Opposites on a Number Line

Contributor: Ashley Nail. Lesson ID: 13899

Today is Opposite Day! Did you know that numbers have opposites? In this lesson, you will use number lines to find the opposite of positive and negative numbers.

categories

Integers/Rational Numbers and Operations, Middle School, Pre-Algebra

subject
Math
learning style
Auditory, Visual
personality style
Lion, Otter, Beaver, Golden Retriever
Grade Level
Middle School (6-8)
Lesson Type
Quick Query

Lesson Plan - Get It!

Audio:

Raymond and his younger sister are getting ready for school. It’s Opposite Day, and they decide to dress for the opposite temperature!

Raymond looks up the temperature on his phone. It says the temperature is -8° F. Both of them go and get dressed before breakfast.

Raymond walks into the kitchen in summer clothes. Raymond’s sister walks in with a big puffy winter coat.

Raymond and his sister

  • Who is dressed correctly for the opposite of -8° F?

We know -8° F is cold, really cold. We also know the opposite of cold is hot.

  • But what is the opposite of -8?

Let’s look at other examples of opposite numbers!

  • How can we find the opposite of 5?

First, we’ll find positive 5 on the number line. It is 5 to the right of 0.

5 on a number line

An opposite integer is on the other side of 0, but the same distance from zero.

So, for example, the integer +5 is on the right side of 0 and 5 spaces away from 0.

To find the opposite of +5, we need to look to the other side of 0. We will find the integer that is also 5 spaces away from 0 but this time to the left.

opposite of 5

The opposite of +5 is -5.

  • Seems pretty simple, right?

Give it a try.

Now, let’s take it a step further.

  • How can we rewrite the phrase the opposite of with simpler math symbols?

In math, we can use the negative symbol to show opposites.

The opposite of x is -x.

So we could write the opposite of 7 as simply -7.

  • How would we write the opposite of -y?

If the negative symbol tells us to find the opposite, we can write it as -(-y).

Let’s try it!

Look at y on the number line. We want to find the value of -(-y).

y on number line

First, we see that y = 2.

Next, let’s find -y. We know the negative symbol tells us to find the opposite of y.

opposite of y on number line

The opposite of y is -y.

-y = -2

Lastly, let's find -(-y).

- -y on number line

-(-y) is telling us to find the opposite of -y or the opposite of the opposite of y.

-(-y) = 2

  • Are you ready to try finding opposites on a number line on your own?

If you think you need more review first, watch Opposite Numbers (6.NS.6) from School 21:

When you are ready to practice, click NEXT to visit the Got It? section.

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