What do you notice about the numbers below?
C'mon... play along.
Think of at least 4 things that you notice
Take as much time as you need...
I am happy to give you time to ponder and play!
- Maybe you noticed the number was a 3-digit number.
- Perhaps you noticed that it looks like a highway sign.
- Did you also notice that the numbers on the sign were in consecutive order?
- (Yes, I know that is only 3 things. But I am completely confident that you came up with a fourth item to add to our list on your own, right?)
Okay, let's have a little math fun with these numbers.
- Begin by multiplying the first and last digits (3x5)
- Now take the center number and square it (4x4)
- What do you notice when you compare the products of those calculations?
I WONDER if there is a mathematical pattern? This is only exciting if there is some sort of pattern that occurs. If I do these steps again with a different 3-digit number that also has consecutive values (perhaps a number like 789), will I get the same PATTERN of results? Let's try it!
- Begin by multiplying the first and last digits (7x9)
- Now take the center number and square it (8x8)
- What do you notice when you compare the products of those calculations?
Well, what did you discover? Is there a pattern when looking at the relationship of the products of the two calculations? I would LOVE to hear your discoveries – If you're willing, please post a comment in the comment section at the bottom of this page so we can "discuss" this as a math community?
Now you've got me wondering all sorts of things:
- Does this pattern work if I use decimal values that are consecutively separated by a value of 1, for example, 1.5, 2.5, and 3.5?
- Does a pattern occur in when I do the two calculations if the numbers are evenly spaced by a value of more than 1 (try 4, 6, 8)? If there is a pattern, is the pattern the same as before? If the pattern is not the same as before, how are the products of these calculations related?
- Can I generalize the patterns that I am discovering?!
I heard this statement today and it really resonated with me:
So my day started out with me suddenly realizing that it was the last day of the month, and as many of you know, I always put out the latest edition of MathSnack during the first week of the new month. Well, at 8am this morning, I had no ideas for the topic of March's post [read as "panic"]. By 9am, however, I knew exactly what would be on this month's MathSnack.
Today I attended a professional development opportunity with a few county colleagues and other educational leaders from across the state. The morning keynote address was facilitated by Dr. Raj Shah (I think I'm his newest groupie!). Within minutes of the customary introductions of the speaker, he had the room buzzing with math excitement after presenting a three-digit number task similar to the one above.
We spent the day playing with math and engaging in discussions that focused on rich tasks, productive struggle, and growth mindset. The tasks were, indeed, rich. The struggle was real. And our minds certainly grew!
I left with several pages of ideas that I want to share with you. For this post, let's begin with the idea of "curiosity". Dr. Shah shared a few bullet points about the power of curiosity:
- Curiosity enhances learning and memory
- Retention of the information lasts longer when we were curious to learn it in the first place
- Curiosity influences academic performance – in other words, students perform better on tasks that piqued their curiosity
Dr. Shah gave us the "recipe for success" – he challenged us to spark student curiosity by shifting the manner in which we engage students. Below are 3 ideas to get you started :)
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Want to learn more about Rich Tasks and get some instructional activity ideas for April's Module for your grade level? Come to our next Diving Deeper Into Mathematics Content PD opportunities on March 26th and 27th.
- Grades 3-5 – Monday, March 26th @4:45-7:30 at Barstow
- Grades K-2 – Tuesday, March 27th @4:45-7:30 at Barstow
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