Mental Subtraction: Count Back and Count up

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1 Getting Started
2 Watch and Notice
3 Try It Together
4 Sort Them in Your Copy
5 Class Challenge
6 What Did We Notice?
7 What's Next
Pupil practice

1 - Getting Started ~4 mins

Illustration for Getting Started Here is a quick one to do in your head: what is 62 − 58?

When you have an answer, think about how you got it. Did you take 58 away from 62, step by step? Or did you start at 58 and count up to 62? Both can work, but one of them is much faster here.

Teacher Notes

Take three hands-up answers, not open call-outs. Ask each pupil how they did it, not just the answer. Listen for the split between "I took away" and "I counted up".

Because 62 and 58 are very close, counting up (4) is far quicker than counting back fifty-eight steps. Hold that contrast — it is the whole lesson.

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~9 mins

Four subtractions, one at a time: 53 − 8, 71 − 68, 84 − 30 and 93 − 88.

Say each one aloud before the arcs appear, then decide: do we count back, or count up? Look at how far apart the two numbers are before you choose.

Teacher Notes

Name the choice before each set of arcs, and give the recording word the first time it appears: take away is took away, find the difference is found the difference.

53 − 8: far apart, small amount, so count back (took away) — back 3 to 50, then back 5 more, landing on 45.

71 − 68: very close, so count up (found the difference) — ask "how many steps from 68 to 71?" Up 2 to 70, then up 1, difference 3.

84 − 30: far apart, one tidy back-jump of 30, no bridging, lands on 54 (took away).

93 − 88: very close, count up through 90 — up 2, then up 3, the gap of 5 is the answer (found the difference).

Big idea to draw out: close numbers reward counting up, far-apart numbers reward counting back.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~11 mins

Now we work four subtractions together on the one number line: 45 − 7, 66 − 62, 79 − 40 and 83 − 78.

For each one, a pupil comes up and does three things: tap the start number and type the number we are subtracting from, say whether the two numbers are far apart or close together, then add the jumps. Far apart means count back. Close together means count up. The rest of the class agrees or corrects out loud before we move on.

Count back or count up?

Teacher Notes

This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud. Work one subtraction at a time, re-setting the number line for each so the close pairs (66 − 62, 83 − 78) show on a zoomed-in scale where the small hops are clearly visible; the far-apart pairs use a wider scale.

For each one, ask first: far apart or close together? Then let the pupil draw the arcs.

45 − 7 — far apart, count back through 40 (−5, then −2).
66 − 62 — close, count up 4 from 62.
79 − 40 — far apart, one back-jump of 40.
83 − 78 — close, count up 5 from 78.

Revoice a strong answer: so because 78 and 83 are nearly touching, counting up is the short way.

+15 XP

4 - Sort Them in Your Copy ~3 mins

COPYBOOK MOMENT

In your maths copy, work these three subtractions. Beside each answer, write either took away (when you counted back) or found the difference (when you counted up) to show the strategy you chose.

75 − 6
63 − 59
80 − 35

Teacher Notes

Walk the room glancing at the strategy word beside each answer — this is whole-class copybook practice, not marking. Look for pupils who count up for 63 − 59 (close, found the difference) and take away for 75 − 6 (far apart, small amount, took away).

+10 XP

5 - Class Challenge ~8 mins

Now you work these four on your own, one at a time: 56 − 9, 52 − 48, 84 − 30 and 93 − 88.

For each one, decide the strategy before you touch anything. Far apart means count back. Close together means count up. Then add the jumps until you land on the answer, and press Check.

Reach the answer

Teacher Notes

These are the practice questions — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.

56 − 9 — far apart; count back through 50 to 47.
52 − 48 — very close, count up 4 from 48 to 52.
84 − 30 — far apart; count back 30 to 54.
93 − 88 — very close, count up 5 from 88 to 93.

Ask before each: are the two numbers far apart or close together? That is the decision the lesson is drilling.

+15 XP

6 - What Did We Notice? ~3 mins

MATHS TALK

Look at the gap between the numbers — that gap is how many jumps counting up would take.

Why is counting up the quick way for 91 − 88 but the slow way for 91 − 4? For 91 − 88 the gap is tiny, so counting up is only a few short hops. For 91 − 4 the gap is huge, so counting up would mean lots of hops — it is quicker to take 4 away.

Teacher Notes

Listen for pupils naming the gap between the numbers as the deciding thing. For 91 − 88 the gap is tiny, so counting up is three short hops; for 91 − 4 counting up would mean eighty-seven hops, while taking away 4 is quick. Revoice: so we pick the strategy that gives the fewest jumps.

+10 XP

7 - What's Next ~2 mins

Today we learned

Subtraction can be done two ways: take away (count back) or find the difference (count up).
Close numbers are quicker to count up; far-apart numbers are quicker to count back.
Jump arcs let us see each step of the strategy on the number line.

Coming up

Next we move on to writing addition out in columns, where we regroup across the place-value columns.

Teacher Notes

Recap the two strategies by pointing back at one close pair and one far-apart pair from the board.

+5 XP

Pupil practice

Module 2 · The Four Operations: Mental and Written Number

Lesson 15 · Mental Subtraction: Count Back and Count up

Download Activity Book page (PDF)

End of lesson

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This lesson is copyright of Coding Ireland 2017 - 2025. Unauthorised use, copying or distribution is not allowed.

Teacher Class Feed

1 - Getting Started ~4 mins

2 - Watch and Notice ~9 mins

3 - Try It Together ~11 mins

Count back or count up?

4 - Sort Them in Your Copy ~3 mins

5 - Class Challenge ~8 mins

Reach the answer

6 - What Did We Notice? ~3 mins

7 - What's Next ~2 mins

Today we learned

Coming up

Unlock the full learning experience

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