Examples of what pupils should know and be able to do
Continue to use mental methods (see Step 4).
Know there is more than one way to find a percentage using a calculator. For example, to find 12% of 45:
- convert a percentage calculation into an equivalent decimal calculation: 0.12 × 45;
- convert a percentage calculation into an equivalent fraction calculation: 12/100 × 45.
Recognise that the second method is less efficient than the first.
- FTM(S) Y789 p. 70 - Acrobat pdf document (34Kb)
- FTM(S) Y789 p. 72 - Acrobat pdf document (72Kb)
- FTM(S) Y789 p. 74 - Acrobat pdf document (32Kb)
- Grid percentages test question - Rtf (rich text format) document (94Kb)
- Fractions and decimals example of pupil's work - Acrobat pdf document (454Kb)
Probing questions
What sets of equivalent percentages, fractions and decimals do you know?
Explain how you can use these to find other equivalent sets.
How would you use a calculator to find 12% of ... using:
- the × and ÷ keys;
- only the × key?
Why do both work? Which method is more efficient?
10% is the same as 
, so 20% must be the same as 
. Is this true or false? Why?
What percentages of given quantities can you easily work out in your head? Talk me through a couple of examples.
When calculating percentages of quantities, what percentage do you usually
start from? How do you use this percentage to work out others?
What if pupils find this a barrier?
'Clouding the picture' is a teaching approach to enable pupils to link related facts. See Teaching mental mathematics from level 5: number page 22.
Sorting and classifying activities also help pupils secure ideas of equivalence. Use and adapt the card sort from How to get more pupils from L3 to L5.
- TMM from L5: number pp. 20–22 - Acrobat pdf document (44Kb)
- How to get more pupils from L3 to L5 in mathematics part 2: Learning from misconceptions: Fractions and Decimals Resource sheet A5. (Cards to classify into equivalent sets.) - Acrobat pdf document (30Kb)
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