hoped. Instead, just wait... for just 3-5 short seconds allowing everyone in the room to process the answer given by their classmate and to begin deciding on their own if they agree, disagree, or even understand the response given. </span></li>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigGWrZq14X66Mjn1Om9-tmuqs33CnJQmVHjxArhZ_T2VsN0gZLR0BZytiTqJ3WTeHz6Zbba8usO9g-rKOxnMK1FKKAt-BnxyI_WGKb9oNWwaftd2eJijLyuj-eBJ7fw7Z_vp26EOCDkmxG/s1600/Screen+Shot+2019-08-25+at+12.25.12+AM.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="243" data-original-width="227" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigGWrZq14X66Mjn1Om9-tmuqs33CnJQmVHjxArhZ_T2VsN0gZLR0BZytiTqJ3WTeHz6Zbba8usO9g-rKOxnMK1FKKAt-BnxyI_WGKb9oNWwaftd2eJijLyuj-eBJ7fw7Z_vp26EOCDkmxG/s200/Screen+Shot+2019-08-25+at+12.25.12+AM.png" width="186" /></a><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: normal;">If you Google RBF, you will likely get images of a scowling Anna Kendrick or Kristen Stewart or perhaps an article touting that science has proven that RBF is real. R<u>M</u>F, on the other hand, has no photos of contemptuous megastars, but I assure you, <i>Resting Math Face</i> is very real and very powerful in the classroom - </span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">and having it is a GOOD thing!</span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: normal;"> </span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: normal;">Do your students seem to stop short of the perfect complete answer? In many cases, it's because we have sent them the message that they have said enough when we do not maintain our Resting Math Face and allow facial expressions and body language to slip out too soon. Consider this common scenario: You ask a question. You remember to use Wait Time (hooray!). You call on a student. The student begins with an answer that you just know is going to be perfect by how it starts off. You begin nodding and smiling to encourage the student to keep going. And the student suddenly stops talking. Wait! She started off so strong and it seemed she would have so much to say. Why should she continue? You have already given her the praise she was seeking for a good answer by nodding and smiling. Now let's say a student does not start off with what you know will be a perfect response, so you crinkle your nose and tilt your head ever so slightly. Oops! The student knows his answer has started off on the wrong track by your expression and body language. So he stops talking - which means he stops thinking and processing. He has shut down (perhaps for the rest of the class period). The best way to encourage students to <i>keep going</i> and to expand their ideas is by maintaining a </span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: normal;"><i>Resting Math Face (RMF)</i>.</span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: normal;"> Let's say the answer calls for a simple number as the response. The student says, "12". While maintaining your RMF, you ask, "How do you know the answer is 12?" The student stumbles and falters thinking that she must have answered incorrectly since you did not immediately nod and praise her correct response, so she changes her answer to "11". Using the same tone and continuing to maintain your RMF, ask, "How do you know the answer is 11?" This forces the student to consider why that answer is correct. Yep, it'll be awkward at first because we have conditioned our students through the years to look for teacher cues, but they'll soon catch on that they need to fully explain because they'll be initially met with the teacher's Resting Math Face every time. </span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">6. A Few Fries Short of a Happy Meal</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuhTcXWNirk5P0TJXoUF2nG8zYvbKmHImbCgVZJe_YnPC894-Kf1on50PFrh6qNAbz7hCiPLC-pqMhB09nYn5ppejxKCwKW6KQTAeuuubUbzy9P1LttIzqJRSvhpUtOtkLu5kKksW6EKOE/s1600/Screen+Shot+2019-08-25+at+12.36.28+AM.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="209" data-original-width="296" height="141" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuhTcXWNirk5P0TJXoUF2nG8zYvbKmHImbCgVZJe_YnPC894-Kf1on50PFrh6qNAbz7hCiPLC-pqMhB09nYn5ppejxKCwKW6KQTAeuuubUbzy9P1LttIzqJRSvhpUtOtkLu5kKksW6EKOE/s200/Screen+Shot+2019-08-25+at+12.36.28+AM.png" width="200" /></a><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: normal;">Okay, forgive me for the quirky little title of #6, but, according to my children, I use these types of sayings more than I am aware😏. </span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: normal;">When asking students questions, it's true that we are often a few questions short of getting to their deeper understanding (or their misunderstandings) because we don't use questioning to push their explanations (and their thinking) farther. When students answer, we should push/probe/challenge their ideas. Part of our job is to help our students develop their ability to engage in mathematical discourse. To do this, we need to encourage them to explain/elaborate/clarify their thinking. Remember the "teacher wall" I mentioned earlier? The sign I had hanging on my wall in more recent years said "How do you know?" </span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: normal;">– I wanted to remind myself to ask students (often) to explain their thinking. Students will become so accustomed to every answer they give being followed by the question "How do you </span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: normal;">know?" that they will automatically begin giving an answer AND a reason as part of their initial response.</span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoBC89ykMdIvyLi2sg0Ag9GJgscXreQIKwTsM04hkHFPbmURkTutv6raVUCWAlrLOXk2lhBqhFQKsqbDpkoHbWqFyWFRmUwru1GX4o3gLsNhDtCinx6HqnGqsTiI2qB-kmxntFnBFOe_WH/s1600/Screen+Shot+2019-10-20+at+10.21.32+PM.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="154" data-original-width="402" height="152" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoBC89ykMdIvyLi2sg0Ag9GJgscXreQIKwTsM04hkHFPbmURkTutv6raVUCWAlrLOXk2lhBqhFQKsqbDpkoHbWqFyWFRmUwru1GX4o3gLsNhDtCinx6HqnGqsTiI2qB-kmxntFnBFOe_WH/s400/Screen+Shot+2019-10-20+at+10.21.32+PM.png" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Love my new laptop sticker designed by my daughter Erin</td></tr>
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<span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">7. The Mind Needs More Space Than the Body</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif; font-size: small;"><span style="font-size: large;"><span style="font-weight: normal;">I heard this saying somewhere and it has stuck with me, especially when I'm working with students. As we ask students to talk to each other about their ideas, it is critical that we give them time and space with their partner/group to play with those ideas. We will gain great insight into our students' thinking and understanding as we listen to their discussions – but it is important that we do not hover or interject our own ideas as we walk around from group to group. [</span><span style="font-weight: 400;">An alternate title for this one could be "</span></span><i style="font-weight: 400;"><span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;">A </span><span style="font-family: "arial" , "helvetica" , sans-serif;">Watched Pot Never Boils</span></span></i><span style="font-size: large; font-weight: 400;">"]. </span><span style="font-size: large; font-weight: normal;">Just listen. Take notes. Let the students grapple with the learning. Let them talk and really listen to each other's ideas. Give them space to reason, question, debate, and yes, even to stumble and struggle a bit. Then use what you heard as you walked around listening to their mathematical ideas to </span><span style="font-size: large;"><a href="http://www.mctm.org/mespa/5Practices.pdf" style="font-weight: normal;" target="_blank">orchestrate productive math discussions</a><span style="font-weight: normal;">.</span><span style="font-weight: normal;"> </span></span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">8. Keep the Home Fires Burning</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: normal;">This one may be last on my list, but it is perhaps the most important one! If we hope to create powerful mathematical discourse in our classrooms, we MUST begin by establishing a supportive learning environment. And once established, we must continuously "stoke" the fire to keep it burning. I find that the best way to get the fire started is by being genuinely curious about students' ideas. We sometimes get so wrapped up in the "right" answer and the specific procedure that we fail to listen to what our students know and what they are ready to learn next. There are many ways to foster a supportive learning environment. Want a few more ideas to help stoke the fires? Try these: </span><br />
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<li><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: normal;">Promote student-to-student discourse every day </span></li>
<li><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: 400;">Encourage students to be mathematically curious </span></li>
<li><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: 400;">H</span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: 400;">elp students focus and form new ideas by a</span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: normal;">sking questions that probe thinking </span></li>
<li><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: 400;">Model a growth mindset</span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; font-weight: 400;"> </span></li>
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<span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">So... w</span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; text-align: center;">hich "teacher move" do you think is the most powerful </span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large; text-align: center;">for generating mathematical thinking and discourse? And more importantly, which move(s) can you begin cultivating right away to increase mathematical discourse?</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span><i style="font-weight: normal;"><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Check out the highlight notes on my <a href="http://mathsnack.blogspot.com/2019/05/june.html" target="_blank">summer</a></span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><a href="http://mathsnack.blogspot.com/2019/05/june.html" target="_blank"> page</a></span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"> for the books I read from my Summer Stack! I'm not done, yet....</span></i><br />
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<br />:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comtag:blogger.com,1999:blog-543907520077188162.post-43274907649543776722019-06-01T11:18:00.000-07:002019-11-07T19:34:21.421-08:00Toes in the Sand Professional Development<b><span style="font-size: large;"><br /></span></b>
<b><span style="font-size: large;">I spent the day today gathering the books that I wanted to put on my bedside table and in my beach bag for my personally-designed professional development. As I made my list and gathered some of the books, I made an important discovery....</span></b><br />
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<span style="font-size: large;">I'm sure I won't get through all of these books this summer, and I'm not even positive that every one of these will be worth the time I put into reading them – but I'm hopeful to find a few gems or at least some ideas that either affirm or (best case scenario) cause me to reflect and question my own thinking. As you consider how you will renew yourself for the fall, consider ways that you can rejuvenate through some self-selected professional development. Perhaps professional reading has a place on your summer agenda, too :) </span><br />
<span style="font-size: large;"><br /></span><span style="color: red; font-size: medium;"><i><span style="font-size: large;">EDIT </span>(June 21)<span style="font-size: large;">: For my own accountability, I decided to come back and make additions to the original post by writing a "highlight statement" for each book that I successfully complete from my list. Perhaps it will motivate me to finish most of them and will provide me with some bullets points that I hope to make part of an action plan.</span></i></span><br />
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<span style="color: red; font-size: medium;"><i><span style="font-size: large;">EDIT 2 </span>(July 3)<span style="font-size: large;">: It seems that my list just keeps growing as "way leads to way" and one book or idea leads me to a new idea and book! What a fantastic rabbit hole to fall into! </span></i></span><br />
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MY SUMMER STACK</span></h2>
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<a href="https://www.amazon.com/gp/product/1416626999/ref=ox_sc_saved_title_5?smid=ATVPDKIKX0DER&psc=1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="335" data-original-width="267" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgeLP6rlTRZVcX51iS-cHu8bn5c5wxVGge8jIhLOYSuNIuiatgecoBy4WgT0l_gu-hLShZcLXQnbBcVGdweKoDcN-lHotDqkfolFrc_WmRmEyuo3SLIPqRTDBiHISJNidgq2LU0TA1dVspw/s200/0+fluency.PNG" width="158" /></a>Fluency through games? Two of my favorite topics. I'm sure I'll find tons of ideas to share when we come back together after reading this one!<br />
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<span style="color: red;">This </span><i style="color: red;">Math Fact Fluency</i><span style="color: red;"> book is not one of those books that you are likely to read cover to cover, page by page. I read the first 13 pages as the foundation for understanding how fluency was characterized in this book. Then I began flipping through the book reading the introduction to each chapter, skimming the various activities, and reading the concluding statements. Here are two of the take-away ideas that have stuck with me: </span></div>
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<li><span style="color: red;">Fluency DEVELOPS through a process; it is not something that is taught</span></li>
<li><span style="color: red;">Timed tests do NOT assess fluency since they do not effectively assess the four components of fluency: (1) accuracy (2) efficiency (3) flexibility and (4) selection of an appropriate strategy</span></li>
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<a href="https://www.amazon.com/gp/product/0873537742/ref=ox_sc_saved_title_2?smid=AOJ03FJ34ENIN&psc=1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="232" data-original-width="164" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZeN6vAcChuS62bnbssqSil5aHdVNJAjvBf_5S0MU7cM3XlndRtcLdIasDy3EKdeZqMKckoUtECcSY_uktIARJw7h8S_XYA3r0tVwdcNXdAitnEWMc09OFLNckSmMVr-usO6uobQJ4A_Gb/s200/0+action.PNG" width="141" /></a>I have read NCTM's <i style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; box-sizing: border-box;">Principles to Actions</i> several times over the past four years, and always find something new that encourages me to refine my own thinking and practice each time I read it.<i style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; box-sizing: border-box; color: #0086b8;"> </i>This book "connects research with practice. Specific, research-based teaching practices that are essential for a high-quality mathematics education for each and every student...." I often see this title listed on other mindful educators' suggestions of "must reads" when asked what titles they recommend.<br />
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<span style="color: red;">No matter how many times I read this book, I always find a new nugget of wisdom within its pages - perhaps it is the perspective I have gained since my last reading of the pages or perhaps, like all learners, I simply need to digest the information one small bite at a time. My nugget of wisdom gained this time focuses on Mathematical Discourse (a topic that I am presenting on at the CMC-S conference in Palm Springs in November - so excited!). As we include mathematical discourse as a regular part of instruction, we must be careful not to allow that time to become an "elaborate show-and-tell", but rather, we must orchestrate which approaches will be discussed, the order in which we have students share, and the questions we will ask that help our students to make important connections. To learn how to orchestrate these discussions more fully, check out the book<span style="font-family: "times" , "times new roman" , serif;"> </span></span><span class="a-size-medium a-color-base a-text-normal" style="box-sizing: border-box; line-height: 1.255 !important; text-decoration-line: none; text-rendering: optimizelegibility;"><span style="color: red; font-family: "times" , "times new roman" , serif;"><i>5 Practices for Orchestrating Productive Mathematics Discussions </i><span style="font-family: "times";">that was co-authored by Margaret (Peg) Smith who is also a collaborative author of</span> <i>Principles to Actions. </i></span></span></div>
