What does counting up to subtract mean?

Instead of counting backwards, you start at the smaller number and count forward to the bigger one. The number of steps you take is the answer to the subtraction.

Why does counting up give the right answer?

Subtraction can mean finding the gap, or difference, between two numbers. Counting up measures that gap directly, so it gives the same answer as taking away.

When should I count up instead of counting back?

Count up when the two numbers are close together, like 12 − 9, because the jump is small and you are less likely to make a mistake.

Counting Up to Subtract | Math

Two meanings of subtraction

Subtraction can mean two things. The first is taking away — you have 12 sweets, you eat 9, how many are left? The second is finding the difference — Tom is 12 and his sister is 9, how many years older is Tom?

Both give the same answer, but the second meaning unlocks a lovely strategy: counting up. Instead of counting backwards (which is fiddly), you start at the smaller number and count forward to the bigger one. The size of your journey is the answer.

How counting up works

Take 12 − 9. Start at 9 and count up until you reach 12, keeping track of your jumps:

9 → 10 (1 jump)
10 → 11 (2 jumps)
11 → 12 (3 jumps)

You made 3 jumps, so 12 − 9 = 3.

Why does this work? Because the gap from 9 up to 12 is exactly the same as the gap from 12 down to 9. Measuring the difference either way gives the same number — and counting forwards is easier for our brains than counting backwards.

If counting on a line is new to you, our lesson on the number line shows the jumps clearly.

A number line in your head

Picture a number line. To subtract, put a finger on the smaller number and hop along to the bigger one, counting the hops.

Subtraction	Start at	Count up to	Jumps	Answer
12 − 9	9	12	3	3
15 − 13	13	15	2	2
20 − 17	17	20	3	3
31 − 28	28	31	3	3

See how the numbers in each row are close together? That is when counting up shines.

Worked example 1: a small gap

Work out 15 − 13.

Start at 13: 14 (one), 15 (two). You made 2 jumps.

So 15 − 13 = 2.

Worked example 2: bridging a ten while counting up

Work out 23 − 18.

Start at 18. First hop up to the tidy ten: 18 → 20 is 2 jumps. Then 20 → 23 is 3 more jumps. Altogether 2 + 3 = 5 jumps.

So 23 − 18 = 5. Stopping at the tidy 10 keeps the counting neat.

Worked example 3: shopping change

You buy a toy for £8 and pay with a £10 note. How much change?

Count up from 8 to 10: 9, 10 — that is 2. Your change is £2. Shopkeepers have counted up to give change for hundreds of years!

Why this strategy matters

Counting back is where many subtraction mistakes happen — it is easy to lose your place. Counting up turns the problem into forward counting, which is far more reliable, especially when the numbers are close. It also builds the idea of difference, which you will use in time problems, money problems and measuring.

Try it yourself

You will need a number line drawn from 0 to 30 (or use a ruler).

Choose two close numbers, like 14 and 11.
Put your finger on the smaller one and hop to the bigger one.
Count your hops aloud: "12, 13, 14 — three hops!"
Write the matching subtraction: 14 − 11 = 3.
Challenge: Try a pair that crosses a ten, like 22 − 17, and hop to the tidy ten first.

What's next?

Counting up is one of several subtraction tools. Compare it with written methods in addition and subtraction, and see how it helps with money in calculating with money.

Counting Up to Subtract

Key takeaways