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Written Addition with Trading

Maths · Y3 Add & Subtract
Year 3
Lesson Guide
Explanation
Written addition is all about tidy columns. Line the numbers up from the RIGHT, so ones sit under ones and tens under tens. 342 + 25: the 5 goes under the 2 (both ones), the 2 goes under the 4 (both tens). The hundreds column has only the 3 — that's fine.
Your Turn
Set out 431 + 56 in columns on paper. Check: 6 under the 1, 5 under the 3, and the 4 alone in the hundreds.
Watch Out
Never line up from the left! 342 + 25 with left lining would add hundreds to tens — messy and wrong.
Explanation
Always add starting from the ones column, then move left. 342 + 25: ones first, 2 + 5 = 7. Then tens, 4 + 2 = 6. Then hundreds, just the 3. Answer: 367. When no column adds past 9, it's this smooth every time.
Your Turn
Work 431 + 56 in columns. Check: ones 1+6=7, tens 3+5=8, hundreds 4 → 487.
Watch Out
Right to left, always — the next step shows why. Starting from the left falls apart as soon as trading appears.
Explanation
Sometimes the ones column overflows: in 47 + 36, the ones give 7 + 6 = 13. But 13 is really 1 ten and 3 ones! So write the 3 in the ones place and TRADE the ten up — write a little 1 above the tens column. Then add the tens: 1 + 4 + 3 = 8. Answer: 83.
Your Turn
Work 58 + 27 with a trade. Check: 8+7=15 → write 5, carry 1; then 1+5+2=8 → 85.
Watch Out
The little carried 1 is a real ten — don't forget to add it in the next column, and never write '13' inside one column.
Explanation
Bigger numbers just mean more of the same. 368 + 257: ones, 8 + 7 = 15 — write 5, carry 1. Tens, 1 + 6 + 5 = 12 — write 2, carry 1 again. Hundreds, 1 + 3 + 2 = 6. Answer: 625. One column at a time, carrying whenever a column passes 9.
Your Turn
Work 476 + 348. Check: 6+8=14 (write 4, carry 1); 1+7+4=12 (write 2, carry 1); 1+4+3=8 → 824.
Watch Out
Write each carry down the moment it happens. Holding carries in your head is where answers go wrong.
Explanation
Great mathematicians check their work with a rough estimate. 368 is about 400, 257 is about 300 — so the answer should be around 600–700. We got 625: sensible! If you'd got 265 or 1625, the estimate would shout 'check again!'. It usually catches a forgotten carry.
Your Turn
Estimate first, then work exactly: 189 + 214. Check: estimate ≈ 200 + 200 = 400; exact = 403 ✓. Now do the quiz and exercises!
Watch Out
An estimate is a rough friend, not the answer — always finish with the exact column sum.
Step 1: Introduction
Step 1 of 5
3 4 2+ 2 5 Ones under ones, tens under tens ones line up ↓ Rule 1: line up from the RIGHT. 342 + 25: the 2 and 5 (ones) sit together, the 4 and 2 (tens) sit together.
3 4 2+ 2 53 6 7 Right to left: ones, tens, hundreds ones: 2 + 5 = 7 · tens: 4 + 2 = 6 · hundreds: 3 → 367
14 7+ 3 68 3 47 + 36 — the ones overflow! 7 + 6 = 13 = 1 ten and 3 ones Write the 3, carry the little 1 ten to the tens column.
1 13 6 8+ 2 5 76 2 5 368 + 257 — two trades ones: 8+7=15 → write 5, carry 1 · tens: 1+6+5=12 → write 2, carry 1 hundreds: 1+3+2=6 → answer 625
Does 625 make sense? 368 + 257 ≈ 400 + 300 = 700-ish Exact answer 625 — close to 700? Yes ✓ Round each number, add roughly, compare. If your exact answer is far from the estimate, hunt for a lost carry!
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