Number Lines: Operations and Comparing Integers

Lesson Plan - Get It!

Audio:

All numbers can be represented by points on a number line.

A number line can help us visualize integers and add and subtract values. It can also be used to express real-world situations, like temperature and recording yardage in football!

Look at the number line below.

Points to the left of zero represent negative numbers — their value is less than zero. Points to the right of zero represent positive numbers — their value is greater than zero. Zero (0) is neither positive nor negative.

^{By Martin Smith-Martinez [Public domain], via Wikimedia Commons}

Number lines continue in both directions indefinitely — that means forever! It would be impossible to write all the numbers on a number line, so that is why arrows are used on each end to show it goes on forever.

Number lines can show different sets of numbers, as explained below:

Counting numbers

Any number you use for counting things, such as 1, 2, 3, but not zero or fractions.

Whole numbers

Numbers beginning at zero, such as 0, 1, 2, 3 … but not fractions.

Integers

Negative and positive numbers, such as -2, -1, 0, 1, 2, but not fractions.

Number lines can also help you understand absolute value.

Absolute value is the distance between a number and the origin (or zero) on a number line. Absolute value is always a positive value.

For example, the absolute value of -3 is 3, because it is 3 units from 0.

Absolute value is shown by two vertical bars on both sides of a number. A question might ask you to find the absolute value of |−3|.

Since the vertical bars on both sides represent absolute value, then you would take the positive value of that number, which would give you 3.

• Now that you know what a number line shows you, what can you do with the information?

Number lines can be used to order and compare numbers.

Example

Arrange these integers in order from least to greatest: -2, 0, 4, 2.

For practice, look at the number line below and arrange the numbers in order as they appear from left to right: -2, -5, 2, 4, -7, 8:

Number lines can be used to graph a point on a number line.

Example

Graph these numbers on a number line: -5, 3, 0.

Number lines can be used to add and subtract numbers.

Example

Solve: -2 + 5 =

An interactive Number Line from Mathlearningcenter.org allows you to explore using negative and positive numbers on a number line.

1. Once at the site, select the icon on the bottom that displays a number line.
2. Check the box on the pop-up that says, "Show Negative Numbers" and click Done at the top.
3. Then, select the icon that shows a box with a curved arrow above it. This will allow you to determine how many units are in-between integers to perform addition and subtraction problems.
4. Place the left edge of the box on the beginning number, which is –2, as shown in the example below.
5. Then, click on the right edge of the rectangle to increase the length of the units on the number line. Since you are adding 5, the rectangle should extend 5 units to the right.
6. The ending value is your solution — in this example, 3.
7. If you were subtracting, you would still select the right side of the rectangle, but drag it to the left. It will turn red to indicate subtraction.

Below, you can see the above example being displayed:

On your own, solve 3 - 7 = .

Start at 3 on the number line. Since you are subtracting, move 7 units to the left.

• What number do you end on?

You should end on -4.

Below, you can see this example being displayed:

Discuss with an adult or teacher:

• Do the numbers increase or decrease when you move left to right on a number line?
• Do the numbers increase or decrease when you move right to left on a number line?
• Explain how to use a number line to find the absolute value of a number, such as |−7|.

Number lines are used for showing us many concepts, including integers, adding, subtracting, and absolute value.

Move on to the Got It? section to practice using number lines.