Number Line Subtraction
A number line makes subtraction visible. Subtracting means moving left — the opposite direction to addition.
Take-Away on a Number Line
Start at the minuend (the number you're subtracting from) and jump left by the size of the subtrahend (the number being taken away).
Why it works: Subtraction means taking an amount away, and on a number line, moving left is exactly what "taking away" looks like — each step left reduces the total by one. Wherever you land after all the jumps is exactly what's left, so you can see the answer instead of just calculating it.
Calculate 10 − 4 using a number line.
Start at 10. Since we are subtracting 4, make one jump of 4 spaces to the left. You land on 6 — that's the answer.
Counting Up to Find the Difference
Start at the subtrahend and count up (to the right) to the minuend. The number of steps you take is the difference.
Why it works: This is the method a shopkeeper uses to work out change — instead of subtracting, they count forward from the price to the amount paid. The distance you travel counting up from the smaller number to the larger one is always exactly the same as the difference between them, and it's often faster and less error-prone than jumping left, especially when the two numbers are close together.
Calculate 13 − 8 using a number line.
Start at 8 (the smaller number) and count up to 13 (the larger number). That's a jump of 5 spaces to the right — so the difference is 5. Notice that here, the size of the jump is the answer, not the number you land on.
Calculate 82 − 47 using a number line by counting up in friendly hops.
Start at 47. Jump +3 to reach the friendly number 50. Jump +30 to reach 80. Jump +2 to reach 82. Add up the hops: 3 + 30 + 2 = 35.
Bridging Through Ten
For subtractions that cross a multiple of ten, jump left to the nearest ten first, then subtract the remaining amount.
Why it works: It's much easier to picture a jump that lands exactly on a round number like 20 than one that lands on an awkward number like 15 directly. Splitting the jump into "enough to reach the ten below" plus "the rest" turns one tricky hop into two easy ones.
Calculate 23 − 8 using a number line.
Start at 23. Split 8 into 3 + 5. Jump left 3 first to land exactly on 20, then jump left the remaining 5 to land on 15.
Large-Jump Method
For bigger numbers, jump left by the tens first in one large hop, then by the ones.
Calculate 67 − 34 using a number line.
Start at 67. Split 34 into 30 + 4. Jump left 30 to land on 37, then jump left 4 more to land on 33.
Which Method?
| Method | Best for | Direction |
|---|---|---|
| Jump left | Small subtrahends, visual learners | Left |
| Count up | Numbers close together | Right |
Key Takeaways
- Subtraction on a number line = jumping left.
- Counting up from subtrahend to minuend gives the same answer more efficiently when numbers are close.
- Bridging through ten is powerful when a subtraction crosses a multiple of 10.
Practice: Jump Left
Subtract using number-line jumps — a big jump left for the tens, then a small jump for the ones. If you get it wrong (or leave it blank), we'll show every jump.