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J.2 Subtraction up to 10 using number lines

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Subtraction on a Number Line

A number line is a tool that helps us subtract by moving backward. We start at the larger number and hop to the left to subtract the smaller number.

Examples:
  • Problem: 7 − 2 = ?
    Solution: Start at 7 on the number line. Hop back 2 spaces. Land on 5. So, 7 − 2 = 5.
  • Problem: 6 − 4 = ?
    Solution: Start at 6. Move 4 hops left. Land on 2. So, 6 − 4 = 2.
Helpful Hint

On a number line, subtraction always means hopping to the left.

Hopping Backward

Each hop to the left takes away one. The number of hops shows how many we subtract.

Examples:
  • Problem: 9 − 3 = ?
    Solution: Start at 9. Move 3 hops back. Land on 6. So, 9 − 3 = 6.
  • Problem: 5 − 1 = ?
    Solution: Start at 5. Move 1 hop back. Land on 4. So, 5 − 1 = 4.
Helpful Hint

Count each hop carefully. Every hop lowers the number by one.

Finding the Difference

Subtraction also shows the distance between two numbers on the number line. The difference is how many hops it takes to move from one number to the other.

Examples:
  • Problem: What is 8 − 5?
    Solution: Start at 8. Hop back until you reach 5. Count 3 hops. So, 8 − 5 = 3.
  • Problem: What is 7 − 2?
    Solution: Start at 7. Hop back to 2. Count 5 hops. So, 7 − 2 = 5.
Helpful Hint

Think of subtraction as finding how far apart two numbers are on the number line.

Word Problems on the Number Line

We can solve subtraction stories by showing them on a number line. Start with the total, then hop back to find what remains.

Examples:
  • Problem: Alex has 8 stickers. He gives 3 away. How many are left?
    Solution: Start at 8. Move 3 hops back. Land on 5. So, 8 − 3 = 5.
  • Problem: There are 6 balloons. 2 pop. How many balloons remain?
    Solution: Start at 6. Move 2 hops back. Land on 4. So, 6 − 2 = 4.
Helpful Hint

Draw a number line for each story problem. Show the hops to make the subtraction clear.

Practice with Everyday Situations

We use subtraction on number lines to solve problems about daily life, such as sharing, using, or losing items.

Real-Life Examples:
  • Problem: You have 7 cookies. You eat 2. How many are left?
    Solution: Start at 7. Move 2 hops back. Land on 5. So, 7 − 2 = 5.
  • Problem: There are 10 chairs. 4 are moved away. How many chairs remain?
    Solution: Start at 10. Move 4 hops back. Land on 6. So, 10 − 4 = 6.
Try This

Create your own subtraction stories. Use a number line to show the hops and find the answer.

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