In math, a number line is a visual representation of sequential numbers on a straight, horizontal line. Let’s learn all about this useful mathematical tool!

Author

Katie Wickliff

Published

August 29, 2023

Author

Katie Wickliff

Published

August 29, 2023

Author

Katie Wickliff

Published

August 29, 2023

Key takeaways

- Number lines strengthen mental math skills by bridging concrete and abstract knowledge.
- Number lines are used to understand how numbers relate to one another and to solve mathematical operations.
- Number lines aren’t just used in the classroom–they’re found in many places in real life.

Table of contents

A** number line** is a horizontal line with sequential numbers placed at evenly spaced intervals. While a number line can stretch indefinitely, some have specific starting and ending points. These are called closed number lines. On a number line, the value of the numbers increases as we read from right to left.

A number line, or **number line graph**, is used to compare the values of different numbers. Seeing numbers visually on a number line helps students develop strong mental math strategies. Number lines are especially useful for students moving from concrete representations of numbers (i.e. blocks, counters)– to abstract understanding. Students learn that the numbers on the number line get bigger as we move from left to right (or forward), and get smaller when we move from right to left (or backward).

Number lines are also used to perform arithmetic operations, such as adding, subtracting, multiplying, or dividing.

Integers include positive numbers, negative numbers, and zero. Integers are also always whole numbers, which means that fractions and decimals are not considered integers.

The graphic above is an example of a **negative and positive number line **and is an effective visual aid when students first learn the concept of negative numbers. A **number line with negatives** allows students to see that the positive numbers are to the right of the zero, and the negative numbers are to the left.

Plotting **fractions on a number line** allows students to compare fractions and determine their place value. As we’ve learned, the value of fractions on a number line increases as we move from left to right. Representing **fractions on a number line** helps students grasp the concept of fractions as part of a whole, as shown in this example:

Just like with fractions, a decimal is part of a whole number. A decimal is made up of an integer and a fractional part, and these two parts are separated by a decimal point. On a **decimal number line**, the decimals are plotted between two whole numbers and can be both negative and positive. Let’s check out these two examples.

Positive decimals on a number line:

Negative decimals on a number line:

Teachers and students aren’t the only ones who use number lines. In fact, our world is full of number lines that serve different purposes. Here are a just a few real life examples:

- Ruler
- Tape measure
- Thermometer
- Pressure gauge
- Long jump event
- Physicians scale

Now that we’ve learned about number lines, it’s time to practice. Complete the exercises below or head over to our math app to build more confidence in using number lines.

**Compare the numbers 12 and 17 on a number line. Which is greater?**

**Compare the numbers -7 and -2. Which is greater?**

**Using a number line to 20, solve the addition problem 8+6.**

**Using the number line, solve the subtraction problem 12-7.**

**Use the number line to multiply 2×8.**

The number 12 is to the left of the number 17, so **12 < 17**.

The number -7 is to the left of the number -2, so **-7 < -2**.

**8+6= 14**.

** 12-7=3**.

To multiply 2×8, we begin at zero and jump 8 spots 2 times. So,** 2×8=16**.

To address common questions and misconceptions, let’s dive into some frequently asked questions about number lines:

In math, a number line is a visual way to represent numbers in sequential order.

A number line is used to compare numbers and to help the student perform mathematical operations.

One example of a number line in real life is a thermometer.

Lesson credits

Katie Wickliff

Katie holds a master’s degree in Education from the University of Colorado and a bachelor’s degree in both Journalism and English from The University of Iowa. She has over 15 years of education experience as a K-12 classroom teacher and Orton-Gillingham certified tutor. Most importantly, Katie is the mother of two elementary students, ages 8 and 11. She is passionate about math education and firmly believes that the right tools and support will help every student reach their full potential.

Katie Wickliff

Katie holds a master’s degree in Education from the University of Colorado and a bachelor’s degree in both Journalism and English from The University of Iowa. She has over 15 years of education experience as a K-12 classroom teacher and Orton-Gillingham certified tutor. Most importantly, Katie is the mother of two elementary students, ages 8 and 11. She is passionate about math education and firmly believes that the right tools and support will help every student reach their full potential.

Parents, sign up for a DoodleMath subscription and see your child become a math wizard!

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