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Using a Number Line to Subtract Up to 20

This lesson shows how to use a number line to subtract numbers up to 20. Students learn to place a starting number, jump backward the correct number of spaces, and read off the answer where they land, with a labeled diagram and worked examples.

What a Number Line Shows

A number line is a straight line marked with evenly spaced points for the numbers 0 through 20. Each point sits the same distance from its neighbors, so moving one space to the right always means adding 1, and moving one space to the left always means subtracting 1. This simple picture turns subtraction up to 20 into something you can see and count, instead of something you have to memorize right away.

Because subtraction means "how many are left" or "how far apart are two numbers," a number line is a natural tool for it: you start at one point and move backward (to the left) the number of spaces you are subtracting.

How to Subtract Using a Number Line

To subtract two numbers using a number line, follow these steps.

1. Find the first number (the one you start with) on the number line.
2. Count backward, one space at a time, for each unit in the number being subtracted.
3. The point where you land after the last jump is the answer.

For a subtraction sentence such as \( 12 - 5 \), the 12 is where you start, and the 5 tells you how many spaces to jump backward. This step-by-step jumping approach works the same way no matter which two numbers up to 20 you are working with, and it connects closely to understanding the subtraction sign as an instruction to move left.

Worked Example: 12 Minus 5

Start at 12 on the number line, then move backward 5 spaces, one at a time: 11, 10, 9, 8, 7. After the fifth jump, the landing point is 7, so \( 12 - 5 = 7 \).

Starting at 12 and jumping back 5 spaces lands on 7, so 12 minus 5 equals 7.

Worked Example: 8 Minus 3

The same method works for smaller numbers. Start at 8, then jump backward 3 spaces: 7, 6, 5. The last jump lands on 5, so \( 8 - 3 = 5 \). Whether the numbers involved are small or large, the pattern never changes: begin at the first number, jump backward once for each unit in the second number, and read the answer at the final landing spot. This is the same idea used when building up the general set of subtraction facts up to 20.

Comparing to Counting Forward

Some students prefer counting forward from the smaller number up to the larger one to find the difference, an approach covered in counting forward to subtract up to 20. Both methods use the same number line and the same spacing between numbers; the number line just makes the backward jumps for subtraction visible so you can check your counting as you go.

Common Mistakes to Avoid

Watch out for these errors when using a number line to subtract:

Counting the starting point as the first jump, which gives an answer that is one too high.
Jumping the wrong direction, moving right instead of left, which turns subtraction into addition.
Losing track partway through a long jump sequence; marking each landing point with a small tick helps.

Practicing the jumps slowly and out loud, saying each number as you land on it, builds accuracy before speed. This same careful counting habit carries over to subtracting with digits up to 20 once the numbers no longer need a drawn line.

Practice Problem

Try modeling \( 15 - 6 \) on your own number line: start at 15, jump backward 6 spaces one at a time, and see where you land. Then check your work by writing out the full subtraction statement, a skill also built through completing subtraction statements up to 20.

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