The CRA Process for Learning About Attributes
This month we have been taking a deeper look at the data from PARCC assessments from 2017 (if we haven't been to your school, yet, we'll be there sometime this month). One of the documents that we viewed during that data session to gain a deeper understanding of the Standards was the PARCC Informational Guide. During that session, if you scrolled all the way to the bottom of that document, perhaps you noticed this information related to Standard 4.MD.A.1. The ones listed below are in addition to the ones that are already named in the standard itself.
When I read Standard 4.MD.A.1, it says that students should be able to record measurement equivalents in a two-column table. A table of mathematical values? That is pretty abstract, isn't it This is definitely NOT the starting place for this Standard – this is the ending place. So where do we begin?
Phase I: CONCRETE
Let's begin with something simple. Gather a collection of interesting items – it doesn't really matter what the items are but the more engaging they are, the better. I think for this example I am going to bring a wide variety of candies – that'll get their attention!
- Begin by stating that today you are going to investigate a unit of measure called a METER.
- Show the students ONE METER of a licorice lace (yes, measure and cut it so it is exact!). Stretch it out so they can see its full length.
- Tell the students that if you cut the lace into 100 hundred pieces to share with the class, EACH piece is exactly 1 centimeter long.
- Begin cutting the lace into 1 centimeter pieces and giving it to students - don't let them eat it, yet!
- Ask students to compare their 1 centimeter piece to the width of their pinky finger (for most 4th graders, it will be about the same width).
- Ask them to describe how their pinkie width and the licorice piece compare in size (accept all reasonable answers and discuss a bit why some say it is exactly the same and some say it is either a little bigger or smaller than their pinkie).
- Ask again, "Boys and girls, how long is your piece of the licorice lace?" (1 centimeter)
- Allow them to eat the licorice (if desired). Trust me, it will lead to a brain hook being created about the size of a centimeter.
- Ask, "Boys and girls, how long was the licorice lace before I cut it?" Show them another full lace as a model when asking this (1 meter).
- Ask, "How big was the piece that I gave you to eat?" (1 centimeter)
- Ask, "Exactly how many pieces did I have to cut the 1 meter lace into in order to make pieces that were exactly 1 centimeter?" (100 pieces)
- "If I wanted to eat 1 meter of licorice lace, how many of those little pieces would I need to eat?" (100)
- "How many centimeters then are in 1 meter?" (100 - may seem obvious to us, but ask it anyway to ensure the connection is made between the candy and the measurements)
- "What if I cut the lace into 90 pieces? Would each piece still be 1 centimeter?" (No)
- "Would the pieces be larger or smaller than 1 centimeter?" (This one may be tricky, give Think Time – the pieces would be larger than 1 cm because you used the same 1 meter of licorice to share among fewer people -- only 90 instead of 100)
- Show the students a different candy (perhaps a Snickers or a DumDum pop). Ask them, "How many of the little licorice pieces do you think I will need to line up end to end to make it as long as this candy?" Encourage discussion.
- "How many of these Snickers/DumDums do you think I would need to make it equal to 1 meter of candy?" Again encourage discussion.
- Use the candy to find out if they were correct. Celebrate with them their good estimates and reasonings.
Do similar investigations with other measurement systems. How far is a meter? How far is a kilometer? Perhaps you can walk a kilometer to help students understand. Challenge them to take a step that is exactly 1 meter big (it will be difficult, but fun to try, for most). How many of these giant 1 meter steps would you need to take to walk 1 kilometer? (1000). At recess, challenge them to walk 1 kilometer by taking 1000 giant steps!
Phase II: REPRESENTATIONAL
After students have some concrete experiences with measurement units, they will be able to use Representational drawings to explain measurement conversions within a system. Keep in mind that just because they had concrete experiences with centimeters, they will not have a readiness for grams – they have to have concrete experiences with each measurement system in order to develop a conceptual understanding of each.
Let's use weights for this example. We will fast-forward past the part where you gave students an opportunity to explore weights by bringing in scales that weigh grams (check your science supply closet or ask your science supervisor if you need scales to explore this topic). Once students have some concrete experience with weights, we can begin to use representational images to talk about weights.
Print out pictures or display pictures on a SmartBoard. Ask students, "Which of these items do you think weighs almost exactly 1 kilogram?" Then continue by asking them to group the items into 3 categories: About 1 kilogram, More Than 1 Kilogram, Less Than 1 Kilogram. Encourage discussion. Listen for comparisons to items they weighed on the scales earlier in the lesson progression.
Did you guess the kitten, the liter of water, and the pineapple are all about 1 kilogram. The dog and car are more than 1 kilogram. And the paperclip and dollar bill are less than 1 kilogram (those two items are actually only about 1 gram each).
Continue the discussion by helping students understand that they would need 1000 small paperclips to weigh about the same as a kitten – if you can get enough boxes of paperclips to make 1000, do it, so student can experience the weight of 1000 small paperclips and consider how it compares to the weight of a kitten or a liter of water.
Phase III: ABSTRACT
Okay, so we've had some concrete experiences, we've used pictures of items to classify weights into groups and to determine how many of one items we'd need to equal the weight of another, now we're ready for some abstract skills in measurement. Click HERE to see several worksheets like the one below from Common Core Sheets that support Standard 4.MD.A.1.
I can picture this worksheet enlarged, cut apart, and glued to cards at various stations. Students move from station to station recording their thoughts after having rich discussions with their team and using concrete materials, as needed, to formalize their ideas about measurements within each system.
Remember that the Standard calls for students to create 2-column tables of equivalent amounts, so be sure to include some of that, too! Here's an example of a 2-column table of equivalent measures.
ONLINE ACTIVITY: CONVERTING UNITS WITHIN A MEASUREMENT SYSTEM
Take a look at this online activity from Greg Tang. Students have to convert within various unit systems by regrouping (this image shows the inches to feet activity, but there are other options, too) – Conceptual understanding and flexible thinking are required because regrouping in this measurement system requires us to move units in groups of 12s, not 10s. Click HERE to check it out. This would make a great whole-group discussion activity before allowing students to try it on their own.
 |
