Tuesday, November 5, 2013

Comparing Numbers with the CRA Model

In our math workshop, we are working on comparing numbers using greater than, less than, and equal to.  I don't know about you, but I used to just go right to the symbols.  Here's the numbers, figure out the symbol kids.  Maybe throw in an alligator to help you.  However, in learning more about the Common Core and the need for deeper understanding, I've come to learn the importance of teaching kids using the CRA model: concrete, representational (pictorial), and abstract.  So, this year, I decided to try something a little different in my guided math groups.  

First, we built two numbers using base ten blocks and just verbally compared them.  I had the kids count each group, and we talked about how to look at the biggest "place" to see which number is greater or less.  Then, when we were ready for the symbols, I still stuck with the base ten blocks so the comparisons would be very concrete.  I asked the kids to build two numbers and compare them, using popsicle sticks to make the symbol.  FYI - I took these pictures from across the table, so they are upside down.  I tried to rotate them, but they just looked weird.  So, upside down it is.

Some of them were very extreme in their comparisons...1 < 80 :)

This kiddo did 22 = 22.  Of course, the blocks has to be perfectly lined up and arranged.  Anyone else have kids who need their base ten blocks to be "just so"?? :)

Then, we moved onto representational (aka pictorial...I've heard it both ways).  I had the kids draw the base ten blocks so they could still visualize the tens and ones in the numbers.  I also taught them that when they draw the symbol, the little number gets the point.  I used a dot to model which way to draw the lines.  Apparently, it kinda stuck, and now they all draw a dot like it's part of the symbol!  Haha!

Finally, some kids were ready to compare using numerals.  I've learned that numerals and symbols of any kind are very abstract for kids...while you and I can read a numeral and instantly understand what it means, it's a skill that's more difficult for some kids, especially kids who struggle in math.  I'm learning to slooooowwww down my teaching and really make things concrete and representational before I throw in any abstract symbols.  

I had them create the symbol with their popsicle sticks first, then they needed to write 2 numbers that would make it true.  It's fun to see the different numbers they come up with! :)

I purposely have not mentioned any alligators or special "tricks" this year...I've found that the alligator trick helps them know which way to point the symbol, but not necessarily know what the symbol is called.  (Case in point:  They learned the alligator trick in Kindergarten, and when I first introduced the symbol and asked kids if they knew what it was, one of them raised their hand and told me, "the mouth".  Haha!)  I want them to know the name of the symbol and what it represents, not just "the alligator eats the bigger number".  So far, I think it's really helped

Happy hump day tomorrow!


  1. This is great! How long did this take you? One long lesson (if so, how long was the lesson), or did you split it up into several days?

    1. Thank you! We worked on comparing numbers for about a week in our mini-lessons. We stayed on each "step" for 1-2 days before moving on. We also worked on it in small guided math groups. I started the groups in different places, depending on what I saw from the kids during the mini-lesson. Hope that helps!

  2. Starting with the concrete is so important when teaching a math skills! I was searching Pinterest to come up with some new ideas to teach comparing numbers and I found your post. I will be doing this in my small groups next week!


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