Addition & Subtraction • Topic 3 of 5

Mental Mathematics

Mental maths is not just doing the written algorithm in your head; it is choosing a smarter route, and the NCF (2005 and 2022) wants teachers to value the route a child invents over a single official method. For addition the workhorse strategies are: making tens, where you bridge through 10 (9 + 6 becomes 9 + 1 + 5 = 15); adding in chunks by place value (34 + 25 becomes 30 + 20 then 4 + 5, giving 59); doubles and near doubles (8 + 9 is 8 + 8 + 1 = 17); compensation, where you round to a friendly number then adjust (29 + 15 is 30 + 15 - 1 = 44); and counting on from the larger number, helped by the commutative property (think of 2 + 19 as 19 + 2 = 21). For subtraction: counting back for small amounts (45 - 3 = 42); counting up to find a difference, the shopkeeper's method (203 - 198 = 5 by counting 198 up to 203); subtracting in chunks (76 - 32 is 76 - 30 then - 2 = 44); compensation (65 - 19 is 65 - 20 + 1 = 46); and using the inverse, turning subtraction into a missing-addend question. CTET often shows a child's working and asks you to name the strategy, so recognise these patterns rather than just being able to use them.

✅ Solved examples

1. Add 58 + 24 using compensation, and name each step.
Round 58 up to 60, which adds 2 too many. So 60 + 24 = 84, then subtract the extra 2: 84 - 2 = 82. The answer is 82. The strategy is compensation (round and adjust).
2. Find 203 - 198 by counting up, and explain why this is efficient here.
Count up from 198: to 200 is 2, then 200 to 203 is 3, total 2 + 3 = 5. The answer is 5. Counting up is efficient because the numbers are very close, so borrowing would be wasted effort.
3. Add 47 + 36 by adding in chunks (place-value partitioning).
Add the tens of the second number first: 47 + 30 = 77. Then add the ones: 77 + 6 = 83. The answer is 83.
4. A child solves 65 - 19 by saying "65 - 20 is 45, then add 1 to get 46". Which strategy is this?
Compensation. The child rounded 19 up to 20, subtracted too much by 1, then added that 1 back. The answer, 46, is correct.

✏️ Practice — try these, take hints as needed

1. Use making tens to add 8 + 5 mentally and show the bridge.
Split the 5 to complete a ten with 8.
8 + 2 = 10.
13 (8 + 2 = 10, then 10 + 3 = 13)
2. Find 76 - 32 by subtracting in chunks.
Take away the tens, then the ones.
76 - 30 first.
44
3. Name the strategy: a child works out 6 + 7 as "6 + 6 = 12, then 12 + 1 = 13".
It builds on a known double.
6 + 6 is the anchor.
Doubles / near doubles
4. Add 29 + 15 by compensation.
Round 29 to a friendly ten, then adjust.
30 + 15, then take 1 back.
44

📝 Topic test — 8 questions

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