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<a href="https://www.amazon.com/gp/product/0325059659/ref=ox_sc_saved_title_4?smid=ATVPDKIKX0DER&psc=1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="396" data-original-width="269" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinOm5bwFCJRbcB3HtiDp2UI_LcJn2hc1KqeYgrP0l_SRZ9YTzItnpXe3wU-nTIHX9nZvVx3qJIIIHl7K8IRzbN-QwtPFZ9tpnU4i9OvTKnZU69-UKX3aR9Iuf49Gqm5e9vesHCydu4nHtF/s200/0+basic+facts.PNG" width="134" /></a>Discussion around basic math fluency is always a hot topic. I have been looking forward to reading this title and getting more insight into the balance between memorizing basic facts and helping students to learn the concepts in a way that is conceptual so it sticks!<br />
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<span style="color: red;">This book (as well as its counterpart by the same authors <i>Mastering the Basic Math Facts in Addition and Subtraction</i>) offers 11 of its 12 chapters on specific strategies encouraging classroom teachers to build fact fluency with conceptual-based strategies that go beyond simple memorization. </span></div>
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<a href="https://www.amazon.com/gp/product/0470894520/ref=ox_sc_saved_title_1?smid=ATVPDKIKX0DER&psc=1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="333" data-original-width="271" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi28Sz4qG4Szt9jLPQy6Qe9JVJYjt4HT-odxoE_TDEiCqHKeiQ1UBoJfUsRFWePXVXKVef4j8GT4QOBSq3RRzoKnDx4rb1J2UR_Gfkv4h2_H3MgtQXx-OK9NrvYrneE9eeddPErg_oVuwcK/s200/0+mindset.PNG" width="162" /></a>The name Jo Boaler and effective, progressive math instruction go hand-in-hand. This one has been on my shelf for quite a while waiting for me to really read it thoroughly. So far, I've only had an opportunity to peruse it - can't wait for a deep read of this title.<br />
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<span style="color: red;">Lots of bookmarked pages that I'll return to again and again and so much discussion happening around this title on social media among fellow teachers. </span></div>
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<a href="https://www.amazon.com/gp/product/1948334100/ref=ox_sc_saved_title_6?smid=A3TJVJMBQL014A&psc=1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="353" data-original-width="238" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPH_kfB1DhwUAy0mNGn4S1Awv5WjzRfBEo9nUpRGJ7VD5802r-Hjw_KA5R03Ul0LBXWUFmrfrNzf72nO0sdKBmOUhelNNeklA_pfshIOeNBcKpGJ8PS3QXcytM-2W9xFoTn7hxfpC8eQtM/s200/0+singh.PNG" width="133" /></a>I saw Sunil speak this past April at the NCTM Mathematics Conference and knew I had to buy his book. I should have bought it while I was there, but my suitcase was already past capacity -- I got reprimanded at the SouthWest ticket counter for being two pounds over the limit on my return flight!<br />
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<span style="color: red;">I started this one today (6/26). I'll report back when I finish :)</span><br />
<span style="color: red;">It's two months later, and I'm still only 1/3 the way through. It's been an incredibly busy summer getting curriculum written - I'm looking forward to picking up where I left off once the new school year rush calms a bit. </span></div>
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<a href="https://www.amazon.com/Visible-Learning-Mathematics-Grades-K-12/dp/150636294X/ref=sr_1_2_sspa?keywords=visible+learning&qid=1559153309&s=gateway&sr=8-2-spons&psc=1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="327" data-original-width="269" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYKbkDj1gBEqdATqWT7KQ96hyphenhyphen_yS-M3YILetOiFy1HwJQucEtcGQVB8ivIpo4tcTXpQofqVTWvduRFNoBo3wt9KDYfiFQTg4yDGqRoEkExuZbczEt0lI3Xlc9J2YBlToGuce_vf-OFawVI/s200/0+visible.PNG" width="164" /></a>As folks in my district know, we've spent some time looking at the Hattie research on highly effective teaching practices, so this title is a natural addition to my reading list. I think I'll start with this one this weekend since it's been looming from my bedside for quite some time now.<br />
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<span style="color: red;">Much of what I read in the pages of </span><i style="color: red;">Visible Learning for Mathematics </i><span style="color: red;">aligned to my own thinking and to the current practices of my school district. One of the highlights, for me, was the Effect Size chart in Appendix A. </span><b style="color: red;">Classroom Discussions</b><span style="color: red;"> have an effect size of 0.82 (for reference, 0.4 is considered the hinge point value for impact) while </span><b style="color: red;">Teacher Subject Matter Knowledge</b><span style="color: red;"> only produced an effect size of 0.09 (what?!). It seems that understanding how to orchestrate an effective classroom discussion has a much more powerful impact than whether or not the teacher is an expert in the field. </span></div>
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<a href="https://www.amazon.com/gp/product/1625310889/ref=ox_sc_saved_title_9?smid=ATVPDKIKX0DER&psc=1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="330" data-original-width="266" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWT0-Eh_6O5kTZU8OtHhjkWBbKvLjjwLY133RjD8WJfg1RvYGpjsVoGcQm2MRs7xY0ifbsQFJhnaAZAnm87I5wOHJwA4lmfsaRF-3N2sMCrXDXsO-9bdWVdZ1LdaLQw4EMP1pLlK8ygxw0/s200/0nsr.PNG" width="159" /></a>I read the K-3 edition of this book last summer and it played an important role as we developed the daily Number Sense Routines for grades 1-5 in our district. I am looking forward to seeing how this edition stretches the ideas into the intermediate grades.<br />
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<span style="color: red;">Truth be told, this title is still sitting in my Amazon cart waiting for me to clear the rest of the stack. </span></div>
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<a href="https://www.amazon.com/Impact-Identity-K-8-Mathematics-Equity-Based/dp/0873536894/ref=sr_1_2?keywords=impact+of+identity&qid=1559153633&s=books&sr=1-2" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="353" data-original-width="250" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9H01z04MhvHOriThynoPBNUrutL2dK8JvsAptrAHYKgqRBdACaeAc52ygme4ijSJFt7b_0ILW5nuk-HcvyDCxtoToWzYulgiSOw5D2sh2is7zbJXu77PPWHHdupERzrIypoxaTNsFHWfb/s200/0+equity.PNG" width="140" /></a>I feel like I need to do more to understand equity as it relates to mathematics instruction, so I added this title to my pile. It's a short read, so I should be able to read the pages in a few short hours, but I suspect understanding the impact of those words will take much longer.<br />
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<span style="color: red;">When I read books for my own professional development (like the ones listed here in my summer stack), I always keep a pack of Post-It Notes handy to jot ideas from the book that I want to make actionable for myself. Although this book has fewer than 120 pages, I ended up with a surprising number of notes sticking out when I was finished. Among the numerous take-away ideas is the list of Mr. C's Promises found on page 50 (</span><span style="color: red;">this one is sure to find its way into some PD session or PLC meeting somewhere soon):</span><span style="color: red;"> </span><br />
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<li><span style="color: red;"><b>I will work with you until you understand</b></span></li>
<li><span style="color: red;"><b>I will not waste your time – every activity is tied to a learning standard</b></span></li>
<li><span style="color: red;"><b>I will ensure that our classroom functions as a positive learning community</b></span></li>
<li><span style="color: red;"><b>I am open to suggestions</b></span></li>
<li><span style="color: red;"><b>I will learn along with you</b></span></li>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEie6ruPLGF_W34tcY5fyfBffiry5hu6niQcdyfUeJKfPguNJXwnrCb0nT5c6a6s4z8iM_sZwjw7fgW3mAvOFmr8SNaWFHHFv6p1dKTpp3kGI-xeIgtD3XUhI3ROS0ha_u_WbiyR61HTBVWN/s1600/book.PNG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="156" data-original-width="112" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEie6ruPLGF_W34tcY5fyfBffiry5hu6niQcdyfUeJKfPguNJXwnrCb0nT5c6a6s4z8iM_sZwjw7fgW3mAvOFmr8SNaWFHHFv6p1dKTpp3kGI-xeIgtD3XUhI3ROS0ha_u_WbiyR61HTBVWN/s200/book.PNG" width="144" /></a></div>
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Several of the educators in my district are reading this title. I've put it on my list for this summer so I can join the great conversations surrounding the content.<br />
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<a href="https://www.amazon.com/Choral-Counting-Collections-Transforming-Classroom/dp/1625311095/ref=sr_1_1_sspa?crid=1EC6G1R0Q7L8E&keywords=choral+counting+and+counting+collections&qid=1559156429&s=gateway&sprefix=choral%2Caps%2C286&sr=8-1-spons&psc=1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="232" data-original-width="187" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgupUgGn8t54XoQnl3kKd5d3wruXW4mRoIbVyP381T7dmBs0mSKKiIlsDvBFkUdpQpMCkpZzY_r37bNvHnG1QQLrHzo2T3tHpTibEF8HF3hX4Hf_g-xQolAvqIudV79uPWcYErHkCXlIpzF/s200/0+choral.PNG" width="160" /></a><br />
Okay, one more title.... I've been promising my mathematics supervisor that I would read this one for over a month now, so let me add it to the list. It has a 5-star rating currently on Amazon and we've been slowly changing our Count Around the Circle routine to make use of choral counting, so it will likely be a good fit.<br />
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<span style="color: red;">Last year, I worked with teachers in my school district to write daily Number Sense routines for each grade level (gr.1-5) that included Count Around the Circle activities. We love those activities, but later came to discover the power of Choral Counting when we participated in a session while at NCTM San Diego. I knew we needed to somehow integrate our Count Around the Circle activities with Choral Counting to get the biggest benefit in building our students' number sense. As I read this book, the anecdotal examples written in each chapter helped me to better understand the purposeful planning that precedes the routine and the focused questioning that follows it. The chapters of this book helped bring together the routine I experienced at NCTM with words I could use to to explain the routine and its benefits to others. Looks like I'll be refining a few of our daily routines to incorporate Choral Counting more purposefully 😄</span></div>
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Always room for one more, right?! I am preparing a professional development session that I will be presenting at the CMC conference in Palm Springs in November and I came across this book and knew I HAD to read it as it seemed to be directly linked to my topic (and it was!). When the book arrived, I decided to flip through it before placing it on my ever growing stack of summer reads. Flipping through turned into skimming which, somehow, turned into an all out sit down and read from cover to cover. I finished the book in about 3 hours – with tons of little notes scribbled on a notepad as I moved from one meaningful sentence to the next. Below is a picture of the notes I was creating as I read; they will eventually be assembled into some useful form.<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidFK8Nh4YkTCLicCIzKFN96CrRrPdNLDFhgipvEc1q4FUs_nOil9QPJ8NqtRY0wHj_04m6LfFHPTDxnbwNhRGGRSIQX42SQoIlxljMe-HF1I0ZiYIAt0gtOw6L98KzarA7xG9dw6BabzGc/s1600/file.jpeg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1196" data-original-width="1600" height="148" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidFK8Nh4YkTCLicCIzKFN96CrRrPdNLDFhgipvEc1q4FUs_nOil9QPJ8NqtRY0wHj_04m6LfFHPTDxnbwNhRGGRSIQX42SQoIlxljMe-HF1I0ZiYIAt0gtOw6L98KzarA7xG9dw6BabzGc/s200/file.jpeg" width="200" /></a><br />
<span style="color: red;"><br /></span><span style="color: red;">This turned out to be one of those books that mirrored my own thoughts and ideas -- it made me wish that I had written it myself while simultaneously feeling delighted that someone did write it. </span><br />
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<span style="color: red;">There were SO MANY great ideas, and they were presented in a way that made every sentence accessible to all educators and in a sequence that just makes sense. The "take away value" of the content is tremendous – The book is a great resource filled with many ideas that can be applied to classrooms immediately; not just theory, but actionable ideas complete with planning templates and specific teacher moves for leading productive mathematical discussions in the classroom. </span><br />
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<span style="color: red;">My Big Take Away: Next year will be the 10th anniversary of CCSS-M. As the nation refocused its priorities away from simple "answer getting" to a focus on deep understanding, we guided students to discover a wide range of conceptual-based strategies. <b>Our next steps must now focus on helping students to (1) know how and when to apply </b></span><span style="color: red;"><b>those strategies, (2) understand which strategy will be most efficient and effective in a given situation, and (3) learn how to articulate their understandings so they can participate in the larger math dialogue.</b> </span><br />
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<span style="color: #134f5c; font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: x-large;">What's </span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: x-large;"><u>YOUR</u></span></span></h2>
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<span style="font-size: x-small;"><span style="color: #134f5c; font-family: "arial" , "helvetica" , sans-serif; font-size: x-large;"><span style="font-family: "courier new" , "courier" , monospace;"><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">rejuvenation</span><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"> </span></span>plan </span></span></h2>
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<span style="color: #134f5c; font-size: x-large;"><span style="font-family: "arial" , "helvetica" , sans-serif;">this summer?</span><span style="color: #0b5394; font-family: "arial" , "helvetica" , sans-serif;"> </span></span></h2>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgs68s4eT-oO-084wzcyIJ-fqst68ZoEpQ1zYIj7hxbZCc78RALeSwEwaFVKShfpweypQgEIEqE1EKKRgLBSD1NAkh6yI2UUcHw4-x_yoehcBnuZUky72CoTbyHPQdH_JYxeLUfUXIXKd7C/s1600/dawn+fun.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="378" data-original-width="383" height="390" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgs68s4eT-oO-084wzcyIJ-fqst68ZoEpQ1zYIj7hxbZCc78RALeSwEwaFVKShfpweypQgEIEqE1EKKRgLBSD1NAkh6yI2UUcHw4-x_yoehcBnuZUky72CoTbyHPQdH_JYxeLUfUXIXKd7C/s400/dawn+fun.PNG" width="400" /></a></div>
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<span style="font-size: medium;"><span style="font-family: inherit; font-size: large;">I know it looks like all I'm doing is reading this summer, </span></span><span style="font-family: inherit; font-size: medium;"><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif; font-size: large;">but don't </span></span><span style="font-family: inherit; font-size: medium;"><span style="font-size: large;">worry -- there will be a healthy mix of </span><span style="color: #990000; font-size: large;"><b>biking</b></span><span style="font-size: large;">, </span><span style="color: blue; font-size: large;"><b>kayaking</b></span><span style="font-size: large;">, </span><span style="color: orange; font-size: large;"><b>beach visits</b></span><span style="font-size: large;">, and a few </span><span style="color: #6aa84f; font-size: large;"><b>house projects</b></span><span style="font-size: large;"> <i><span style="color: #666666;">(truthfully, I find painting and organizing closets to be strangely satisfying).</span><span style="color: #999999;"> </span></i></span></span><br />
