Mental Subtraction Strategies Within 100

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1 Getting Started
2 Watch and Notice
3 Try It Together
4 Mark Your Choice 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 subtraction from a hurling scoreboard: 53 − 48.

One way is to count back: start at 53 and take away forty-eight, jump by jump. Another way is to count up: start at 48 and see how far it is up to 53. Which way would you pick, and why?

Tip

Put your hand up to share. There is no wrong answer yet — we are just thinking out loud.

Teacher Notes

Display the two numbers and take two or three hands-up answers. Don't resolve which is better yet — let the noticing sit. The point pupils should land on: 48 and 53 are close, so jumping back forty-eight times is a lot of work.

Give five seconds of quiet think-time before any hands go up.

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~9 mins

Illustration for Watch and Notice

47 − 5

Watch as we take away five in small back-jumps. We start at 47 and hop back one at a time until five are gone. Where do we land?

60 − 30

Now one big back-jump of thirty. There is no need for thirty little hops when one tidy jump does it.

52 − 47

This time the two numbers are close together. Instead of counting back forty-seven, we jump up from 47 to 52 to find the gap. How big is that gap?

84 − 79

Again the numbers are close. We jump up from 79 to 84. The size of the gap is our answer.

Teacher Notes

Walk each example aloud, one at a time.

47 − 5 — small take-away, counting back is fine; land on 42.
60 − 30 — emphasise one tidy jump of thirty rather than thirty hops; land on 30.
52 − 47 — this is the key idea: the answer is the length of the gap (5), not the landing number. Say the answer is hiding in how far we jumped.
84 − 79 — repeat the count-up idea so it lands: a gap of 5 again.

For the last two, ask why would counting back forty-seven be silly here? before revealing the jump.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~8 mins

Key point

Let's work one together at the board: 46 − 4. We decide first — count back to take away, or count up to find the gap? Then a pupil makes the jumps and reads the answer.

While we work, everyone decides the route in your own head. Thumbs up if you agree with the answer on the board, thumbs sideways if you would change something.

After that we call out three more together: 80 − 20, then 63 − 58, then 71 − 67. For each one, say whether you would count back or count up before anyone answers.

Count back or count up?

Teacher Notes

This round is for talking it through together. Run only 46 − 4 on the board interactive (its range fits 40–50). The other three — 80 − 20, 63 − 58 and 71 − 67 — are decided and called aloud as a class; do not re-range the board for them. Sketch them quickly on the IWB pen if you want a visual.

Before each one, ask the class: are the numbers far apart or close together? Far apart with a small take-away (46 − 4) suits counting back; close together (63 − 58) suits counting up. Revoice a good choice: so because 58 is nearly 63, counting up is the quick route.

Watch for the common slip on count-up subtractions: pupils read the landing number (63) instead of the gap (5). Catch it by asking how far did we jump?

+15 XP

4 - Mark Your Choice in Your Copy ~2 mins

COPYBOOK MOMENT

In your maths copy, write three of the lesson's subtractions, one under the other:

52 − 47
60 − 30
84 − 79

Beside each one, write whether you counted back or counted up, and one word on why you chose that route.

Teacher Notes

Walk the room glancing at each pupil's choice and reason — this is whole-class copybook practice, not marking. Look for pupils naming "close together" or "small gap" as the reason for counting up.

+10 XP

5 - Class Challenge ~7 mins

Now you spot the smart route. We work through these one at a time: 38 − 6, then 70 − 30, then 61 − 58, then 95 − 88. The numbers get closer together as we go, so watch for the moment the gap is small enough that counting up wins.

Tip

Decide your route in your head before the pupil at the board starts. Thumbs up when you are ready with a choice.

Count back or count up?

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.

The bank is ordered so 38 − 6 invites counting back (small take-away, numbers far apart) while 61 − 58 and 95 − 88 strongly reward counting up. For each close pair ask is the gap small enough to count up? before the pupil starts. Confirm each answer with the Check button as part of your narration — yes, that's it.

+15 XP

6 - What Did We Notice? ~3 mins

MATHS TALK

One pupil says counting up can never really be subtracting, because you are adding jumps. Are they right? Where is the subtraction answer hiding when we count up to find the gap?

Teacher Notes

Listen for pupils explaining that the length of the gap is the answer — the jumps add up to the difference between the two numbers. Revoice a strong answer: so when we jump up from 58 to 61, the three steps we counted IS the answer to 61 minus 58.

Head off the lingering confusion that the landing number (61) is the answer; steer them back to how far did we travel?

+10 XP

7 - What's Next ~2 mins

What we learned today

You can subtract by counting back to take away, or by counting up to find the gap.
Both routes give the same answer — counting up is quicker when the two numbers are close together.
Look at the numbers first to choose the smart route before you start jumping.

Coming up

Key point

Next we move from jumps in our heads to writing addition down in tidy tens-and-units columns, carrying a ten when a column fills up past nine.

Teacher Notes

Keep this brief. Recap the one big idea: look first, then choose count back or count up.

+5 XP

Pupil practice

Module 2 · The Four Operations: Mental and Written Number

Lesson 14 · Mental Subtraction Strategies Within 100

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

47 − 5

60 − 30

52 − 47

84 − 79

3 - Try It Together ~8 mins

Count back or count up?

4 - Mark Your Choice in Your Copy ~2 mins

5 - Class Challenge ~7 mins

Count back or count up?

6 - What Did We Notice? ~3 mins

7 - What's Next ~2 mins

What we learned today

Coming up

Unlock the full learning experience

XP