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

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

53 − 8 (take away)

The numbers are far apart and we are taking away a small amount, so we count back. We call this took away. Watch the back-jumps from 53.

71 − 68 (find the difference)

These two numbers are very close. Instead of taking away, we count up from 68 to 71. We call this found the difference. The small gap we cross is the answer.

84 − 30 (take away)

The numbers are far apart, so we count back: one clean back-jump of 30 from 84.

93 − 88 (find the difference)

These two numbers are very close, so we count up from 88 to 93. The small gap we cross, 5, is the answer.

Teacher Notes

Walk each example aloud, one at a time, and name the choice before the arcs appear. Say the recording word the first time each strategy appears: take away is took away, find the difference is found the difference.

53 − 8 — far apart, small take-away, so count back through 50 (took away).
71 − 68 — very close, so count up; ask the class "how many steps from 68 to 71?" (found the difference).
84 − 30 — far apart, one tidy back-jump, no bridging needed (took away).
93 − 88 — very close, count up through 90 (found the difference).

The big idea: 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

Today we work through these subtractions together on the number line, one at a time: 45 − 7, 66 − 62, 79 − 40, 83 − 78. Before we draw the arcs each time, decide: are the numbers far apart or close together? That tells us whether to count back or count up.

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

Today we work through these together on the board: 56 − 9, then 52 − 48, then 84 − 30, then 93 − 88. Each one, decide the strategy first — far apart means count back, close together means count up — then add the jumps to reach the answer.

Reach the answer

Teacher Notes

This round is the practice bank — 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 14 · Mental Subtraction: Count Back and Count up

Download Activity Book page (PDF)

End of lesson

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Teacher Class Feed

1 - Getting Started ~4 mins

2 - Watch and Notice ~9 mins

53 − 8 (take away)

71 − 68 (find the difference)

84 − 30 (take away)

93 − 88 (find the difference)

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

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