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<span style="font-family: inherit; font-size: small;"><i><span style="color: red; font-size: medium;"><br /></span></i></span><span style="font-family: inherit; font-size: small;"><span style="color: red; font-size: medium;"><u>Summer Rejuvenation Update - September 15</u></span></span><br />
<span style="font-family: inherit; font-size: small;"><i><span style="color: red; font-size: medium;">Summer has officially come to an end. School has been back in session for a couple of weeks now. I biked only once. Finished a couple of the house projects. And didn't meet the goal of "10 new kayaking sites before the summer ends". But my husband and I did explore 9 new kayaking sites (so close!) - some of which were simply amazing. We had two trips that were particularly spectacular: (1) The Pocomoke River where the tannic acid from the cypress trees turns the river into a beautiful rich coffee colored reflective lens creating the illusion that the cypress trees are both above and below you and (2) </span></i></span><i style="font-family: inherit;"><span style="color: red; font-size: medium;">Mallows Bay where we paddled over sunken WWI ships (see the cool Google Map photo below). We're not disheartened by our missed goal; we have simply decided to "extend summer" and plan to do our 10th new site as a fall trip to enjoy the cooler temperatures and to see the changing colors of the leaves over the water - heck, we may even keep going beyond the ten new sites for as long as the weather holds out. </span></i><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNUitJN20nAxaC41TAb0mNMxLjnBgijEi-PJqtccyXmEpjwPn0qXSd6Q8xVJBljFaSQS3ZgCDD_eH6NueMvmIpPLHbByvg1EYv3W095vOR4qyDjVVvNJDsPpKEvH-NfcCvTNzej8mU-ztp/s1600/Screen+Shot+2019-10-01+at+11.17.07+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1125" data-original-width="953" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNUitJN20nAxaC41TAb0mNMxLjnBgijEi-PJqtccyXmEpjwPn0qXSd6Q8xVJBljFaSQS3ZgCDD_eH6NueMvmIpPLHbByvg1EYv3W095vOR4qyDjVVvNJDsPpKEvH-NfcCvTNzej8mU-ztp/s640/Screen+Shot+2019-10-01+at+11.17.07+PM.png" width="542" /></a></div>
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<span style="font-size: medium;"><span style="font-family: "courier new" , "courier" , monospace; font-size: x-large;"><u><span style="font-family: "courier new" , "courier" , monospace;">Light</span><b> SUMMER READING</b></u></span></span></div>
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<span style="font-size: large;">I've included 6 short articles that may interest you. The article titles are hot-linked to the respective websites, so just click the title of the article that catches your eye!</span><br />
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<a href="https://www.weareteachers.com/unconventional-summer-professional-development-for-teachers/" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;" target="_blank"></a><a href="https://www.teachhub.com/top-12-ways-teachers-can-rock-summer-break" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="100" data-original-width="622" height="63" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiErS70-HwhMzWlrBXl7GLyIW-ezmkXIJuy742FgTFpJpP3TDHzwBjjT0wtdljTjfmFnlV1SfPrU15TFfHHnHEhfOaStKvqDg5fKsLWP0eeKE-ne-Yo0AQTrYVxz6JDDwzOKwXvBcutBMkl/s400/rock.PNG" width="400" /></a></div>
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<a href="https://www.weareteachers.com/unconventional-summer-professional-development-for-teachers/" style="clear: left; display: inline !important; margin-bottom: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="286" data-original-width="760" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPP4DGyNVkxBDGDUYJqZUJek1KQiN8O5vkZ8EHH50Z0DfynzSLtuhPfmU8dKXN5bcoXjxjfp8pKnmxHZvlYPbXqMxDmQMTyWKZjTBYHeHZl753D9vHehwrPweb1Dy9H_Xt4laoLbvVJmgC/s400/PD+ideas.PNG" width="400" /></a></div>
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<a href="https://www.weareteachers.com/teacher-bored-during-summer/" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;" target="_blank"></a><a href="https://www.coolcatteacher.com/e330/" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="195" data-original-width="715" height="106" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiu2MEPQ0QK_QHahE1_N16zsGW559LAeNFSpKkiMeWpkchFZC55o8b916fFEMOhn6UABt6o-HEbe4H81-caOwABM6AdHkD_j0CwpJWRSgOwtf5DR5SvYheLVvNsufxEnEPzWhSTMZBj1dsl/s400/5+things.PNG" width="400" /></a></div>
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<a href="https://www.weareteachers.com/teacher-bored-during-summer/" style="clear: left; display: inline !important; margin-bottom: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="273" data-original-width="759" height="143" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhL8wvOTndW2MTzoBCB9JxN6SG44W6BdKw1KKGK1DNP-kP6K_qNtcL7C_owdPXG9HbuUmSO7UyRbx8XqmOmYyyFUx_kDOlp2JOUmGMaW2OqSPK77IbzWvLMM1LRp_lrUfOi5m-mRwjY84qZ/s400/summer+ideas.PNG" width="400" /></a></div>
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<a href="https://howweteach.com/10-books-growing-my-math-teaching-practice/" target="_blank"><img border="0" data-original-height="75" data-original-width="640" height="43" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAmHAQihyphenhyphenYGOJtdBVJrXsdgQY2lk6_uj3tVxgg958YCucEg4xRxjl1O7TF1lV9AyvVRxVVZGTL3Xbuuk8SvJkud_tXwb0hVakPLrWhXpJcXQAqLhED-wd4h3FYhBteFrRSw_RQDw7sJGt_/s400/book3.PNG" width="400" /></a></div>
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<br />:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comtag:blogger.com,1999:blog-543907520077188162.post-83284172155022406292019-05-03T19:41:00.000-07:002019-10-03T10:00:35.538-07:00Using Card Games to Practice Mathematics<div class="separator" style="clear: both; text-align: center;">
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<b style="color: #444444;"><span style="font-size: x-large;">Raise your hand if you think </span></b><br />
<span style="color: #444444; font-family: , sans-serif;"><b style="background-color: white;"><span style="font-size: x-large;">LEARNING SHOULD BE FUN!</span><span style="font-size: large;"> </span></b></span></div>
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: xx-small;">Image source: Pixabay</span></td></tr>
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<span style="background-color: white; font-family: , sans-serif; font-size: 16px;"><i><span style="color: #444444;">When you’re having fun, you </span><b><span style="color: red;">boost your positive emotions</span></b><span style="color: #444444;"> which </span><b><span style="color: blue;">activate the learning centers in your brain</span></b><span style="color: #444444;">. That means you are </span><b><span style="color: #6aa84f;">connecting with more of the brain power</span></b><span style="color: #444444;"> you have and hence you’ll be more alert in noticing new things and learning through them. When you’re having fun, you’re also much </span><b><span style="color: orange;">more creative and innovative</span></b></i><span style="color: #444444;"><i> which means you’ll be able to engage with whatever you’re learning by coming up with new ideas as well as challenging things. </i> </span></span></blockquote>
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<span style="background-color: white;"><span style="font-family: , sans-serif; font-size: 16px;"><span style="color: #444444;">-</span></span><a href="https://happyologist.co.uk/growth/why-learning-through-play-is-effective-fun/" style="text-align: right;" target="_blank">Susanna Newsonen</a><span style="color: #444444; font-family: , sans-serif; text-align: right;"> </span></span></blockquote>
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<span style="font-size: small;"><br /></span><span style="font-size: x-large;"><b>Deal Me In!</b></span></div>
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<span style="font-size: x-large;"><span style="color: red;"><span style="color: magenta;">P</span><span style="color: blue;">L</span><span style="color: red;">A</span><span style="background-color: white; color: #6aa84f;">Y</span><span style="color: #674ea7;">I</span><span style="color: orange;">N</span><span style="color: blue;">G</span><span style="color: red;"> </span><span style="color: red;">C</span></span><span style="color: blue;">A</span><span style="color: #6aa84f;">R</span><span style="color: magenta;">D</span></span><span style="font-size: x-large;"> </span><span style="color: #e69138; font-size: x-large;">A</span><span style="color: #674ea7; font-size: x-large;">C</span><span style="color: red; font-size: x-large;">T</span><span style="color: magenta; font-size: x-large;">I</span><span style="color: blue; font-size: x-large;">V</span><span style="color: red; font-size: x-large;">I</span><span style="color: #741b47; font-size: x-large;">T</span><span style="color: #e69138; font-size: x-large;">I</span><span style="color: #6aa84f; font-size: x-large;">E</span><span style="color: red; font-size: x-large;">S</span><span style="font-size: x-large;"> </span><span style="font-size: x-large;">that</span><span style="font-size: x-large;"> </span><span style="color: blue; font-size: x-large;">T</span><span style="color: #e69138; font-size: x-large;">E</span><span style="color: red; font-size: x-large;">A</span><span style="color: #6aa84f; font-size: x-large;">C</span><span style="color: magenta; font-size: x-large;">H</span></div>
<span style="font-size: small;"><br /></span>
<span style="font-size: small;">Check out these videos to learn a wide range of card games designed to reinforce math standards in the classroom. Remember that older students still need practice with foundational skills, so be sure to also consider the games highlighted below that are designed around standards from previous grade levels. Click on each image to view the video directions. The game boards that are shown in some of the videos can be downloaded by clicking the game board link at the bottom of this page.</span><br />
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Have Fun!</h2>
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LINKS to GAME BOARD Templates:<br />
<ul>
<li><a href="https://drive.google.com/open?id=1EScd1xrRs4br2ZJON-rjiIm5b2cXOtOv" target="_blank">Close Call 100</a></li>
<li><a href="https://drive.google.com/open?id=1_ZIkddlzTkMr2X2-7y2yPDpdp9THx-je" target="_blank">Get to Zero 10-Frame</a></li>
<li><a href="https://drive.google.com/open?id=15BxHT0LTl22O61JTqg5w2qrMn0lYgIxM" target="_blank">Four in a Row - Products</a></li>
<li><a href="https://drive.google.com/open?id=1bARtulz45A5zX_u1-wISWLKVy5Udvftf" target="_blank">Multi-Digit Multiplying Madness</a></li>
</ul>
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<span style="font-size: x-large;">
Got Pics?</span></h2>
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Got pictures of your class playing these math fluency card games?<br />Share them and I'll post them here!</h3>
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</style>:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comtag:blogger.com,1999:blog-543907520077188162.post-37143177141839112742019-04-01T06:14:00.000-07:002019-04-18T06:07:54.789-07:00Turn Up Achievement with Practice Turns & Feedback<div class="separator" style="clear: both; text-align: center;">
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In the March edition, I mentioned that I was reading the book <i>Great Instruction Great Achievement for Students with Disabilities </i>by John L. O'Connor. I was surprised to find that so much of the book spoke to me. Most of the teachers with whom I work are not special educators (although nearly all of them have students with disabilities in their classrooms) and, despite the title of the book, I found the strategies to be good for ALL LEARNERS, not just those with disabilities.<br />
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The author poses the question, "Can we make a list of<b> instructional practices</b> that if implemented effectively, would<b> increase the achievement of a large majority of students</b>?" He makes his list and goes on to make a compelling case for the first item listed: <span style="color: purple; font-size: large;"><b>Drastically increase practice turns and feedback</b></span>. I have always known that these are important, but something about this section of the book really spoke to me on a new level and has impacted both my thinking and my practice.<br />
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<span style="font-size: large;"><b>Making The Case<br />FOR INCREASED PRACTICE TURNS & FEEDBACK</b></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgabhRp09Ej5rd6kg-qtq9WIQAKWY1ATEpmtZz0eJebOcJswf4PbhzC3YPXsmbnIctAf5mQGA_ESPET5j9sRFzBWRKISlWoA3NMY0Q0TdHllyH7L1ivoua8ZUjwngB6mlw0Yml5b4xmApul/s1600/5935538711_5b6c64c8e6_b.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="768" data-original-width="1024" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgabhRp09Ej5rd6kg-qtq9WIQAKWY1ATEpmtZz0eJebOcJswf4PbhzC3YPXsmbnIctAf5mQGA_ESPET5j9sRFzBWRKISlWoA3NMY0Q0TdHllyH7L1ivoua8ZUjwngB6mlw0Yml5b4xmApul/s320/5935538711_5b6c64c8e6_b.jpg" width="320" /></a>After reading this section of the book, I looked around and began noticing just how important practice turns and feedback really were in terms of learning -- and I don't just mean "school learning" but all learning! Think about it... we learn by making attempts and receiving feedback. When my trio of teenagers was learning to drive, we often went out together to practice (I have triplets, so all three of them got their learner's permit at the same time!). When we were practicing parallel parking, I made sure that they each had many many practice turns behind the wheel. They <b><u>each</u></b> needed practice turns <span style="font-family: "calibri" , sans-serif; font-size: 13.5pt; line-height: 107%;">– they <u style="font-weight: bold;">each deserved feedback</u> that was constructive and specific</span>. After all, <b><span style="font-size: large;">you can't learn to parallel park by simply sitting in the car while someone else practices</span></b>. With each practice turn, they each received plenty of feedback from multiple sources: </div>
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<li>THE CAR: Did the car do what they expected? </li>
<li>THE CURB: Did they successfully get the car between the orange cones without hitting the curb? </li>
<li>THEIR MOM: And, of course, they also received feedback from me as I gasped, clenched, and silently made noises that weren't so silent! </li>
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The feedback they received, played a role in their next practice attempt until each of them was finally able to successfully parallel park. </div>
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We see the importance of practice turns and feedback in the realms of athletics, academics, the fine arts, and in any other field that includes demonstration of skill and knowledge. If you ask virtually anyone how you get better at playing the piano (or blocking a tackle, solving equations, or singing), the answer is invariably, "practice practice practice". Any teacher, coach, professor, or construction worker will tell you that you get better at a skill by doing that skill. <span style="font-size: x-small;">(O'Connor, p.26) </span></blockquote>
In the mathematics classroom, this does not mean going back to the days of long, repetitive worksheets with 57 math equations! Think about the skills that we want students to be able to do? If we want them to develop skill in reasoning with numbers and articulating their ideas, then we need to offer them practice turns that require reasoning and involve them in discussions where they articulate their ideas about their reasoning. We'll talk about some specific classroom strategies to increase practice turns and feedback in a minute, but first, let's talk about the importance that <i>feedback</i> plays in the learning process.<br />
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<span style="font-size: large;"><b>Practice doesn't do much if we don't receive feedback about that practice</b></span>. Imagine that I was trying to learn sign language. I practice learning words and constructing sentences, but I never receive any feedback about whether I am signing the words correctly or putting the words together in a way that makes sense – I need feedback. I need to use that language with someone who understands sign language to see if they can understand me. I need to participate in a conversation to see if I understand them. If they look confused or laugh, well, that's feedback. Ask me about the summer I was a lifeguard at a summer camp for the deaf and had twenty teenage boys rolling with laughter (unintentionally!) because I confused two signs that are similar as I (inappropriately) welcomed them to camp....<span style="font-size: large;"> I received feedback that day and knew I needed to adjust. </span>I needed more practice (a lot of it!), and I needed to be mindful of the feedback I received so I could make the appropriate adjustments that would eventually allow me to successfully communicate with the campers that summer.<br />
