Look at this: 73 − 28.

If you had to do it in your head right now, would you count up from 28 until you reach 73, or would you start at 73 and take 28 away?

Watch three subtractions on the number line. The same subtraction can be done two different ways — and a bigger subtraction tells us when one way fits better than another.

Counting on: 73 − 28 = 45

Start at 28. Jump forward to 30 (+2), then to 70 (+40), then to 73 (+3). The forward jumps total 45 — that is the answer.

Counting-on works best when the two numbers are close together — the gap is small enough to hop across in a few friendly jumps.

Take away: 73 − 28 = 45

Start at 73. One single back-jump of 28 lands you on 45. Same answer, completely different picture.

Take-away works best when the number you are subtracting is small and easy to hold in your head as one back-jump.

Decomposition: 305 − 178 = 127

Now the numbers are bigger. Break 178 into 100 + 70 + 8 and take each chunk away in its own back-jump.

Decomposition works best when the numbers are bigger or messier — breaking the subtraction into place-value chunks is friendlier than one massive back-jump.

Today's exploration on the number line: for each subtraction called out, pick a strategy that you think fits — counting-on, take-away, or decomposition. Sometimes more than one works, and that is fine — be ready to say why you chose yours.

One pupil at a time comes to the board, names their chosen strategy out loud, and drags the jumps. Before they touch the screen, think which strategy you would choose — you might pick a different one.