The idea, step by step
Choose a strategy to suit the numbers
There is more than one accurate method. For 19 × 7, use twenty groups then remove one: 20 × 7 − 7. For 35 × 8, double 35 and halve 8, giving 70 × 4. Both changes preserve the total product.
Explain what changes and what stays the same. Doubling one factor only would double the answer. Doubling one and halving the other balances the change. Check with partitioning if you are unsure.
Use friendly parts for division
To divide 96 by 4, split it into 80 + 16. Those parts divide by 4 exactly, giving 20 + 4. This is easier than counting groups of four one at a time.
Use the relationships between facts to reduce work without hiding your reasoning. Multiplying by 5 can be done by multiplying by 10 then halving. In a multi-factor product, group 2 and 5 to make 10. Pick a method you can explain and check.
A common trap
Changing 18 × 5 into 36 × 5 and expecting the same answer.
Instead: Doubling only one factor doubles the product. To keep the same product, halve the other factor too, or use a different strategy such as 18 × 10 ÷ 2.
See the thinking
Double and halve
Calculate 35 × 8 efficiently.
- Double 35 to 70 and halve 8 to 4.
- 70 × 4 = 280.
- Check another way: 30 × 8 + 5 × 8 = 240 + 40 = 280.
Divide using friendly parts
Find 96 ÷ 4.
- Split 96 into 80 + 16.
- 80 ÷ 4 = 20 and 16 ÷ 4 = 4.
- 20 + 4 = 24. Check: 24 × 4 = 96.
Check your understanding
Find 62 × 5 by multiplying by 10 then halving.
Show answer
310.
62 × 10 = 620; half of 620 is 310.
Your turn
6 questions · 9 marks · Work at your own pace.
Read the questions online
- Use a near-round number to find 19 × 7.2 marks
- Use doubling and halving to find 25 × 8.1 mark
- Find 84 ÷ 4 using 80 + 4.1 mark
- Find 2 × 7 × 5 by grouping useful factors.1 mark
- A school buys 18 packs of 5 pencils. Show two different ways to find the total.2 marks
- A learner changes 16 × 6 into 32 × 3. Is this valid? Explain and calculate.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Use a near-round number to find 19 × 7.2 marks
20 × 7 = 140.
Remove one group of 7: 140 − 7 = 133.
133. - Use doubling and halving to find 25 × 8.1 mark
25 × 8 = 50 × 4 = 100 × 2 = 200.
200. - Find 84 ÷ 4 using 80 + 4.1 mark
80 ÷ 4 = 20; 4 ÷ 4 = 1.
20 + 1 = 21.
21. - Find 2 × 7 × 5 by grouping useful factors.1 mark
2 × 5 = 10, so the product is 7 × 10 = 70.
70. - A school buys 18 packs of 5 pencils. Show two different ways to find the total.2 marks
Method 1: 10 × 5 + 8 × 5 = 50 + 40 = 90.
Method 2: 18 × 10 ÷ 2 = 180 ÷ 2 = 90.
90 pencils. - A learner changes 16 × 6 into 32 × 3. Is this valid? Explain and calculate.2 marks
One factor is doubled and the other halved, so the product stays the same.
32 × 3 = 96; check 16 × 6 = 10 × 6 + 6 × 6 = 60 + 36 = 96.
Yes; both products equal 96.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Facts to 10×10; related division; larger calculations; multiples/powers of ten; efficient strategies.
Official curriculum source ↗