Examples of what pupils should know and be able to do
Use factors. For example:
- 3.2 × 30 = 3.2 × 10 × 3
- 156 × 6 = 156 × 3 × 2.
Use partitioning. For example:
For multiplication, partition either part of the product:
7.3 × 11 = (7.3 × 10) + 7.3
= 80.3
Use 
= 0.2 to convert fractions to decimals mentally. For example: 
= 0.2 × 3 =0.6
Use mental calculations. For example:
of 20 = 2.5 (e.g. find one quarter and halve it)- 75% of 24 = 18 (e.g. find 50% then 25% and add the results)
- 15% of 40 (e.g. find 10% then 5% and add the results)
- 40% of 400kg (e.g. find 10% then multiply by 4).
- FTM(S)Y789 p 92 - Acrobat pdf document (44Kb)
- FTM(S)Y789 p 94 - Acrobat pdf document (32Kb)
- FTM(S)Y789 p 96 - Acrobat pdf document (26Kb)
- FTM(S)Y789 p 98 - Acrobat pdf document (30Kb)
- FTM(S)Y789
p 100 - Acrobat pdf document (29Kb)
- Thinking Fractions question - Rtf (rich text format) document (20Kb)
Probing questions
Explain how you would do this multiplication by using factors. e.g. 5.8 × 40.
What clues do you look for when deciding whether you can do a multiplication mentally? e.g. 5.8 × 40.
Give an example of how you could use partitioning to multiply a decimal by a two-digit whole number. e.g. 5.3 × 23.
What if pupils find this a barrier?
Give pupils a large set of calculations to sort into those they can do mentally (with jottings) and those where they need to use formal written methods. Make sure that most should be done mentally.
After the initial sorting in pairs, get pupils to work in fours to discuss the mental methods they would use. Take feedback on those causing difficulties and use this to focus teaching.
When given a calculation encourage pupils to first decide whether they can do it in their heads before using other methods.
- Teaching mental calculation strategies to L5 - Acrobat pdf document (554Kb) pages 15-44. You will need to modify the activities as appropriate to the objective.
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