This lesson plan with student handouts details how to helps students develop a conceptual understanding of adding and subtracting integers using zero pairs. The lesson begins with students using concrete manipulatives and moves them step by step into a more abstract understanding. In addition to concrete manipulatives, teachers can also use virtual manipulatives found on Virtual Tools for Learning Addition & Subtraction with Integers/Signed Numbers with this lesson. 

Here’s a brief overview of how to use 2-colored counters to learn how to add and subtract integers:

Let’s say I want to do 3 + (-5).

I can start with 3 yellow counters, each representing (+1). 

 

Since I want to add (-5), I will add 5 red counters.

In the picture above, we have 3 zero pairs. A zero pair is the sum of one and negative one, which is zero. We are left with 2 red counters, so we can see 3 + (-5) = (-2).

 

How about 4 – (-6)?

We start with 4 yellow counters.

 

Because we are subtracting (-6), we need to take away 6 red counters. But we don’t have any! Here’s where zero pairs can help. 

What if we add 6 zero pairs? What is the value of all the counters in this picture?

 

Since each zero pair is equal to zero, the value of all the counters is still 4.

It’s basically 4 + 0 + 0 + 0 + 0 + 0 + 0.

But now we can remove 6 red counters, leaving us with 10 yellow counters. 

So, 4 – (-6) = 10. 

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