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<span style="font-size: large; font-weight: bold;">When students struggle, they need MORE </span><span style="font-size: large;">practice turns and more feedback than those who are not struggling,</span><span style="font-size: large; font-weight: bold;"> but often get less</span>. Let's go back to my summer camp experience: I was not very skilled at signing, so the other lifeguard was the one who communicated with the campers most often. That OTHER lifeguard got a lot of practice; I shied away from signing with the campers and didn't get much opportunity to practice. Those who were better at it did most of the "talking" and received most of the practice turns. In reality, I needed even more practice than the other lifeguard, but actually got much less. The same thing happens in our classrooms. Mr. O'Connor explains it better than I can possibly paraphrase, so I'll quote him instead:<br />
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With twenty-five or more students in many classrooms, it is hard "to see" these students [the ones who need more practice turns]. They become invisible. The students don't answer questions. They don't volunteer to lead groups. They don't get engaged in those healthy discussions or debates in class. They don't disagree when a student or teacher says something that doesn't make sense, and they certainly don't ask for help. When the students are assigned independent work, they are masters at pretending they are engaged, but their apparent engagement is an act, a survival mechanism. They often don't understand the work and they don't want the other students or the teacher to understand that they don't understand. These students are invisible and they take very few practice turns and receive very little feedback. The youngsters who need the greatest number of practice turns take the fewest. (p.28)</blockquote>
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<span style="font-size: large;"><b>An Action Plan<br />TO INCREASE PRACTICE TURNS & FEEDBACK</b></span><span style="font-size: large;"><b><br /></b></span></div>
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The truth of the matter is, in most classrooms, <i>the teacher</i> is the one who gets the most practice turns – I think we can agree that the teacher is the one who needs the least amount of practice, right? So let's work to remedy who is getting the most practice turns....<br />
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Let's consider a few ideas about how we can design our lessons and structure our classroom practices <b>to facilitate a drastic increase in practice turns and feedback</b>:</div>
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Every student in your classroom should be offered many (many!) practice turns every day. These practice turns are a key element of all learning. Along with increased practice turns, we MUST offer feedback that is timely, specific, and actionable, as well. Imagine that Tom practices his golf swing for 3 hours every day but never receives any feedback as to whether he is doing it correctly. How will he know if his swing is effective? He won't. If he is practicing his swing with a golf ball on a tee, the golf ball itself can provide feedback: Did the ball leave the tee? Did the ball go where he intended? How far did the ball travel? If Tom has a coach offering additional feedback, the coach may recommend a different grip on the club, suggest that he follow-through on the swing, or perhaps explain how a certain club such as the putter or driver works better in specific situations. For Tom to just go out and swing the club without receiving feedback will certainly not make Tom a better golfer. In fact, it may even lead to some bad golfing habits and beliefs about how to swing a golf club that are counter-productive and difficult to undo later down the road.<br />
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As you think about instruction in your classroom, ask yourself if you provide every student with an abundance of practice turns -- remember, EACH STUDENT must have many opportunities to swing the club himself and receive feedback about his swing. If the teacher just demonstrates the swing without providing many practice turns for the learner, the only one getting ample practice is the teacher! Our job is not to swing the club – our job is to provide feedback to our students as THEY swing the club. Our students will experience greater levels of achievement as WE become more mindful and purposeful with <span style="color: #38761d; font-size: large;">"<b>drastically increasing the number of practice turns and feedback</b>".</span></div>
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:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comtag:blogger.com,1999:blog-543907520077188162.post-82967236360934028382019-03-01T01:00:00.000-08:002019-09-04T04:43:27.402-07:00Estimation<div style="text-align: center;">
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<span style="color: #cc0000; font-size: x-large;"><b>UNDER</b>ESTIMATING<span style="font-weight: bold;"> </span>the <b>IMPORTANCE OF ESTIMATION</b></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLsjE3m6_P-NztaE7fCkOIjWzuVo12bs_RO4ZRCGciPDTRwr6B87N1wTJKgxTZ5YoNeUMaSnse6eUQUifnfNm1f6BNkKSuQSdKdal-RTwf_YkYDpVoJMZse9whHssv9T2nPqYk4fvCp9qN/s1600/estimate+quotes.PNG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="431" data-original-width="559" height="308" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLsjE3m6_P-NztaE7fCkOIjWzuVo12bs_RO4ZRCGciPDTRwr6B87N1wTJKgxTZ5YoNeUMaSnse6eUQUifnfNm1f6BNkKSuQSdKdal-RTwf_YkYDpVoJMZse9whHssv9T2nPqYk4fvCp9qN/s400/estimate+quotes.PNG" width="400" /></a>It probably won't surprise you to learn that in daily life <span style="color: #134f5c;"><b>most people typically think in terms of estimations more often than exact values</b>. </span>Despite what our math classes may have led us to believe, exact solutions are not necessary in every mathematical situation. When I go to the grocery store, I know they will expect me to pay the exact amount for my groceries when I get to the register, but do I really need to know the <i>precise</i> cost of each item as I shop to have a sense of whether the $50 in my pocket will be enough? Every day, I drive to and from several schools, but I have no idea of the exact number of miles between the schools, and yet, even without a precise measure of the mileage, I am still able to estimate what time I should leave to arrive at the next school on time (day of the week, construction, weather, and a number of other factors will play into my estimated driving time, anyway!). You get the idea - at times, exact values are necessary, but more often than not, an estimate serves the purpose just fine. </div>
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Let's establish a working definition of estimation: <b>An e</b><b>stimation is a rough calculation of value based on incomplete or inexact data. The goal of estimating it to get an answer that is close enough in magnitude to the exact solution to be useful</b> (context is an essential component for defining "close enough"). </div>
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I'm just going to lay it out there: <b><span style="color: #444444;">Our students are not good at estimating </span></b>(and many adults aren't that great at it either!). Because of the way math has been taught for generations, <span style="color: #a64d79;">we are much better at calculations than estimations</span>. Despite estimation being a pervasive part of our daily lives, we just haven't given our students enough structured experience with estimation strategies. And now, with a calculation device in the back pocket of nearly every person around, the <b>ability to determine the "reasonableness"</b> of the number on our phone's screen is <u style="font-weight: bold;">more important than ever</u><span style="font-weight: bold;">. Yes, MORE important than ever </span><i>[That statement may seem backwards at first glance, but pause and take a moment to consider the truth behind it].</i> Push a button out of order and you may find yourself leaving a $2 tip on a $95 dinner bill and you didn't give it a second thought because the calculator app on your phone showed $1.71 when you typed in .018x95 (see the problem?!) Good for your wallet; bad for the poor server who refilled your water glass all night long.</div>
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In the math classroom, <span style="color: #990000;"><b>the critical step of thinking about an estimated solution prior to each calculation, is often neglected</b></span> -- and when the skill of estimation <i><b>is</b></i> addressed, it is often reduced to an instructional unit that lasts for just a few days and focuses solely on rounding. A few years back, I was proctoring a state test. The students were asked to <i>estimate</i> the most reasonable solution to a multi-digit addition equation. As I watched a student answer the question, I noticed that he solved the problem to get a precise solution and then rounded his precise solution to a less precise solution in order to answer the estimation question. Hmmm??? The student must have been asking himself, "What was the point of that?" As I watched the student, I asked myself, "<i>How can I teach my students a range of estimation strategies and to understand the purpose of each one in a way that is useful, authentic, and purposeful?</i>" </div>
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ESTIMATION IS SO MUCH MORE than simple rounding. And it is definitely not intended to occur <i>after</i> a precise calculation is completed in order to find the correct multiple choice answer on a test. So let's take a closer look at what we can do in our classrooms to develop these essential skills more fully with our students.</div>
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There are some very specific estimation strategies that we can teach. You may not know about them because, like me, you may not have been taught them, so let's continue learning together about a few different estimation strategies. Unlike traditional algorithms, estimation strategies go beyond procedural applications and require us to apply mathematical thinking in flexible ways. This type of adaptive problem solving really is the fundamental goal of all mathematics.<br />
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Below are FOUR different types of Estimation Strategies. <b>Did we even know estimation had types!? </b>There are probably more than just these four, each with its own nuance, but this list should get us started as we begin to consider how to <b>be more purposeful</b> in our teaching of estimation to students:</div>
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~ Putting Estimation Strategies Into Practice in Our Classrooms ~</h3>
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Remember that question I was asking myself as I watched my students take the state math test?</div>
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<b><span style="color: red; font-size: large;">How can I teach my students estimation skills </span></b></div>
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<b><span style="color: red; font-size: large;">in a way that is useful, authentic, and purposeful?</span> </b></div>
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Here's the answer I came up with....</div>
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<li><span style="font-family: "times" , "times new roman" , serif;"><b><span style="color: #674ea7; font-size: large;">Make estimation a part of the DAILY routine</span> </b>and not just a unit of instruction that occurs as an isolated event -- consistently ask students to estimate a reasonable answer BEFORE any expectation that they calculate a precise solution.</span></li>
<li><span style="font-family: "times" , "times new roman" , serif;"><span style="color: #674ea7; font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif; font-size: large;"><b>Purposefully</b> (and regularly)<b> teach the various types of estimation strategies</b></span> and help students to understand when to use each type. </span></li>
<li><span style="font-family: "times" , "times new roman" , serif;"><b><span style="color: #674ea7; font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif; font-size: large;">Use estimation activities to build number sense</span></b> -- Number sense is the foundation of all mathematical thinking. <b>Estimation builds greater number sense and greater number sense leads to better estimates. </b>Check out these sites for some terrific Estimation activities: </span></li>
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<li><span style="font-family: "times" , "times new roman" , serif;">Steve Wyborney's "<a href="https://www.stevewyborney.com/?p=1483" target="_blank">Estimation Clipboard</a>" and "<a href="https://www.stevewyborney.com/?p=1744" target="_blank">Esti-Mysteries</a>" </span></li>
<li><span style="font-family: "times" , "times new roman" , serif;">Andrew Stadel's "<a href="http://www.estimation180.com/" target="_blank">Estimation 180</a>" </span></li>
<li><span style="font-family: "times" , "times new roman" , serif;">Graham Fletcher's "<a href="https://gfletchy.com/3-act-lessons/" target="_blank">3-Act Task</a>" geared toward elementary </span></li>
<li><span style="font-family: "times" , "times new roman" , serif;">Dan Meyer's "<a href="http://blog.mrmeyer.com/category/3acts/" target="_blank">3-Act Tasks</a>" geared more to secondary math</span></li>
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<li><span style="font-family: "times" , "times new roman" , serif;"><b><span style="color: #674ea7; font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif; font-size: large;">Accept estimated solutions as the <u>final</u> solution when appropriate</span></b> -- try to keep in mind that, in the real world outside of the math classroom, an estimated value is often enough to meet the intended needs and an exact solution may be unnecessary - the purpose and context of the situation should be considered.</span></li>
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<span style="color: #b45f06;">ONE OF MY FAVORITES:</span> The "Goldilocks" Estimation strategy</h4>
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Want even more? Try out the Goldilocks estimation strategy that I learned while attending one of Dan Meyer's conference sessions. The strategy encourages mathematical risk-taking and helps students develop their estimation abilities even further. The basics of this routine go something like this:</div>
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<li>Present an estimation opportunity</li>
<li>Ask students, "What estimate is definitely too large? When you look at this jar of pennies, what number do you know is too many to possibly fit in the jar?" --- this gives an entry point for all since 1 million is, in fact, an acceptable "too large" response for the number of pennies in the jar. </li>
<li>Write down all of the "too large" ideas on a list as you encourage students to take bigger risks by estimating numbers that are still too large but perhaps closer to the actual number of pennies in the jar.</li>
<li>Through collective agreement, see which "too large" estimate is the LOWEST value that your students can agree is "too large" --- let's say that everyone in room agrees that 35 is too large but several students believe that it could be as low as 30. Since all of the student agreed on 35 as definitely being too large, you have established a ceiling value of 35.</li>
<li>Next ask your students for a value that would definitely be "too low" --- again, anyone can enter the conversation because zero is obviously "too low" and would be an acceptable response.</li>
<li>This time, come to a group decision about which number from the list represents the HIGHEST number that everyone can agree is too low --- imagine your students going back and forth between the 14 and the 18 that is listed on the board. Some think that 18 is too low, but all believe that 14 is too low, so go with the 14 that everyone agrees is too low. The number 14 is now the group's lowest possible value, the floor value. </li>
