Subtraction Strategies: Counting on, Take Away, Decomposition

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1 Getting Started
2 Watch and Notice
3 Try It Together
4 Work It Three Ways in Your Copy
5 Class Challenge
Pupil practice

1 - Getting Started ~4 mins

Illustration for Getting Started Here is a subtraction: 73 − 28. Would you count UP from 28 until you reach 73, or would you take 28 AWAY from 73? Both give the same answer, but one might feel easier. Which would you pick, and why?

Teacher Notes

Take three hands-up answers, not open call-outs. Do not confirm which is 'right' yet — the point is that two very different routes reach the same answer. Give five seconds of quiet think-time first.

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~9 mins

Three subtractions, each shown with the strategy that suits its numbers. Counting on is quick when the two numbers are close; taking away suits subtracting a small amount; decomposition handles a bigger one. Watch how each jumps along the line and where it lands.

Teacher Notes

Counting on 73 − 28: start 28, +2 to 30, +40 to 70, +3 to 73. Answer is the size of the jumps, 2+40+3 = 45, NOT where we land. This is the trap — press on it.

Taking away 73 − 28: one back-jump of 28 from 73 lands on 45. Contrast the landing here — we land ON the answer, not on the big number. Ask which route they'd rather do in their head.

Decomposition 305 − 178: break 178 into 100+70+8. Back 100 to 205, back 70 to 135, back 8 to 127. Pause for two hands-up predictions (hands up, not call-outs) of where the final −8 lands, then confirm it is 127.

Point of the last one: the same rule scales to three digits.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~11 mins

We work through three subtractions together on the board. For each one, choose a strategy first, then predict where the arc will land before you draw it: 64 − 39, then 52 − 27, then 246 − 123.

Choose a strategy and draw the arcs

Teacher Notes

This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud.

Run each subtraction in two beats. First ask the whole class which strategy fits and take two hands-up answers before anyone touches the board. Then ask where the first arc will land and take a couple more hands-up answers before the pupil at the board draws it. Listen for pupils reaching for count-on when the numbers are close (64 − 39) and for take-away or decomposition when they are far apart. Revoice a strong answer: so when the numbers are near each other, counting on is only a few short hops.

+15 XP

4 - Work It Three Ways in Your Copy ~3 mins

COPYBOOK MOMENT

In your maths copy, work each subtraction using a different strategy and label which strategy you used. Try these three:

81 − 46 (count on)
90 − 35 (take away)
428 − 215 (decomposition)

Write the strategy name beside each one so you can see which felt easiest.

Teacher Notes

Walk the room and glance for a sensible strategy label beside each subtraction — this is whole-class copybook practice, not marking. Prompt any pupil who used the same strategy three times to try a different one on at least one.

+10 XP

5 - Class Challenge ~8 mins

Key point

When we count ON, the answer is the TOTAL of our jumps, not the number we land on.

Today we take turns at the board and use the jump route shown for each subtraction: 73 − 28, then 64 − 39, then 305 − 178, then the stretch 1,000 − 487. Remember: when we count ON, the answer is the TOTAL of our jumps, not the number we land on. For 1,000 − 487 we count on and land on 1,000, but the answer is the size of the jumps added together. That last one has an empty thousand full of zeros — think about whether counting on from 487 might beat taking away.

Reach the answer in the fewest jumps

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.

The stretch 1,000 − 487 is the key one. Counting on from 487 takes a short jump of +3, then +10, then +500. Add those jumps: 3 + 10 + 500 = 513, so the answer is 513 even though we land on 1,000. This avoids the cascade of borrowing that take-away forces through all those zeros. Say the totalling aloud so the count-on trap is closed off. Contrast aloud with the cascade of borrows take-away would need through the zeros.

+15 XP

Pupil practice

Module 2 · Operations and Computational Fluency Number

Lesson 19 · Subtraction Strategies: Counting on, Take Away, Decomposition

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Teacher Class Feed

1 - Getting Started ~4 mins

2 - Watch and Notice ~9 mins

3 - Try It Together ~11 mins

Choose a strategy and draw the arcs

4 - Work It Three Ways in Your Copy ~3 mins

5 - Class Challenge ~8 mins

Reach the answer in the fewest jumps

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