Key ideas
Chimney sums
Put the bigger number on top. Line up the units, tens and hundreds.
Start from the right. If a column adds to 10 or more, carry the ten into the next column.
Exchanging
When subtracting, if the top digit is too small, exchange: take 1 from the next column and make the digit 10 bigger.
Never take the top from the bottom.
In your head
Round to a friendly number, then fix it.
398 + 245: 400 + 245 = 645, then − 2 = 643.
Counting on
To subtract, count up from the smaller number to the bigger one in hops, then add the hops.
Great for 1000 − 364 or working out change.
Check
Check a subtraction by adding: if 742 − 385 = 357, then 357 + 385 should give 742.
Adding with a chimney sum
Calculate 476 + 358(2 marks)
Set it out.Bigger number on top. Units under units, tens under tens, hundreds under hundreds.✓1
In plain EnglishLining up the columns matters more than anything else in a chimney sum.
Add each column, starting on the right.
476 + 358 = 834✓2
| 1 | 1 | ||
| 4 | 7 | 6 | |
| + | 3 | 5 | 8 |
| 8 | 3 | 4 |
In plain EnglishUnits: 6 + 8 = 14. Write 4 and carry the 1 ten. Tens: 7 + 5 + 1 = 13. Write 3 and carry 1 hundred. Hundreds: 4 + 3 + 1 = 8.
Calculate 736 + 2489(2 marks)
Bigger number on top.2489 + 736✓1
In plain English2489 has more digits, so it goes on top. Line the 6 up under the 9: both are units.
Add, carrying each time.
= 3225✓2
| 1 | 1 | 1 | ||
| 2 | 4 | 8 | 9 | |
| + | 7 | 3 | 6 | |
| 3 | 2 | 2 | 5 |
In plain EnglishEvery column here makes 10 or more, so there is a carry each time. The small green digits are the carries.
Subtracting with exchanging
Calculate 742 − 385(2 marks)
Units: 2 − 5.You can't take 5 from 2, so exchange 1 ten✓1
In plain EnglishTake 1 ten from the 4 tens (leaving 3) and give it to the units: 2 becomes 12. 12 − 5 = 7.
Keep going.
742 − 385 = 357✓2
| 67 | 134 | 122 | |
| − | 3 | 8 | 5 |
| 3 | 5 | 7 |
In plain EnglishTens: 3 − 8 won't go, so exchange again: 7 hundreds become 6, and 3 tens become 13. 13 − 8 = 5. Hundreds: 6 − 3 = 3. Check: 357 + 385 = 742.
Calculate 5003 − 1268(2 marks)
Units: 3 − 8.No tens or hundreds to exchange from, so go to the thousands✓1
In plain EnglishTake 1 thousand from the 5 (leaving 4). That makes 10 hundreds: keep 9 and pass 1 on. That makes 10 tens: keep 9 and pass 1 on. The units become 13.
Subtract each column.
5003 − 1268 = 3735✓2
| 45 | 90 | 90 | 133 | |
| − | 1 | 2 | 6 | 8 |
| 3 | 7 | 3 | 5 |
In plain English13 − 8 = 5, 9 − 6 = 3, 9 − 2 = 7, 4 − 1 = 3. Check: 3735 + 1268 = 5003.
⚠ A common mistake: taking the smaller digit from the bigger one in every column (8 − 3 = 5). Always take the bottom from the top, and exchange when you need to.
Adding and subtracting in your head
Work out 398 + 245 in your head.(1 mark)
Round to a friendly number.398 is 2 less than 400400 + 245 = 645
In plain English398 is awkward, but 400 is easy to add.
Adjust.645 − 2 = 643✓1
In plain EnglishYou added 2 too many, so take 2 back off.
Work out 563 − 199 in your head.(1 mark)
Round to a friendly number.199 is 1 less than 200563 − 200 = 363
In plain EnglishTaking away 200 is easy: just change the hundreds digit.
Adjust.363 + 1 = 364✓1
In plain EnglishYou took away 1 too many, so add 1 back on.
Counting on
Calculate 1000 − 364(2 marks)
Count on to a friendly number.364 → 400 is + 36✓1
In plain EnglishStart at the smaller number. Hop to the next hundred first.
Add the hops.400 → 1000 is + 60036 + 600 = 636✓2
In plain EnglishThe total of the hops is the difference between the two numbers.
A game costs £278. How much change from £503?(2 marks)
Count on from 278.+ 2, + 20, + 203✓1
In plain EnglishMake small hops to friendly numbers: 280, then 300, then the big hop to 503.
Add the hops.2 + 20 + 203 = £225✓2
In plain EnglishThis is exactly how a shopkeeper counts out change.
Problems in context
A school raised £1248 at a bake sale and £975 at a sponsored walk. It needs £3000 for a trip. How much more does it need to raise?(3 marks)
Total raised so far.
£1248 + £975 = £2223✓1
| 1 | 1 | 1 | ||
| 1 | 2 | 4 | 8 | |
| + | 9 | 7 | 5 | |
| 2 | 2 | 2 | 3 |
In plain EnglishFirst add the two amounts together. Bigger number on top.
How much more?
£3000 − £2223 = £777✓2
| 23 | 90 | 90 | 100 | |
| − | 2 | 2 | 2 | 3 |
| 7 | 7 | 7 |
In plain EnglishTake what has been raised away from what is needed. You could also count on: 2223 → 2300 (+ 77) → 3000 (+ 700).
Answer the question.The school needs £777 more.✓3
In plain EnglishWrite a sentence that answers the question, with units.
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Your turn
No calculator! Set out a chimney sum on paper, or use a mental strategy, then type your answer. Stuck? Tap Need a hint?