<li>We have now reduced an infinite set of numbers to a discreet set of values with everyone in the class agreeing that the "just right" estimate must be somewhere between 14 and 35.</li>
<li>At this point, ask students to individually determine their "just right" estimate --- remind them that they have agreed that it is a number between 14 and 35. If someone does not believe the "just right" amount is within this range, the range needs to be adjusted to fit the number values that EVERYONE can agree upon. </li>
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<span style="font-size: large;"><span style="color: #cc0000;"><b style="background-color: #ffe599;">Think about what just happened in your classroom:</b><span style="background-color: white;"> </span></span></span><br />
<span style="font-size: large;"><span style="background-color: white;"><span style="color: #990000;">✅ </span></span></span><span style="background-color: white; color: #990000; font-size: large;">Students felt safe to enter the conversation because early steps are manageable for all</span><br />
<span style="font-size: large;"><span style="background-color: white;"><span style="color: #990000;">✅ </span></span></span><span style="background-color: white; color: #38761d; font-size: large;">S</span><span style="background-color: white; color: #38761d; font-size: large;">tudents worked together to crowd-source a list of possible values</span><br />
<span style="font-size: large;"><span style="background-color: white;"><span style="color: #990000;">✅ </span></span></span><span style="background-color: white; color: #b45f06; font-size: large;">Students crafted justifications for their ideas and listened to the ideas of others</span><br />
<span style="font-size: large;"><span style="background-color: white;"><span style="color: #990000;">✅</span></span></span><span style="color: #0b5394; font-size: large;"> Students made a final independent estimate based on data (not just a guess!)</span><br />
<span style="font-size: large;"><span style="background-color: white;"><span style="color: #990000;">✅</span><span style="color: #990000;"> </span><span style="color: #741b47;"><b><span style="color: #cc0000;">Everyone in the room just became a little better at estimating!</span><span style="color: #741b47;"> </span></b></span></span></span></div>
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:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comtag:blogger.com,1999:blog-543907520077188162.post-7385137772023484262019-02-08T20:57:00.001-08:002019-03-01T20:45:29.067-08:00Anchor Charts<h2 style="text-align: center;">
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The 5 Tenets of ANCHOR CHARTS</h2>
<span style="font-size: large;">Anchor charts are designed to serve an important purpose and, no, it's not to cover cracks in your walls or even to "add a splash of color" to your classroom - no matter what the walls of the amazing Pinterest-clad classroom down the hall wants us to believe, anchor charts are intended to support learning ➕➖✖➗</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxw2GVO_4CVnNihHDGNPvpvqzeYE47fmlmvncqXyMymd2Ok1A2E-kfDwaJ_WIEjvBex9Ynpw1yVJ8kYCXeGdfsNNRHc1y3E7AX0RKzIk4-n3cEtCcUdGNr69uPnsTQZtK12IB_gOyb_voJ/s1600/Screen+Shot+2019-02-08+at+2.47.30+PM.png" imageanchor="1" style="font-size: xx-large; font-weight: lighter;"><img border="0" height="104" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxw2GVO_4CVnNihHDGNPvpvqzeYE47fmlmvncqXyMymd2Ok1A2E-kfDwaJ_WIEjvBex9Ynpw1yVJ8kYCXeGdfsNNRHc1y3E7AX0RKzIk4-n3cEtCcUdGNr69uPnsTQZtK12IB_gOyb_voJ/s640/Screen+Shot+2019-02-08+at+2.47.30+PM.png" width="640" /></a></div>
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<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">Late Thursday night, I sent out an email to the PK-5 math teachers in our school district asking them to send me a few mathematics anchor chart examples that they currently have in their classroom so I could share them with you – I awoke Friday morning to nearly two dozen replies in my inbox! Every anchor chart below is hanging in one of our CCPS classrooms. THANK YOU... keep 'em coming.</span><br />
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<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">An anchor chart is a tool that is used to support student learning in a wide range of areas: Reading, Writing, Math, Self-Regulation of Behaviors, Classroom Routines, Etc... </span></div>
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<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">We don't need to see the research data to know that students must see new concepts more than once before that information is stored in long-term memory (I'm thinking back to when my children were learning to drive and remembering how many times – <i>oh so many times</i> – I needed to remind them to check the cross traffic before proceeding across an intersection as the light turned green to avoid being hit by red-light runners). We don't need the research, but there is plenty of it that suggests that students (of all ages and ability levels) need multiple views of new information before the information is stored in long-term memory - 17 times to be exact!</span></div>
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<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">In mathematics, there are several types of anchor charts that can be categorized by their purpose:</span></div>
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<li><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><b><span style="color: blue;">Procedural anchor charts </span></b>reinforce classroom routines and procedures. You might find a procedural anchor chart near the technology center outlining the procedure for getting and returning the laptops to the cart. Another may be hanging that helps students know how to discuss and debate mathematics with classmates during a group discussion. Procedural anchor charts typically hang on the walls all year long and are removed and stored for use next year.</span></li>
<li><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><b><span style="color: blue;">Informational anchor charts </span></b>provide students with information about the topic. Many of the anchor charts that were sent to me today fall into this category. Look for the one anchoring the ideas about What is a fact family? or the one that helps students use correct vocabulary when discussing division.</span></li>
<li><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><b>Process anchor charts</b> </span>walk students through a wide variety of processes. The anchor chart that helps students remember how to find perimeter would fall into this category as would the one that teaches the student the process for measuring length with a ruler or the kindergarten chart that shows them to determine "how many more?" when comparing to trains of snap cubes. </span></li>
<li><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><b style="background-color: white;"><span style="color: blue;">Strategy anchor charts</span><span style="color: magenta;"> </span></b>support students as they work to solve problems that require a strategy - much of the shift in mathematics education in the past decade is related to strategy, so we are likely to see a lot of these on the walls to support math learning. Examples of strategy anchor charts from the collection above include the one that shows how to find the the product of basic multiplication facts, beyond simply memorizing all of the facts. Also, the one showing various methods for counting was created in a PreK classroom to support our youngest learners and did you also notice the one that supports strategies for adding large numbers created with upper elementary students? </span></li>
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<b style="color: #990000;"><span style="font-size: x-large;">💡</span>Check out this EXCEPTIONAL IDEA</b><b> from Ms. Lee at CES: </b><span style="color: #666666;">(added 2/27/19)</span><span style="color: #666666;"> </span></div>
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Between ELA and math, <b>organization of all the anchor charts can become quite the challenge</b>. I recently visited Ms. Lee's 5th grade classroom; she has a self-contained class and teaches math, ELA, and all the rest! When I entered her room, I saw anchor charts that reflected current learning on the walls, <b>but her walls were not covered in them</b> as I have seen in some classrooms -- <b><span style="color: blue;">s</span></b><span style="color: blue;"><b>he shared her brilliant strategy with me</b></span>: After they make an anchor chart, she snaps a picture of it with her smart phone. When it is time to make a new anchor chart, the older one comes down and <b style="text-decoration-line: underline;">a picture of the anchor chart is added to each group's Anchor Chart Resource Binder</b> that is organized by content area with labeled tabs. The binder sits right in the center of each group's table for all students in the group to access whenever they want it or need it. <b><span style="color: #990000;">Brilliant!</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3f4eD6Nf85eM1rArzu3bFPVLnYS0HXVi8jzz8p3M7yAQsGeqZOot-C1FGuNSxL4XzG4rWY60DOyU4N23ejPe4rOYxUmyjaMQxms5pHK14XNShgPZCU5N-Bo6T6_b6B7hCe4rZZYEO0LdG/s1600/IMG_7400.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3f4eD6Nf85eM1rArzu3bFPVLnYS0HXVi8jzz8p3M7yAQsGeqZOot-C1FGuNSxL4XzG4rWY60DOyU4N23ejPe4rOYxUmyjaMQxms5pHK14XNShgPZCU5N-Bo6T6_b6B7hCe4rZZYEO0LdG/s640/IMG_7400.jpg" width="640" /></a></div>
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<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">Want to read more about anchor charts? Try these links:</span></div>
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<li><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><a href="http://www.literacyworldwide.org/docs/default-source/member-benefits/e-ssentials/ila-e-ssentials-8065.pdf" target="_blank"><span id="goog_1181364272"></span>Imitate and Innovate Anchor Charts</a><span id="goog_1181364273"></span></span></li>
<li><a href="https://www.k-5mathteachingresources.com/math-anchor-charts.html" target="_blank"><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">Math Anchor Charts from K-5 Math</span></a></li>
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:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comtag:blogger.com,1999:blog-543907520077188162.post-83800056551642973752019-01-08T18:39:00.001-08:002019-01-10T18:09:56.966-08:00Coherence Mapping from AchieveTheCore.org<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIhC-TBEXklJ9WgVGOKetOy2n_HyDCzUzs3YQf885p91-6eN2X8KD3hINNPZmSj3kqCP3icdyryKskdfsXCa6b-evYJUQ2Q2fieVseiLi2g5mD8Ya-7yZ9AJR-qgP8Em2hEGOXF2W7pq8l/s1600/Screen+Shot+2019-01-08+at+8.50.03+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="242" data-original-width="953" height="162" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIhC-TBEXklJ9WgVGOKetOy2n_HyDCzUzs3YQf885p91-6eN2X8KD3hINNPZmSj3kqCP3icdyryKskdfsXCa6b-evYJUQ2Q2fieVseiLi2g5mD8Ya-7yZ9AJR-qgP8Em2hEGOXF2W7pq8l/s640/Screen+Shot+2019-01-08+at+8.50.03+PM.png" width="640" /></a></div>
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Before the holiday season, our Special Education department hosted a 3-day professional development event. During that event, I presented a session that helped teachers learn to use <i>Coherence Maps</i> to help with instructional planning – <b>especially when students were struggling due to gaps in foundational understandings.</b> </div>
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These <i>Coherence Maps</i> were created by three of the authors who worked on the Math and ELA Common Core Standards. After writing the Common Core Standards, they formed a group called Student Achievement Partners (SAP) for the purpose of "addressing the need for practical, evidence-based support for teachers and school leaders." SAP maintains a website at <a href="http://achievethecore.org/">AchieveTheCore.org</a> and is committed to sharing standards-aligned resources freely with educators. </div>
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After I presented my sessions on using the Coherence Maps, many of the participants found the information to be so useful that they requested that I find a way to share the information with a wider audience. This special edition of MathSnack is my way of sharing - as promised!</div>
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In the video below, I'll share how and why you should access these <i>Coherence Maps</i> 🎥</div>
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<a href="https://youtu.be/OyoL1lLxQac" target="_blank"><img border="0" data-original-height="498" data-original-width="664" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5BxQlflA5Lz_8iSigua__8-uC7DVeSiZxag7IirU1IAsKvKouIeFPr-k70_Zp2GDpnTvYYY4ekvuZFWlixHh9Blmog86Qf4PqMSXkTAb3Iab2g1M1m8mzl1OoOea-PeTMNUfGF1jbRuRC/s640/Screen+Shot+2019-01-08+at+9.58.41+PM.png" width="640" /></a></div>
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<i><span style="font-size: x-small;">*Skip ahead to 4:04 to see just the information about Coherence Maps</span></i></div>
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<u>Video Timestamp</u><br />
0:00-4:03 Sample Video Lessons by grade and content<br />
4:04-18:43 How to access the Coherence Maps<br />
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:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comtag:blogger.com,1999:blog-543907520077188162.post-12030320434758155202018-12-05T11:39:00.001-08:002018-12-05T18:43:04.951-08:00Manipulatives to Build and Model Understanding<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgN95QyVlezpjmqGzofFCppYYL-L_psbcTdx6TQPY3jBlC_swY2EFyx9VurtJDBfIqMZQUndSA4vTC-l2dYHv2q_jCXU_Tbd8_LH2wiphXGGRG2U3bk2PkXR1cyUNQISMb4sWYOlsFhbWri/s1600/Screen+Shot+2018-11-28+at+8.43.55+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="549" data-original-width="1224" height="286" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgN95QyVlezpjmqGzofFCppYYL-L_psbcTdx6TQPY3jBlC_swY2EFyx9VurtJDBfIqMZQUndSA4vTC-l2dYHv2q_jCXU_Tbd8_LH2wiphXGGRG2U3bk2PkXR1cyUNQISMb4sWYOlsFhbWri/s640/Screen+Shot+2018-11-28+at+8.43.55+PM.png" width="640" /></a></div>
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<span style="background-color: white; color: #444444;">Hello, Math Friends ⛄, so glad you are here!</span><br />
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<span style="background-color: white; color: #444444;">I was looking over the Standards that we have coming up within the next month or so and thought it might be a great idea to include specific ways that you can use manipulatives to help your students BUILD their conceptual understanding and MODEL their understanding of one of the Standards in the Module. Remember, this is just <u>one</u> manipulative paired with <u>one</u> Standard for each of the grade levels -- there are so many ways to make learning concrete by <b>using manipulatives to help your students build and model their understanding -- it is both CRITICAL and endless in its possibilities!<i> </i></b><i>(be sure to check out using <b>Cuisenaire Rods</b> in the <a href="http://mathsnack.blogspot.com/2018/11/cuisenaire-rods.html" target="_blank">November edition of <b>MathSnack</b></a>).</i></span><br />
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...and, you won't want to miss the <i>Math in Practice</i> suggestions given for each grade level, too!<br />
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<span style="color: #b45f06;">PRE-K and KINDERGARTEN</span></div>
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<b><span style="color: #b45f06; font-size: large;">Two-Color Counters</span></b></div>
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<b style="box-sizing: border-box; font-size: 11.76px; text-transform: uppercase;"><span style="color: #b45f06;"><u>(P)K.CC.C.6</u></span></b><br />
<span style="color: #b45f06;"><i>Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.</i><span style="box-sizing: border-box; font-size: 12.6px; font-style: italic; line-height: 0; padding: 0.25em; position: relative; top: -0.5em; vertical-align: baseline;">1</span></span></div>
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<u><b><span style="color: #b45f06;">DROP and COMPARE</span></b></u></div>
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<ul>
<li><span style="color: #b45f06;">Give pairs of students up to 20 counters (the quantity can be adjusted to meet the learning level of the students within each pair)</span></li>
