Math Equation Sorts: Using Logical Reasoning

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One of the first strategies kids use for solving number equations is counting on their fingers.  With my oldest {currently 1st grade}, I began to notice that counting on his fingers {even using small manipulatives} was slowing him down.  He was ready to move on to using a new and “upgraded” strategy. I realized that, for the most part, he knew his math facts to 10 and doubles to 20.  So I used that basic knowledge to help him see that he could solve other equations using logical reasoning.

Modeling the Sort

First, I created a sort (free download) for all the equivalent equations that equal 10. {I really like using sorts because they can be used for multiple purposes, unlike worksheets.}  We used the known math facts as headers. I created addition problems related to each header.  I modeled my thinking with a couple of problems as I sorted them.  For example, “If I know that 5+5=10, that helps me solve 6+5 because all I have to do is add one more in my head.”

Supporting the Student

I turned it over to him, supporting him as he sorted.  I asked him to verbalize his thinking as well.  He quickly discovered that some of the equations could go under more than one header.  For example, 7+4 could go under 7+3 or 6+4.

photo of Math Equation Sort with Equivalent Equations for 10 | The Homeschool Village

Once he had sorted each equation with my support, I went back through them and pointed to a few, asking, “Why did you put this one here?”  I wanted to hear him verbalize his logical reasoning.

Independent Practice

Then, I turned it over to him.  I shuffled the cards and let him re-sort with minimal help.  To take it a step further, he re-sorted all of these again the next day on his own.

Extending the Activity

We repeated this process with another equation sort.  This time, I used doubles as the headers (5+5 to 10+10).


This proved to be a bit more challenging for him, so I supported him further by writing the answers on the head equations.  He sorted them one day and the next day, he re-sorted and wrote the answers to each of the problems.

As we begin to review some of the math concepts we’ve learned this year, I plan on pulling these sorts out again!  I hope they will be of use to you as well.

You can download the both sorts on one download.  You can also find more free math printables I’ve created by clicking here.