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.
Understanding Early Learners: Subtracting on a Number Line
A number line is useful because its spaces have equal size. The gap from zero to one is the same size as the gap from one to two. This makes every step trustworthy.
Before using a number line, check that no numbers are missing and that the marks are evenly spaced. Some lines show every number.
Others label only some marks, such as zero, five, and ten. On those lines, learners need to count the small spaces carefully rather than guessing from the printed labels.
A common mistake is to count the starting number as the first step. That gives an answer that is one too small. The starting point is not a hop.
It is where the counting begins. If a child starts at nine and takes away four, the spaces are nine to eight, eight to seven, seven to six, and six to five.
There are four spaces, so the result is five. Pointing to each landing place while saying the count helps connect the action, the spoken number, and the marks on the line.
Number lines can show more than taking objects away. They can show the distance between two numbers. For example, the distance from three to seven is four spaces.
This connects subtraction with addition. Since three plus four makes seven, seven minus three leaves four. Seeing both facts on one line helps learners notice related number facts.
It also explains why subtraction does not work in the same order as addition. Nine minus two has a different result from two minus nine when working only with whole numbers, because the starting places are different.
Children meet subtraction in everyday situations when a quantity becomes smaller. They may have ten stickers and give away three. They may count down the minutes until a game starts.
A number line is especially helpful when fingers are not enough or when the starting number is larger. Learners should begin with short jumps of one, then try larger jumps after they are confident. A jump of two can be checked as two single spaces.
Drawing hops above the line keeps them from losing track. It is useful to say the answer as a complete sentence, such as five are left, because the words should match the situation as well as the number.
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.