<li><span style="color: #b45f06;">Have students drop the counters into a box or other container (to keep them from getting all over the place!)</span></li>
<li><span style="color: #b45f06;">Have students match each red with a yellow counter until they run out of one color</span></li>
<li><span style="color: #b45f06;">Ask students to say a comparative statement that matches their counters:</span></li>
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<li><span style="color: #b45f06;">"There are more red than yellow"</span></li>
<li><span style="color: #b45f06;">"There are fewer yellow than red"</span></li>
<li><span style="color: #b45f06;">"I have the same number of red as yellow"</span></li>
<li><span style="color: #b45f06;">"There are two more red than yellow"</span></li>
<li><span style="color: #b45f06;">"There is 1 less red than yellow"</span></li>
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<span style="color: #674ea7;">GRADE 1</span></div>
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<b><span style="color: #674ea7; font-size: large;">Two-Color Counters</span></b></div>
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<span style="color: #674ea7;"><span style="font-family: "lato light"; font-size: 16.8px;"><b style="box-sizing: border-box; font-size: 11.76px; text-transform: uppercase;"><u>1.OA.C.6</u></b></span><i><br style="box-sizing: border-box; font-family: "lato light";" /><span style="color: #202020; font-family: "lato light";">Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).</span></i></span></div>
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<b><u><span style="color: #674ea7;">DROP EQUATIONS with two-colored counters</span></u></b></div>
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<ul>
<li><span style="color: #674ea7;">Give pairs of students a small bowl/cup with up to 20 counters (adjust to fit students' learning levels)</span></li>
<li><span style="color: #674ea7;">Students take a handful of the 20 counters (they do not have to use all 20 of the counters)</span></li>
<li><span style="color: #674ea7;">Students drop the counters in a box or other other container (less of a mess)</span></li>
<li><span style="color: #674ea7;">Students sort the counters into red and yellow groups</span></li>
<li><span style="color: #674ea7;">Students count the counters in each group</span></li>
<li><span style="color: #674ea7;">Students write an equation (see attached worksheet or simply use dry erase boards) to match the counters ---- the image above could by 4 + 8 = 12</span></li>
<li><span style="color: #674ea7;">Students pick up the counters and returns them to the cup/bowl</span></li>
<li><span style="color: #674ea7;">Student takes a new handful and continues dropping, sorting, counting, and creating equations. </span></li>
<li><span style="color: #674ea7;">At the end of the activity, bring students together to share one of their equations as you chart the various equations that students created </span></li>
<li><span style="color: #674ea7;">For an added mathematical element have students model the shared equation using their counters -- this reverses the thinking process from the original activity -- students start with an equation to build the model rather than writing an equation from a model</span></li>
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<b><span style="color: #674ea7;">🌟Get a copy of the Drop Equation workspace shown above by <a href="https://drive.google.com/file/d/1-c2lUZ3bvRvDv6dE7jOLk6QchKXkrJ9E/view?usp=sharing" target="_blank">clicking HERE :)</a> </span></b><br />
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<span style="color: #cc0000;">GRADE 2</span></div>
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<b><span style="color: #cc0000; font-size: large;">Base Ten Blocks</span></b></div>
<span style="color: #cc0000;"><b style="box-sizing: border-box; font-family: "lato light"; font-size: 11.76px; text-transform: uppercase;"><u>2.NBT.A.3</u></b><b><br style="box-sizing: border-box;" /></b><span style="font-family: "lato light"; font-size: 16.8px; font-style: italic;">Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.</span></span><br />
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<span style="font-family: "lato light"; font-size: 16.8px;"><span style="color: #cc0000;"><b style="text-decoration-line: underline;">BASE TEN MODELS</b><br />Use base ten blocks to create models of numbers</span></span><br />
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<li><span style="color: #cc0000; font-family: "lato light";"><span style="font-size: 16.8px;">Give pairs or small groups of students base ten blocks (lots of them!)</span></span></li>
<li><span style="color: #cc0000; font-family: "lato light";"><span style="font-size: 16.8px;">Ask students to create a model to show 15 using the base ten blocks</span></span></li>
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<li><span style="color: #cc0000; font-family: "lato light";"><span style="font-size: 16.8px;">note that some students may count out 15 single unit cubes -- this IS a correct way to model 15 -- use questioning to help the student find a more mathematically efficient way to build the model</span></span></li>
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<li><span style="color: #cc0000; font-family: "lato light";"><span style="font-size: 16.8px;">Next, ask students to model the value of 42 using the base ten blocks</span></span></li>
<li><span style="color: #cc0000; font-family: "lato light";"><span style="font-size: 16.8px;">Ask, "If we count each small square on all of the rods and then also count the two unit cubes, how many cubes would we have altogether?" (42)</span></span></li>
<li><span style="color: #cc0000; font-family: "lato light";"><span style="font-size: 16.8px;">Ask, "How many "ones" do we have?" (2)</span></span></li>
<li><span style="color: #cc0000; font-family: "lato light";"><span style="font-size: 16.8px;">Ask, "How many "ten rods" do we have?" (4) "What quantity do 4 ten rods represent?" (40)</span></span></li>
<li><span style="color: #cc0000; font-family: "lato light";"><span style="font-size: 16.8px;">Write the number 42 on the board. Help students to understand that the 2 in 42 represents the 2 unit cubes and the 4 in 42 represent the 4 ten rods which is equal to 40 unit cubes if we break the rods into unit cubes. </span></span></li>
<li><span style="color: #cc0000; font-family: "lato light";"><span style="font-size: 16.8px;">Give more practice with double-digit numbers if needed. </span></span></li>
<li><span style="color: #cc0000; font-family: "lato light";"><span style="font-size: 16.8px;">Now ask students to model 245 using the base ten blocks. </span></span></li>
<li><span style="color: #cc0000; font-family: "lato light";"><span style="font-size: 16.8px;">Ask, "If we count each small square on the flats, and each small square on the rods, and then count the five unit cubes, how many cubes will we have in all?" (245)</span></span></li>
<li><span style="color: #cc0000; font-family: "lato light";"><span style="font-size: 16.8px;">Follow-up this guided practice with a partner game: </span></span></li>
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<li><span style="color: #cc0000; font-family: "lato light";"><span style="font-size: 16.8px;">Ask students to create a model of a 2- or 3-digit number using the base ten blocks.</span></span></li>
<li><span style="color: #cc0000; font-family: "lato light";"><span style="font-size: 16.8px;">Tell students to write the value of the model on a dry erase board without letting their partner (or small group) see the number. </span></span></li>
<li><span style="color: #cc0000; font-family: "lato light";"><span style="font-size: 16.8px;">Have the partner(s) calculate the value of the model. </span></span></li>
<li><span style="color: #cc0000; font-family: "lato light";"><span style="font-size: 16.8px;">See if the values match. Discuss as needed.</span></span></li>
<li><span style="color: #cc0000; font-family: "lato light";"><span style="font-size: 16.8px;">Students change roles. </span></span></li>
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<span style="color: #38761d;">GRADE 3</span></div>
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<b><span style="color: #38761d; font-size: large;">Square Tiles</span></b></div>
<span style="color: #38761d;"><b style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; box-sizing: border-box; font-family: "Lato Light"; font-size: 11.76px; text-transform: uppercase;"><u><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; box-sizing: border-box; font-size: 11.76px;">3</span>.MD.D.8</u></b></span></div>
<span style="font-family: "lato light"; font-size: 16.8px;"><i><span style="color: #38761d;">Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.</span></i></span><br />
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<span style="color: #38761d; font-family: "lato light";"><span style="font-size: 16.8px;"><b><u>UNDERSTANDING AREA & PERIMETER USING SQUARE TILES (Modules 5 & 8)</u></b></span></span><br />
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<span style="color: #38761d;">Building Understanding</span><br />
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<li><span style="color: #38761d;">Give each student/pair/team12 square tiles (this may depend on the number of tiles you have - TIP: Cheez-It crackers make great tiles, too!)</span></li>
<li><span style="color: #38761d;">Ask students to create a rectangle using all 12 of the tiles</span></li>
<li><span style="color: #38761d;">Ask, "Was there only one way to use all 12 tiles to make a rectangle? Look around to see if you can find a team that created the rectangle differently than your team?"</span></li>
<li><span style="color: #38761d;">Ask, "How many tiles did you use to make your rectangle?" (12)</span></li>
<li><span style="color: #38761d;">Say, "Because we all used 12 tiles, we say that our rectangles have an AREA of 12 square tiles. It doesn't matter if you made a long, skinny rectangle (2 by 6 or 12 by 1) or if your rectangle was almost a square (3 by 4) - all of our rectangles are 12 square units because we used 12 tiles to make the rectangle."</span></li>
<li><span style="color: #38761d;">Ask, "What IF we used 24 tiles? What would the area of our rectangle be?" (24 square tiles)</span></li>
<li><span style="color: #38761d;">Ask, "What IF we used 100 tiles? What would the area of our rectangle be?" (100 square tiles)</span></li>
<li><span style="color: #38761d;">Say, "So the area of the rectangle is determined by the number of same-sized tiles that we use." </span></li>
<li><span style="color: #38761d;">Say, "Look at the rectangle you created using the 12 square tiles. We are going to count all of the edges that are not touching another tile." (Note: It may be helpful to use a document camera or to have an image projected on the screen to MODEL HOW to count the edges).</span></li>
<li><span style="color: #38761d;">Ask, "Let's make a prediction: Do you think that every rectangle we made will have the SAME number of edges?"</span></li>
<li><span style="color: #38761d;">Allow time for students to consider your question. </span></li>
<li><span style="color: #38761d;">Ask students to discuss their ideas with their partner/team. </span></li>
<li><span style="color: #38761d;">Ask students to count their edges. </span></li>
<li><span style="color: #38761d;">Ask students to tell you the number of edges they counted. Record all responses.</span></li>
<ul>
<li><span style="color: #38761d;">14, 16, 16, 26, 14, 14, 14, 15, 16, etc.... (note: 15 is not a correct response - do not correct it at this time, simply record)</span></li>
</ul>
<li><span style="color: #38761d;">Show all three of the possible models using 12 tiles </span></li>
<li><span style="color: #38761d;">Ask students to identify the model they created and to tell how many edges they counted.</span></li>
<li><span style="color: #38761d;">Write the number under the model.</span></li>
<li><span style="color: #38761d;">Ask, "What do you notice?" </span></li>
<ul>
<li><span style="color: #38761d;">each model has the SAME area, but DIFFERENT perimeter</span></li>
<li><span style="color: #38761d;">all of the people who said "14 edges" created the 3 by 4 rectangle</span></li>
<li><span style="color: #38761d;">students who did not say "14", "16", or "26" miscounted and may need assistance to better understand how to count the edges</span></li>
</ul>
</ul>
<span style="color: #38761d;">Expanding Understanding </span><br />
<ul>
<li><span style="color: #38761d;">Say, "Listen to this story about Claudia who is building a garden. When I am done telling you about Claudia's garden, you will use the square tiles to build what Claudia's garden might look like."</span></li>
<li><span style="color: #38761d;">Say, "Claudia's garden is 24 square feet. It is a rectangle-shaped garden. What could Claudia's garden look like? Build it?" (TIP: Write the mathematical information on the board)</span></li>
<li><span style="color: #38761d;">Give students time to contemplate, discuss, and build (and rebuild as needed)</span></li>
<li><span style="color: #38761d;">Have students discuss the various ways they built Claudia's garden as you model their ideas on the board or by using tiles under the document camera.</span></li>
<li><span style="color: #38761d;">Ask, "What is the AREA of the garden that each of you created for Claudia?" (24 sq. feet). "How do you know?"</span></li>
<li><span style="color: #38761d;">Say, "Claudia wants to put a fence around her garden so the animals do not eat her vegetables. Will all of these gardens need the same amount of fence?" Give time for students to think about your question. </span></li>
<li><span style="color: #38761d;">Say, "Calculate how much fence Claudia needs if she builds her garden like the one you built with your tiles."</span></li>
<li><span style="color: #38761d;">Allow plenty of time. Encourage students to compare and discuss with others. Help students to notice that gardens that are built the same will have the same area AND perimeter. Gardens that are built with different dimensions will have different perimeters even though the area is still 24 square feet. </span></li>
</ul>
<div>
<span style="color: #38761d;">Modeling Understanding</span></div>
<ul>
<li><span style="color: #38761d; font-family: "lato light";"><span style="font-size: 16.8px;">Say, "I want you to use the square tiles to build a garden that has an area of 20 square units and a perimeter of 42 units."</span></span></li>
<li><span style="color: #38761d; font-family: "lato light";"><span style="font-size: 16.8px;">Ask, "How many tiles will you need to use?" (20)</span></span></li>
<li><span style="color: #38761d; font-family: "lato light";"><span style="font-size: 16.8px;">Ask, "How did you know you would need to use 20 tiles?" (because the area tells you how many tiles to use)</span></span></li>
<li><span style="color: #38761d; font-family: "lato light";"><span style="font-size: 16.8px;">Say, "Okay, work with your partner/team to build a garden that has an area of 20 <b><u>and</u></b> a perimeter of 42." </span></span></li>
<li><span style="color: #38761d; font-family: "lato light";"><span style="font-size: 16.8px;">Give time to trial and error. Circulate around the room observing and asking questions that help students build their understanding. </span></span></li>
</ul>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghzRMarB_uvwwhmK_JrV_nxh4S9HOphkm28SmOsFaJczYKLo8xayqWjKoBgWRklTrQT8UDFx1q5GrGa_1I8rFyQzEF_G1ZTArPtyI09dwg7ov_VxevVQapl-cxBYOVbb5pjBX7BuUDkX5R/s1600/Screen+Shot+2018-12-05+at+1.59.26+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="542" data-original-width="1187" height="292" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghzRMarB_uvwwhmK_JrV_nxh4S9HOphkm28SmOsFaJczYKLo8xayqWjKoBgWRklTrQT8UDFx1q5GrGa_1I8rFyQzEF_G1ZTArPtyI09dwg7ov_VxevVQapl-cxBYOVbb5pjBX7BuUDkX5R/s640/Screen+Shot+2018-12-05+at+1.59.26+PM.png" width="640" /></a></div>
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<i><span style="color: #202020; font-family: "lato light"; font-size: 16.8px;"><br /></span></i>
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<div style="text-align: center;">
<span style="color: #a64d79;">GRADE 4</span></div>
<div>
<div style="text-align: center;">
<b><span style="color: #a64d79; font-size: large;">Snap Cubes</span></b></div>
<span style="color: #a64d79; font-family: "lato light";"><span style="font-size: 11.76px; text-transform: uppercase;"><b><u>4.NF.B.3.D</u></b></span></span></div>
