Hands-on Algebra: Adding and Subtracting Integers

Just as we have used counters to help our students learn addition and subtraction, we can use counters to help them understand addition and subtraction of integers. You will need counters of two different colors, one for positive integers and one for negative integers. We chose green blocks for our positive integers counters and black blocks for our negative integers counters.

The rules for this "game" are as follows:

A zero-pair is formed by pairing one positive counter with one negative counter.

Students can remove or add zero-pair to a set because removing or adding zero does not change the value of the set.

Using these rules, show your student how to use counters to find the sum -3 + (-2).

Place 3 negative counters and 2 negative counters on the mat to symbolize the equation.

Since there are 5 negative counters on the mat, the sum is -5. Therefore, -3 + (-2) = -5. That problem is pretty easy for students to see.

Now, use counters to find the sum -2 + 3.

Place 2 negative counters and 3 positive counters on the mat. Remind your students that it is possible to remove 2 zero-pairs.

Since 1 positive counter remains, the sum is 1. Therefore, -2 + 3 = 1.

Use the counters to find the difference between -4 - (-1).

Place 4 negative counters on the mat. Remove 1 negative counter.

Since 3 negative counters remain, the difference is -3. Therefore, -4 - (-1) = -3.

Use the counters to find the difference between 3 - (-2).

Place 3 positive counters on the mat. There are no negative counters, so you can't remove 2 negatives. 

Add 2 zero-pairs to the mat. Remember, adding zero-pairs does not change the value of the set. Now you can remove 2 negative counters.

Since 5 positive counters remain, the difference is 5. Therefore, 3 - (-2) = 5.

At this point, you can give your student a variety of simple problems that involve adding and subtracting integers, or he can make up some problems of his own. He can solve them using blocks, he can illustrate them in his journal or he can write about how he solved the problems in his math journal.