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Integer Rules Visual References for Addition and Subtraction

We learn how to add and subtract in kindergarten. And this is about the last time addition and subtraction are easier!

When we get to the integers, there are some pretty concrete rules to follow for multiplication and division. But this isn’t so true for addition and subtraction.

This trips kids when working on integer operation problems, solving equations, finding inverses and any other time numbers on either side of zero need to be combined. Kids get to thinking they “can’t do Algebra/Algebra 2/Geometry, etc” when really it’s all integers.
So when I came across this pin leading to Don Steward’s blog post Directed Number Arithmetic Sped Up, it was exactly it. This was the visual I had been searching for to show students the relationship between positive and negative integers when combining.

I reached out to Don to see if he’d allow me to make pdf printables of his visuals, and to my happiness and excitement, he was open to it. What I love most about Don’s visuals is that the integers’ relative sizes are shown with the sizes of the circles, generalizing the “rules” for kids who need it.

There are 8 pages (4 in red/yellow and 4 b&w if you'd like to choose your own color scheme). They cover all of the +/- combination situations when adding and subtracting integers.

Download the integers visuals here.
*Related post: *
Can we really teach number sense?

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