<span style="font-family: "lato light"; font-size: 16.8px;"><span style="color: #a64d79;">Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.</span></span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGbYWWR4I387DB2MlsyukFLd8aQ3Lof0EKNRgvsKBbdKTTEGgadR3ug72WVttAQWxv3ezN9TNB6oMB_eZDjKfQheffbZmPdp7zLBAfNo0z7KCC0xK9ReiyPn4SZ7PLGCtrxDdXJFRuObwH/s1600/download.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: #a64d79;"><img border="0" data-original-height="225" data-original-width="225" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGbYWWR4I387DB2MlsyukFLd8aQ3Lof0EKNRgvsKBbdKTTEGgadR3ug72WVttAQWxv3ezN9TNB6oMB_eZDjKfQheffbZmPdp7zLBAfNo0z7KCC0xK9ReiyPn4SZ7PLGCtrxDdXJFRuObwH/s1600/download.jpeg" /></span></a></div>
<span style="font-family: "lato light"; font-size: 16.8px;"><i><span style="color: #a64d79;"><br /></span></i></span>
<span style="font-family: "lato light"; font-size: 16.8px;"><b><u><span style="color: #a64d79;">MIXED NUMBER ADDITION WITH SNAP CUBES</span></u></b></span><br />
<br />
<ul>
<li><span style="color: #a64d79; font-family: "lato light";"><span style="font-size: 16.8px;">Have the following scenario posted and read it aloud to the class: "Makala is making a recipe that calls for 2-4/5 cups of apple juice and 1-2/5 cups of water. How much total liquid is in the recipe?"</span></span></li>
<li><span style="color: #a64d79; font-family: "lato light";"><span style="font-size: 16.8px;">Ask, "What is this story about? Not what math are we supposed to do, just what is the story about?" (Makala is making a recipe that calls for two different amounts of liquid and we are trying to determine the total amount of liquid needed). </span></span></li>
<li><span style="color: #a64d79; font-family: "lato light";"><span style="font-size: 16.8px;">Say, "Let's use our snap cubes to help us visualize this problem."</span></span></li>
<li><span style="color: #a64d79; font-family: "lato light";"><span style="font-size: 16.8px;">Ask, "What do you notice about the quantities used?" (fractions/mixed numbers)</span></span></li>
<li><span style="color: #a64d79; font-family: "lato light";"><span style="font-size: 16.8px;">Ask, "When we look at the fractions, how many parts are needed to make a whole?" (5 - remind students as needed that the denominator determines how many parts are needed to make a whole).</span></span></li>
<li><span style="color: #a64d79; font-family: "lato light";"><span style="font-size: 16.8px;">Say, "Go ahead and build a snap cube train that represents 1 whole using 5 cubes." </span></span></li>
<li><span style="color: #a64d79; font-family: "lato light";"><span style="font-size: 16.8px;">Give time and walk around checking and asking guiding questions as needed. </span></span></li>
<li><span style="color: #a64d79; font-family: "lato light";"><span style="font-size: 16.8px;">Say, "I notice that Makala needs 2 whole cups and a little more of apple juice. How can we represent the 2 whole cups?" (build 2 trains of 5 cubes each)</span></span></li>
<li><span style="color: #a64d79; font-family: "lato light";"><span style="font-size: 16.8px;">Say, "How much more apple juice does she need?" (4/5) "How can you represent that?" (making a train of 4 instead of 5)</span></span></li>
<li><span style="color: #a64d79; font-family: "lato light";"><span style="font-size: 16.8px;">Students should now have a representation of 2-4/5 (2 trains of 5 and 1 train of 4)</span></span></li>
<li><span style="color: #a64d79; font-family: "lato light";"><span style="font-size: 16.8px;">Say, "Remember, in the story, Makala also needed 1-2/5 cups of water. Use more snap cubes and build a representation of the amount of water she needs." (1 train of 5 and 1 train of 2)</span></span></li>
<li><span style="color: #a64d79; font-family: "lato light";"><span style="font-size: 16.8px;">Ask, "How many cubes are needed to represent 1 whole cup of liquid in this scenario?" (5) "How do we know that it is 5?" (the denominator tells how many makes the whole)</span></span></li>
<li><span style="color: #a64d79; font-family: "lato light";"><span style="font-size: 16.8px;">Say, "Look at your snap cube models. How many <u>whole cups</u> of liquid are needed for this recipe?"</span></span></li>
<ul>
<li><span style="color: #a64d79; font-family: "lato light";"><span style="font-size: 16.8px;">If students say "3", ask them if they have enough cubes to combine the shorter cube trains to make a train that represents one whole. </span></span></li>
<li><span style="color: #a64d79; font-family: "lato light";"><span style="font-size: 16.8px;">If students say "4", ask them to explain how they arrived at 4 whole cups.</span></span></li>
</ul>
<li><span style="color: #a64d79; font-family: "lato light";"><span style="font-size: 16.8px;">Ask, "After we have made all of the whole cups that we can, how many cubes are leftover?" (1)</span></span></li>
<li><span style="color: #a64d79; font-family: "lato light";"><span style="font-size: 16.8px;">Ask, "How many do we need to make another whole cup?" (students may say 5 as the total needed for a whole train or they may say 4 as the number of additional cubes needed)</span></span></li>
<li><span style="color: #a64d79; font-family: "lato light";"><span style="font-size: 16.8px;">Ask "So if we have 1 remaining, what fraction does that 1 represent?" (1/5) Ask students to explain WHY it represents 1/5 (because we need 5 to make a whole in this scenario and we only have 1 of the 5 that are needed).</span></span></li>
<li><span style="color: #a64d79; font-family: "lato light";"><span style="font-size: 16.8px;">Create additional stories to reinforce the concept. There is no need to use large whole numbers which can become cumbersome to model; small whole number values and smaller denominator values will be just as effective in helping students to build their conceptual understanding.</span></span></li>
</ul>
<div>
<span style="color: #a64d79; font-family: "lato light";"><span style="font-size: 16.8px;"><br /></span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxIJyC-FePH2hVjYnAzThAzdXY1MrMBDXooxo2z6KxL5duJOOyEEsBj7n3dnExgXopSwAj3g0WRbSsFxT5Fwrwa0ep4Bmx4GMzAn8dvOVCZ8RjyliaRqT63ajXjaUP2eQ_ElYQ1rO8wGP7/s1600/Screen+Shot+2018-12-05+at+2.21.47+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="628" data-original-width="1167" height="344" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxIJyC-FePH2hVjYnAzThAzdXY1MrMBDXooxo2z6KxL5duJOOyEEsBj7n3dnExgXopSwAj3g0WRbSsFxT5Fwrwa0ep4Bmx4GMzAn8dvOVCZ8RjyliaRqT63ajXjaUP2eQ_ElYQ1rO8wGP7/s640/Screen+Shot+2018-12-05+at+2.21.47+PM.png" width="640" /></a></div>
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<i><span style="font-family: "lato light"; font-size: 16.8px;"><span style="color: #134f5c;"><br /></span></span></i>
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<div style="text-align: center;">
<span style="color: #45818e;">GRADE 5</span></div>
<div>
<div style="text-align: center;">
<span style="color: #45818e; font-size: large;"><b>Two-Color Counters</b></span></div>
<span style="color: #45818e; font-family: "lato light";"><span style="font-size: 11.76px; text-transform: uppercase;"><b><u>5.OA.A.1</u></b></span></span></div>
<span style="font-family: "lato light"; font-size: 16.8px;"><i><span style="color: #45818e;">Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.</span></i></span><br />
<span style="font-family: "lato light"; font-size: 16.8px;"><i><span style="color: #45818e;"><br /></span></i></span>
<span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;"><b><u>BUILDING BASIC MODELS OF COMPLEX EXPRESSIONS</u></b></span></span><br />
<span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">For this activity, stick with small number values so the intended learning is not overshadowed by the task of counting out large quantities of counters. </span></span><br />
<span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;"><br /></span></span>
<span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">Building Understanding</span></span><br />
<ul>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">Ask students to use the two-colored counters to model 3 + 4 (students should put out 3 red and 4 yellow, or vice versa).</span></span></li>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">Ask students to adjust their current model so it shows 1 + 4 (students should simply remove 2 of the 3 same colored counters)</span></span></li>
</ul>
<div>
<span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">Expanding Understanding</span></span></div>
<ul>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">Post this expression on the board for students to see: 2 x ( 1 + 4) </span></span></li>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">Say, "Do not touch your counters, yet. Think about what this expression might mean."</span></span></li>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">Allow think time</span></span></li>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">Say, "Think about how you could use the counters to model this new expression." Give some think time. </span></span></li>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">Say, "Let's talk about this new expression. What do you notice?" </span></span></li>
<ul>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">there are parentheses</span></span></li>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">there is a multiplication symbol</span></span></li>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">there is an addition symbol</span></span></li>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">2x means "two groups of", so we need "2 groups of 1+4"</span></span></li>
</ul>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">Say, "We already have one group of 1 + 4 modeled from our last activity. How can we change it to be two groups of 1 + 4?" </span></span></li>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">Discuss and then ask students to show you the model for 2 x (1 + 4) --- students should have 1 red/4 yellow and then another set of 1 red/4 yellow (remember red/yellow can be reversed as long as the 1 is represented by the same color in both sets and the 4 is represented by the same color in both sets)</span></span></li>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">Say, "Let's try another one. Clear your counters."</span></span></li>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">Write 3 x (2 + 4) on the board. Ask students to model this expression.</span></span></li>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">Discuss, question, and guide as needed.</span></span></li>
</ul>
<br />
<span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">Modeling Understanding</span></span><br />
<ul>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">Show students the following model using counters under the document camera or a prepared slide on the SmartBoard. </span></span></li>
</ul>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuabVKswZChG_RZJyeigKPbAitDIKXbv3cep2gGGzHWUMuAEmrUTliOAzhjjWsuV3lORKqBaUDvakUTTP7JHEdedOKO5m6tMpBXJFZj5LwW5I-t9gWoHuil9ZgWYQ1EhNJQ4DNnWA2CxIT/s1600/Screen+Shot+2018-11-28+at+11.22.37+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: #45818e;"><img border="0" data-original-height="526" data-original-width="797" height="211" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuabVKswZChG_RZJyeigKPbAitDIKXbv3cep2gGGzHWUMuAEmrUTliOAzhjjWsuV3lORKqBaUDvakUTTP7JHEdedOKO5m6tMpBXJFZj5LwW5I-t9gWoHuil9ZgWYQ1EhNJQ4DNnWA2CxIT/s320/Screen+Shot+2018-11-28+at+11.22.37+PM.png" width="320" /></span></a></div>
<div>
<span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;"><br /></span></span></div>
<ul>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">Ask students to WRITE an expression that matches your image. Below are some of the expressions that students may generate. </span></span></li>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">Give plenty of time for students to think and discuss in small groups. </span></span></li>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">Encourage students to come up with multiple ways the model can be written as a mathematical expression. </span></span></li>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">Ask students to share their ideas as you write them on the board.</span></span></li>
<ul>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">15 + 6</span></span></li>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">(5 + 2) x 3</span></span></li>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">3 x (5 + 2)</span></span></li>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">(3 x 5) + (3 x 2)</span></span></li>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">21</span></span></li>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">3 x 7</span></span></li>
<li><span style="color: #45818e; font-family: "lato light";"><span style="font-size: 16.8px;">... and probably other ideas that deserve your classes time and effort to explain</span></span></li>
</ul>
</ul>
<span style="color: #45818e;">The most valuable part of this activity will be the discussion as to WHY the expression represents the model. <span style="font-family: "lato light"; font-size: 16.8px;">If a student offers an incorrect/different expression than expected, do not discourage the solution; instead, ask the student to explain. In most cases, the student will self-correct if needed :) </span></span><br />
<span style="color: #45818e;"><span style="font-family: "lato light"; font-size: 16.8px;"><br /></span></span>
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<i><span style="color: #202020; font-family: "lato light"; font-size: 16.8px;"><br /></span></i></div>
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:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.comtag:blogger.com,1999:blog-543907520077188162.post-57940103851044749972018-11-01T00:01:00.000-07:002018-11-12T14:50:59.437-08:00Cuisenaire Rods<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixAL0CthN-jccx4ubdJh50DUTRbHzIMREAvkq5JnoiQ0QaCxl0TVuQCn7DAhbgT-TnyWuVNmTRh-eXx76HN7ivWKDKFFh8ABASVjk0nB_F9vCmvYnH4E-Eg1i4UMO3BtEq10nKtBTibJ9R/s1600/Focus+on+Cuisenaire+Rods.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="360" data-original-width="814" height="282" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixAL0CthN-jccx4ubdJh50DUTRbHzIMREAvkq5JnoiQ0QaCxl0TVuQCn7DAhbgT-TnyWuVNmTRh-eXx76HN7ivWKDKFFh8ABASVjk0nB_F9vCmvYnH4E-Eg1i4UMO3BtEq10nKtBTibJ9R/s640/Focus+on+Cuisenaire+Rods.PNG" width="640" /></a></div>
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If you have a set of Cuisenaire rods handy, this would be a GREAT time to take them out and USE them as we "play" with ideas about using Cuisenaire Rods for mathematical instruction. If you don't have any Cuisenaire rods readily available, borrow a set of rods from your intermediate grade level classrooms (sets of them were sent this past summer). In the meantime, you can click one of the links below to access an interactive website for Cuisenaire Rods (using physical rods is far better if you have them available!)<br />
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<li><a href="http://mathtoybox.com/numblox/NumBlox.html#.W9dCGkv27ct" target="_blank">Math Toybox Cuisenaire</a></li>
<li><a href="http://pbs.panda-prod.cdn.s3.amazonaws.com/media/assets/wgbh/rttt12/rttt12_int_cuisenaire/index.html" target="_blank">PBS Cuisenaire</a></li>
<li><a href="https://www.mathplayground.com/mathbars.html" target="_blank">Math Playground Cuisenaire</a> </li>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiofm8Ci7VCs2w_9bhJwiNBrI04DXAlK9w0yvu09yXzwiVYWSsjzVWhZznJuYONOZPUtRvTwrMZXK76IZLqv8mHF_fN41rWsbfxE1_XobEnUnLdBn_WXjpFPPZNf1gaoMwWiI-KbpnRequL/s1600/e.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="229" data-original-width="751" height="193" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiofm8Ci7VCs2w_9bhJwiNBrI04DXAlK9w0yvu09yXzwiVYWSsjzVWhZznJuYONOZPUtRvTwrMZXK76IZLqv8mHF_fN41rWsbfxE1_XobEnUnLdBn_WXjpFPPZNf1gaoMwWiI-KbpnRequL/s640/e.PNG" width="640" /></a></div>
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<span style="font-size: large;"><b>STAGES & PHASES</b></span></div>
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Most students (and teachers) have very little experience using Cuisenaire rods for mathematical instruction.<br />
<b>ALL STUDENTS should begin at the beginning</b>. Even our older students (and their teachers!)<b> </b>need to begin by having free play with the Rods before trying to "do something" with them. As you continue reading, look for activity ideas indicated by this icon 🔺.<br />
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<b>GETTING STARTED with FREE PLAY</b></div>
