The idea, step by step
Break a calculation into friendly parts
Partitioning breaks a number into useful parts. To add 247, you can add 200, then 40, then 7. Keep the place values clear and record enough working to follow each step.
Compensation helps with a number close to a round number. Add 198 by adding 200 then subtracting 2. Subtract 198 by subtracting 200 then adding 2 back. Explain the adjustment so you do not move in the wrong direction.
Regroup and check
For a written method, line up ones with ones, tens with tens and hundreds with hundreds. Ten ones can be exchanged for one ten when adding. One hundred can be exchanged for ten tens when subtracting. Every exchange keeps the total value unchanged.
Estimate before calculating. Afterwards, subtraction can check an addition, and addition can check a subtraction. A close estimate helps spot a large error, but it does not prove an exact answer. Choose a method you can explain clearly.
A common trap
For 562 − 198, subtracting 200 and then subtracting another 2.
Instead: Subtracting 200 takes away 2 too many. Add 2 back: 562 − 200 + 2 = 364.
See the thinking
Add by partitioning
Find 386 + 247.
- 386 + 200 = 586.
- 586 + 40 = 626.
- 626 + 7 = 633. Check: 633 − 247 = 386.
Subtract from a round number
Find 800 − 367.
- 800 − 300 = 500.
- 500 − 60 = 440, then 440 − 7 = 433.
- Check: 433 + 367 = 800.
Check your understanding
Use compensation to find 426 + 199.
Show answer
625.
426 + 200 = 626. Subtract the extra 1 to get 625.
Your turn
6 questions · 10 marks · Work at your own pace.
Read the questions online
- Calculate 458 + 236.1 mark
- Calculate 703 − 268.1 mark
- Use compensation to find 645 + 298.2 marks
- Use compensation to find 721 − 299.2 marks
- A library had 625 books. It received 178 more, then lent out 246. How many remained?2 marks
- A learner finds 472 + 189 = 551. Show a correct method and use an estimate to explain why 551 is not sensible.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Calculate 458 + 236.1 mark
458 + 200 = 658.
658 + 30 + 6 = 694.
694. - Calculate 703 − 268.1 mark
703 − 200 = 503.
503 − 60 − 8 = 435.
435. - Use compensation to find 645 + 298.2 marks
645 + 300 = 945.
Subtract the extra 2: 943.
943. - Use compensation to find 721 − 299.2 marks
721 − 300 = 421.
Add 1 back because one too many was removed: 422.
422. - A library had 625 books. It received 178 more, then lent out 246. How many remained?2 marks
625 + 178 = 803.
803 − 246 = 557.
557 books. - A learner finds 472 + 189 = 551. Show a correct method and use an estimate to explain why 551 is not sensible.2 marks
472 + 200 − 11 = 661.
Rounding to hundreds gives about 500 + 200 = 700, much closer to 661 than 551.
The correct answer is 661.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Place-value revision; odd/even properties; addition/subtraction strategies; missing values; rounding/checking.
Official curriculum source ↗