A number line helps you see subtraction as moving backward. When you subtract, you start on the first number and hop left. Each hop takes away 1.
The number you land on is the answer.
For 8 − 3, start at 8 on the number line. Then make 3 backward hops: 8 to 7, 7 to 6, and 6 to 5. Since you land on 5, the answer is 8 − 3 = 5.
This method helps learners count carefully and understand what subtraction means.
Key Facts
- Subtraction means taking away or finding what is left.
- On a number line, subtract by hopping backward to the left.
- In a − b = c, start at a, hop back b spaces, and land on c.
- 8 − 3 = 5 because 3 backward hops from 8 land on 5.
- Each hop on the number line counts as 1.
- Subtracting 0 means no hops, so the number stays the same: 6 − 0 = 6.
Vocabulary
- Number line
- A number line is a straight line with numbers placed in order to help count, add, and subtract.
- Subtract
- To subtract means to take away an amount from a starting number.
- Backward hop
- A backward hop is one jump to the left on a number line.
- Starting number
- The starting number is the number where you begin before subtracting.
- Difference
- The difference is the answer to a subtraction problem.
Common Mistakes to Avoid
- Starting on the second number instead of the first number. In 8 − 3, you must start at 8 because it is the number you are taking away from.
- Hopping forward instead of backward. Subtraction means move left on the number line, not right.
- Counting the starting number as the first hop. A hop happens when you move from one number to the next, so 8 to 7 is the first hop.
- Making too many or too few hops. The number being subtracted tells exactly how many backward hops to make.
Practice Questions
- 1 Use a number line from 0 to 10 to solve 7 − 2.
- 2 Use backward hops to solve 9 − 4.
- 3 Explain why 6 − 3 lands on a smaller number than 6 + 3.