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When introducing math manipulatives, an essential first step is to allow the students some free play with them. Free play should be, just that, free. Giving specific directions or over-organizing this initial activity destroys the essential character of free play. It takes a certain amount of faith to stand by watching children building towers and making animal pictures from the rods - especially when the construction seems to have no particular mathematical significance, but the time to explore will pay off in the end (I promise!).<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguW0tpVmVdQEgQfFBKGEDJTWNmuhiGkX3riXC-ckiZ_Tj7FDEY5HdFxRMVIzXFfPyvQJ_Z2wbvxBPFYxE2jgZ2urpCTlYnmCekH9lT0G2GhVtgn_lcftr1fMN5atTrP1SaoJrfNxjT7g8C/s1600/cuisenaire-rods.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="250" data-original-width="500" height="100" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguW0tpVmVdQEgQfFBKGEDJTWNmuhiGkX3riXC-ckiZ_Tj7FDEY5HdFxRMVIzXFfPyvQJ_Z2wbvxBPFYxE2jgZ2urpCTlYnmCekH9lT0G2GhVtgn_lcftr1fMN5atTrP1SaoJrfNxjT7g8C/s200/cuisenaire-rods.png" width="200" /></a></div>
Free play gives teachers a chance to observe their students' creativity and problem-solving skills and allows for informal conversations about what they see. As students "play", they learn to make choices in regards to which rods to use – this will be an invaluable skill when they use Cuisenaire rods later during instruction.<br />
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Using the math manipulatives during free play is time well-spent, but it doesn't have to happen just during the precious little time you have for math instruction; you might decide to offer the manipulatives that will be used later in the week/month for free play on a rainy day during indoor recess or perhaps as part of a brain break activity.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikOq-73m7e4FL9f2hWE3fwX5MGUNAGNEsDooe0zRwH7C8A-MvpTChFTUiifdWhwabgLcn0gpCj4M3vlpxpnpqokuor46FbR-IEvljuzh_uyv1X8t_AXfwLStrhVD4VUsKf3J_GYzLG_vtG/s1600/z.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="217" data-original-width="531" height="162" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikOq-73m7e4FL9f2hWE3fwX5MGUNAGNEsDooe0zRwH7C8A-MvpTChFTUiifdWhwabgLcn0gpCj4M3vlpxpnpqokuor46FbR-IEvljuzh_uyv1X8t_AXfwLStrhVD4VUsKf3J_GYzLG_vtG/s400/z.PNG" width="400" /></a></div>
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<b>DEVELOPING AN UNDERSTANDING OF EQUIVALENCE</b></div>
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After taking time to explore the Cuisenaire rods in a free play setting, the first concept you will want to formally tackle is <b><i>equivalence</i></b>. Your students should have opportunities to sort, name, order, and use equivalence to form various patterns using the rods. A simple way to begin is to place a pile of Cuisenaire rods in front of students and ask them, "What do you notice?" Give them a bit of time to touch and explore. Do not end this exploration time too soon. Be patient. Encourage small groups to talk. Then stand back and watch the ideas about equivalence pour out:<br />
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"Two red rods are the same length as 1 purple rod."</blockquote>
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"Three white rods are the same length as 1 green rod."</blockquote>
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"A red rod and a green rod together are the same as 1 yellow." </blockquote>
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"If the white rod is 1, then the yellow rod is 5." </blockquote>
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<b>FORMALIZING YOUR EXPLORATION</b></div>
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You've given time for free play and some time to just "notice". Now let's take a look at specific activities you can use in your classroom to develop your students' number sense and their ability to use the Cuisenaire rods to solve math problems. </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9YCJ_ynN3c2fvQ7D8gXcO7RTKxewp-VMZ4RcVxpzyWIAeCYqPe8AAZ4SrQQjWrweHpTFwaHU0WRqvWX9rTtIPlrX9L01F_Q5oRX655miLES-qjbXCiWH2wXXgRO3ONRlfaj5ZEnTCMvJV/s1600/b.PNG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="292" data-original-width="212" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9YCJ_ynN3c2fvQ7D8gXcO7RTKxewp-VMZ4RcVxpzyWIAeCYqPe8AAZ4SrQQjWrweHpTFwaHU0WRqvWX9rTtIPlrX9L01F_Q5oRX655miLES-qjbXCiWH2wXXgRO3ONRlfaj5ZEnTCMvJV/s200/b.PNG" width="145" /></a>🔺<b>Place the YELLOW ROD in front you. How many ways can you make a length that is equivalent to the yellow rod? </b>Can you think of any other ways that are not shown on the graphic to the right?<br />
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🔺<b>Which single rods are equivalent to doubles of another? </b>How many combinations can you find? Do you notice any patterns? Can we predict which rods can be made with a double?<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjVoUUYHSGv4JDhd6Ng5-V34-6R4WhyphenhyphenVmerhkVmm5D_yINZuNkrA8QhFuWVY1cPNai6_QD_Hf_2sqSpuJK7RLTmHO3UAidqJIhBU7j-ZyVgMOEFuK8_EQWCLXq1Fc6oaDQdWekMl9AsYIX/s1600/y.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="353" data-original-width="532" height="265" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjVoUUYHSGv4JDhd6Ng5-V34-6R4WhyphenhyphenVmerhkVmm5D_yINZuNkrA8QhFuWVY1cPNai6_QD_Hf_2sqSpuJK7RLTmHO3UAidqJIhBU7j-ZyVgMOEFuK8_EQWCLXq1Fc6oaDQdWekMl9AsYIX/s400/y.PNG" width="400" /></a></div>
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<b>DEVELOPING AN UNDERSTANDING OF THE WHOLE</b></div>
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Cuisenaire rods are excellent tools for developing flexible thinking. A major component of using the Cuisenaire rods effectively is being mindful of "the whole". The whole can change with each question and understanding what represents the whole helps to bring meaning and context to the rest of the rods. Because the whole is not always the same color rod, it forces us to think more flexibly and to constantly assess the value of each rod in terms of the whole. The whole can even be made of two or more rods that have been pushed together (crazy, I know!).<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRWO5StBY0ZVoowvALp6em0Bg3AcmB4vLCEFiB4BRfWV1n5DD025bTm27QuiC4Z6VKjiqLtNteLRZAXhJp7GdZDV5EXTUEet_27fbKAB9gvPe46fGV6axoMGphNoGJGVZRuQLLPFApvjMt/s1600/cuisenaire+rods.PNG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="491" data-original-width="663" height="235" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRWO5StBY0ZVoowvALp6em0Bg3AcmB4vLCEFiB4BRfWV1n5DD025bTm27QuiC4Z6VKjiqLtNteLRZAXhJp7GdZDV5EXTUEet_27fbKAB9gvPe46fGV6axoMGphNoGJGVZRuQLLPFApvjMt/s320/cuisenaire+rods.PNG" width="320" /></a></div>
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🔺<b> If the blue rod is one whole, which rod represents 1/3? </b>How do you know? What is another way you can know? </div>
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🔺<b> If the red rod represents 1/3, which rod represents the whole? </b>What question did you ask yourself to begin answering this question?<b> </b></div>
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🔺<b> If the whole is the orange rod and red rod pushed together, which rod represents 1/2? </b>What strategy did you use to determine the answer?<b> </b>What other strategy could be used?</div>
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🔺<b> A train that is made from two rods has an equivalent length to brown. If one of the rods is yellow, what color is the other rod? </b>(equivalence)<br />
<i>How would having physical rods help you to discover that the other rod must be light green?</i></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhK4Ynih7J0nIa9WpcI_NJ3bKIYpehkqmf8xqU9Ui1yqdFsVze4il4LQDz1EmxqnwH_eK4-82vIm9MgrRml2wshtjKBqVEX3aySivCmJBP58tN-W9iMYce_UIumehY9ls9TUgbBUSLRDRD1/s1600/c.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="85" data-original-width="228" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhK4Ynih7J0nIa9WpcI_NJ3bKIYpehkqmf8xqU9Ui1yqdFsVze4il4LQDz1EmxqnwH_eK4-82vIm9MgrRml2wshtjKBqVEX3aySivCmJBP58tN-W9iMYce_UIumehY9ls9TUgbBUSLRDRD1/s1600/c.PNG" /></a></div>
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🔺<b> Make a train with 2 rods: One of the rods is half the length of the other rod. What does the train look like? What is the fractional value of each color rod in this model as compared to the whole? What other combinations of rods could be used to build a different train with the same parameters? </b>(fractions)<br />
<i>How would having physical rods help you to discover that there are multiple representations? Is there a pattern to the rods that can/cannot be used to build this train? Notice how using the rods makes the complex idea that the light green (which is 1/2 the length of the dark green) represents 1/3 of the whole. </i></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgc52XtT7VrRVuqUmsUfgy9qfHk0iRokF7dZLXKHjKChsvjpxt70CirW9iI-xbVYBLwPkTogqJXJW4_QY_MhNpyhnnJTizNtWmGTrg0W7hGTqzLFp6JCPNjWYjpJlncz60dCYp_y71GxqDT/s1600/Screen+Shot+2018-10-31+at+4.49.36+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="153" data-original-width="386" height="126" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgc52XtT7VrRVuqUmsUfgy9qfHk0iRokF7dZLXKHjKChsvjpxt70CirW9iI-xbVYBLwPkTogqJXJW4_QY_MhNpyhnnJTizNtWmGTrg0W7hGTqzLFp6JCPNjWYjpJlncz60dCYp_y71GxqDT/s320/Screen+Shot+2018-10-31+at+4.49.36+PM.png" width="320" /></a></div>
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🔺<b> What is 10 divided by 4? How does this model demonstrate the quotient? </b>(division with fractional quotients)</div>
<i>Do you see the solution of 2½ in the model below? The orange rod is 10 units. The purple rod is 4 units. We needed 2½ purple rods to equal the same length of one orange rod</i>.<br />
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🔺<b> Is 21 a multiple of 3? </b><b>How does the model below help you to know? </b>(multiples)</div>
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🔺<b> </b><b>Is 21 a multiple of 4? </b><b>How does the model below help you to know? </b>(multiples)</div>
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<i>Notice that the value of 21 was made from 2 ten rods (orange) and a 1 rod (white).</i></div>
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<i>How does the model below help you to see that 21 is a multiple of 3, but not 4? </i></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivNlj0hTt8tSztZcnojt8dXVRnFBe-sdtkcefJWBpYR2rCWUfy6ejdmRXuQBDKZusKh0QrSEB9xJXSOgKsHyUlpxMUnuL4xQbvsjUzJoof46nMyG6S5m7LoaI28O7c1vJGf92esy1z7cZJ/s1600/g.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="195" data-original-width="586" height="132" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivNlj0hTt8tSztZcnojt8dXVRnFBe-sdtkcefJWBpYR2rCWUfy6ejdmRXuQBDKZusKh0QrSEB9xJXSOgKsHyUlpxMUnuL4xQbvsjUzJoof46nMyG6S5m7LoaI28O7c1vJGf92esy1z7cZJ/s400/g.PNG" width="400" /></a></div>
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🔺<b> Is 3 a factor of 21? </b><b>How does the model above help you to know? </b>(factors)</div>
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🔺<b> Is 4 a factor of 21? </b><b>How does the model above help you to know? </b>(factors)</div>
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<i>How does the model shown above help you to see that 3 IS a factor of 21, but 4 is not? </i></div>
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🔺<b> What is the sum of 3/5 and 1/3. How do you know? </b>(fractions)</div>
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<i>How does this model help you to see that the sum is 14/15? </i></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9HFoYvRwu-KkZNZjDiwvMi1M_IShnyAN9EyTASF8hUAmb0SAV7cisyyFFDUp8-HSeIad6N5SFWXdrlKwrKGkat0RUZqlSr5ZOPGF5S1qSRaei0TN0S1biiVGfSUbQPPtcrNsc026R8vnE/s1600/h.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="375" data-original-width="909" height="264" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9HFoYvRwu-KkZNZjDiwvMi1M_IShnyAN9EyTASF8hUAmb0SAV7cisyyFFDUp8-HSeIad6N5SFWXdrlKwrKGkat0RUZqlSr5ZOPGF5S1qSRaei0TN0S1biiVGfSUbQPPtcrNsc026R8vnE/s640/h.PNG" width="640" /></a></div>
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🔺<b> The area of a rectangle is 56. One side of the rectangle is 7 units. What are the lengths of the other sides? </b>(geometry)</div>
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<i>How does this model help you see that the lengths of the sides are 7, 7, 8, and 8?</i></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgP6m5U4yBov2y07VY8r8ifAb-fTcXBtj4sPkDSM8E2v7lUzlf0Z3adRRl9FRO1LhcdlY7v7HlBPgYcH2HKUtqk7OKjdt3fzU1bl5jGKdlAYySZvoj0N4_UiG_g21YNkYK6uedF23RHVN2u/s1600/w.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="483" data-original-width="641" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgP6m5U4yBov2y07VY8r8ifAb-fTcXBtj4sPkDSM8E2v7lUzlf0Z3adRRl9FRO1LhcdlY7v7HlBPgYcH2HKUtqk7OKjdt3fzU1bl5jGKdlAYySZvoj0N4_UiG_g21YNkYK6uedF23RHVN2u/s400/w.PNG" width="400" /></a></div>
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🔺<b> </b><b>What is 1/2 of 1/3? </b>Use the image below (or better yet, build the model!) to find the solution. (fraction calculation) </div>
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<i>How does this model help you see that 1/2 of 1/3 is 1/6? </i></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiw8Tb-aO1CNkM2O4CQZnm44qr1kAA2XCcnn7jct_7ySEZ_xt2JJ_dDXnD60gywQVD8tXE9xb9of96qbehdtZPJA8xJ4STacjx_Pn_G9t0Bd3hxzUebb5tIVam_-qY5RKwz-NGXtzh43pi4/s1600/m.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="184" data-original-width="353" height="207" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiw8Tb-aO1CNkM2O4CQZnm44qr1kAA2XCcnn7jct_7ySEZ_xt2JJ_dDXnD60gywQVD8tXE9xb9of96qbehdtZPJA8xJ4STacjx_Pn_G9t0Bd3hxzUebb5tIVam_-qY5RKwz-NGXtzh43pi4/s400/m.PNG" width="400" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWPCM7bRXvNljPKAJ2a54oxLwk28quZrwmldtywVshUv5Mu5_r_QB4vkQ7JFmWkqhTgS5O_8cg8skK8NYeh-iMdgc2xFLZm8HFXUN_FLUwBCcFJurjZxvCLGryEvDPaDU8mCCqwJfTCEH9/s1600/role.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="567" data-original-width="825" height="436" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWPCM7bRXvNljPKAJ2a54oxLwk28quZrwmldtywVshUv5Mu5_r_QB4vkQ7JFmWkqhTgS5O_8cg8skK8NYeh-iMdgc2xFLZm8HFXUN_FLUwBCcFJurjZxvCLGryEvDPaDU8mCCqwJfTCEH9/s640/role.PNG" width="640" /></a></div>
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<span style="font-size: large;">🌟<a href="https://drive.google.com/open?id=1ZivjCtfbuOuoVak16X8rfnTEXaejJUpw" target="_blank">CLICK HERE for a <b>.pdf download</b> with MORE Cuisenaire Activities!</a></span></h2>
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<span style="font-size: large;">🌟<a href="https://docs.google.com/document/d/17PpGTDAzxyPRbK_5GWIzj3jEA1QKk7lS9qdNuRkLwn0/edit?usp=sharing" target="_blank">Grade 3 - CLICK HERE for a <b>.pdf download</b> activities related to Modules 3 & 4</a></span></h2>
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🌟<a href="https://www.hand2mind.com/pdf/gridpaper.pdf" target="_blank">CLICK HERE to download <b>1 cm grid paper</b></a></div>
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(NOTE: be sure that "fit to page" is NOT checked when printing)</div>
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<span style="font-size: large;"><b>SOME VIDEO LINKS for PROFESSIONAL GROWTH</b></span></div>
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<li><a href="https://www.youtube.com/watch?v=sbsPK3LXVLc" target="_blank">It's All About the Whole</a> - explore how any configurations of rods can be the whole and use the whole to determine the relational value of the other rods</li>
<li><a href="https://vimeo.com/42344215" target="_blank">Building Number Sense with Cuisenaire Rods</a> - watch a very young child begin understanding the concept of decomposing by building combinations with Cuisenaire rods</li>
<li><a href="https://www.youtube.com/watch?v=kkwWCnEGzX4" target="_blank">Division with Cuisenaire Rods </a>- see how Cuisenaire rods can help to build conceptual understanding of division with fractional remainders</li>
<li><a href="https://www.youtube.com/watch?v=UlPaK4-s6fY" target="_blank">Finding Factors</a> - see how children use Cuisenaire rods to find the factors of a number</li>
<li><a href="https://www.youtube.com/watch?v=0u8UeWlfdRE" target="_blank">Equivalent Fractions </a>- a very quick simple explanation</li>
<li><a href="https://www.youtube.com/watch?v=4NPSMWwYoG" target="_blank">Adding Fractions </a>- a Cuisenaire model approach</li>
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:Dawn Cainehttp://www.blogger.com/profile/07523610366027110702noreply@blogger.com