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Mental Subtraction Strategies

Maths · Y3 Add & Subtract
Year 3
Lesson Guide
Explanation
Subtraction is really asking: how big is the gap between two numbers? When they're close together, like 63 − 58, don't count backwards — count UP from the small one! 58 to 60 is 2, then 60 to 63 is 3. The gap is 2 + 3 = 5. So 63 − 58 = 5, without any hard take-aways.
Your Turn
Count up: 52 − 47 and 84 − 78. Check: 47→50 is 3, 50→52 is 2 → 5; and 78→80 is 2, 80→84 is 4 → 6.
Watch Out
Counting up shines when the numbers are CLOSE. If they are far apart (83 − 21), a different tool is quicker.
Explanation
Jump back is the reverse of the addition jump. 74 − 32: jump back the tens first — 74 − 30 = 44. Then jump back the ones — 44 − 2 = 42. Jumping back tens is easy because only the tens digit changes.
Your Turn
Jump back: 86 − 24 and 97 − 45. Check: 86−20=66, −4 = 62; and 97−40=57, −5 = 52.
Watch Out
Only the SECOND number gets split into jumps. The first number is your starting spot — keep it whole.
Explanation
Here's a secret: you already know most subtraction answers, because they hide inside addition facts. 13 − 8 is the same question as '8 plus what makes 13?' You know 8 + 5 = 13 — so 13 − 8 = 5. Turning take-away into 'what's missing?' uses the facts you're already fast at.
Your Turn
Think addition: 15 − 9 and 12 − 7. Check: 9 + 6 = 15 → 6; and 7 + 5 = 12 → 5.
Watch Out
This tool is for facts you KNOW. If the addition fact is not in your head yet, bridge through ten instead.
Explanation
When you're subtracting a number ending in 9 or 8, subtract the friendly ten instead and fix up after. 52 − 19: take away 20 — that's 32. But you took 1 too many, so give it back: 32 + 1 = 33. Careful: this fix-up is the OPPOSITE direction to the addition one.
Your Turn
Try: 64 − 29 and 45 − 18. Check: 64 − 30 = 34, + 1 = 35; and 45 − 20 = 25, + 2 = 27.
Watch Out
The fix-up direction trips everyone: if you SUBTRACTED too much, you must ADD the extra back.
Explanation
Four subtraction tools: count up when the numbers are close, jump back when they're far apart, think addition when you know the fact, and friendly take-away when subtracting something ending in 8 or 9. Look before you leap: 71 − 68? They're close — count up (3!). 85 − 40? Far apart — jump back.
Your Turn
Pick a tool and solve: 41 − 38, 76 − 23, 60 − 29. Check: 3 (count up), 53 (jump back), 31 (friendly: 60 − 30 + 1).
Watch Out
There is no wrong tool if the answer is right — but the right tool makes you fast AND sure.
Step 1: Introduction
Step 1 of 5
63 − 58: how far apart are they? 586063 +2 +3 When numbers are close, count UP from the small one. 58 → 60 is 2, then 60 → 63 is 3. Gap = 5. So 63 − 58 = 5.
74 − 32 — jump back tens, then ones 424474 −30 −2 74 − 30 = 44, then 44 − 2 = 42. Big jump back first, small jump second.
13 − 8? Ask: 8 + ▢ = 13 13 − 8 = ▢ is the same question as 8 + ▢ = 13 You know 8 + 5 = 13 — so 13 − 8 = 5. Every addition fact you know is a subtraction fact in disguise!
52 − 19 — take 20, give 1 back 19 is nearly 20 52 − 20 = 32 took 1 too many → 32 + 1 = 33 Subtract the friendly ten, then give back the extra. Took 1 too MANY → add 1 back. (Opposite of the addition fix!)
Which tool for which job? Count up numbers close: 63 − 58 Jump back numbers far: 74 − 32 Think addition known facts: 13 − 8 Friendly take-away ends in 8/9: 52 − 19 Look at the numbers first, then pick the easy path. Now show your skills in the quiz and exercises!
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