The idea, step by step
Change the calculation without changing its value
Near-round numbers make some calculations shorter. For 398+247, use 400+247 and remove the extra 2. For 25×16, group the factors as 25×4×4 to create 100.
Explain why a compensation or regrouping works. A short method is useful only if it preserves the value of the original calculation.
Estimate before trusting an answer
Round to convenient values and calculate a rough result. An estimate is not an exact answer, but it can reveal a misplaced digit or a wrong operation.
The context tells you what an answer must mean. A bus-seat problem needs a whole number of buses. An estimate checks the size, while the final calculation decides whether an extra bus is needed.
A common trap
49×8 is exactly 400 because 49 rounds to 50.
Instead: 400 is an estimate. Subtract the extra group of 8 to get the exact answer 392.
See the thinking
Worked example 1
Calculate 599+286 efficiently.
- Use 600+286=886.
- One extra was added, so subtract 1.
Worked example 2
A school buys 18 boxes of 24 pencils. Find the total and check it.
- 20×24=480; remove 2×24=48.
- 480−48=432. The estimate 20×20=400 is of a similar size.
Check your understanding
Choose a sensible estimate for 198×31: 600, 6,000 or 60,000.
Show answer
6,000.
200×30=6,000 is close to the original calculation.
Your turn
6 questions · 12 marks · Work at your own pace.
Read the questions online
- Use compensation to calculate 497+358.2 marks
- Calculate 25×28 by making a factor of 100.2 marks
- Calculate 1,002−498 efficiently.2 marks
- Estimate 61×39 using convenient tens.1 mark
- A calculator shows 7,200 for 48×15. Explain why this is unreasonable, then correct it.3 marks
- A club has 178 people. Each bus seats 40. How many buses are needed?2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Use compensation to calculate 497+358.2 marks
500+358−3=855.
855. - Calculate 25×28 by making a factor of 100.2 marks
25×4×7=100×7=700.
700. - Calculate 1,002−498 efficiently.2 marks
1,002−500+2=504.
504. - Estimate 61×39 using convenient tens.1 mark
60×40=2,400.
About 2,400. - A calculator shows 7,200 for 48×15. Explain why this is unreasonable, then correct it.3 marks
50×15 is about 750. Exactly, 48×10+48×5=480+240=720.
It is about ten times too large; the correct answer is 720. - A club has 178 people. Each bus seats 40. How many buses are needed?2 marks
Four seat 160, leaving 18 people, so one more is needed.
5 buses.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Prime/composite/square numbers; factors/multiples revision; efficient calculation and estimation.
Official curriculum source ↗