*Contributor: Jenna Schooler. Lesson ID: 11546*

It's been said that a picture is worth a thousand words. Did you know that simple pictures can solve a thousand math operations? Learn to easily add positive and negative integers using zero pairs!

categories

subject

Math

learning style

Visual

personality style

Beaver, Golden Retriever

Grade Level

Middle School (6-8)

Lesson Type

Quick Query

Have you ever gotten in an elevator traveling up when you actually wanted to go down? Did you wind up getting stuck traveling all the way to the top floor of the building before you could travel down to reach your destination? This may have happened to you at some point, and surely you were more than a bit annoyed, but did you stop to think about how flights of stairs travel one direction or the other? Math is everywhere, even inside an elevator adventure!

Let's begin by talking about zero pairs and their value.

A *zero pair* is a combination of a red and yellow counter. Keep in mind that red is negative and yellow is positive. These two words are known as *opposites* or *inverses*. In math, opposites cancel each other out to zero. So, one red counter + one yellow counter = 0.

A zero pair is a combination of opposites, a positive and a negative number with the same absolute value. In this example, zero pairs are represented by red and yellow counters:

Let's take a look at a few examples. You will need to use red and yellow counters for this section of the lesson. Also, take a piece of paper and use it as a mat. Place four yellow counters on the mat. Then, place six red counters on the mat.

- How many total counters are on your mat?

If you said 10, you are correct. Now, think about the value of the counters on the mat. In order to find the value, you MUST have only ONE color on the mat.

- How many colors are there now?

Tell your teacher or parent your answer. There are two colors on the mat. In order for you to find the value, you need to eliminate the zero pairs. By eliminating zero pairs, you will have one color on your mat and you will be able to identify the value of the counters on the mat.

Now back to the example:

- How many zero pairs can you eliminate (Remember: one red + one yellow = zero pair)?

If you said four pairs, you are correct!

- After eliminating the pairs, how many counters are left on the mat?

There are two counters remaining. Now the question is,

- "Would the value of the remaining two be positive or negative?"
- How do you know?

The answer in this case is negative. Take a closer look at how to solve this problem:

You just completed an addition problem with rational numbers. Now that you have manipulated this problem, write a number sentence to represent this problem.

- How many counters of each color did you place on your mat?

There were 4 yellows (+4), 6 reds (-6), and the operation in this equation was addition. The number sentence should read as follows: +4 + -6 = -2, or -6 + 4 = -2.

You may see a set of ( ) around negative numbers to keep the signs separate; for instance, +4 + (-6) = -2.

Try a few more:

For this activity, you will need to download and print *Adding It Up: Get It*, located in **Downloadable Resources** in the right-hand sidebar. Place the following counters on your mat, find the value, and write a number sentence to represent the problem:

- 7 red and 4 yellow
- 5 yellow and 2 yellow
- 8 yellow and 3 red

You can check your answers with the *Adding It Up: Get It Answer Key* (**Downloadable Resources**).

For more information on this topic, watch *Adding Integers with Counters*, by Danielle Krueger:

Now that you have gotten a handle on how to add rational numbers using counters, take it to the next level and build your skills even more in the *Got It?* section.

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