Step 7 Objective

Use the equivalence of fractions, decimals and percentages to compare proportions; calculate percentages and find the outcome of a given percentage increase or decrease.

Examples of what pupils should know and be able to do

Convert fraction and decimal operators to percentage operators by multiplying by 100. For example:

Continue to use mental methods for finding percentages of quantities.

Use written methods:
Using an equivalent fraction

Using an equivalent decimal

Using a unitary method

Find the outcome of a given percentage increase or decrease, for example:
An increase of 15% on an original cost of £12 gives a new price of
£12 × 1.15 = £13.80
or
15% of £12 = £1.80
£12 + £1.80 = £13.80

Probing questions

Which sets of equivalent fractions, decimals and percentages do you know?

From one set that you know (e.g. One tenth = 0.1 = 10%), which others can you deduce?

How would you go about finding the decimal and percentage equivalents of any fraction?

How would you find out which of these is closest to One third: Ten thirty oneths; Twenty sixty oneths; Thirty ninety ones; Fifty one hundred and fifty oneths?

Give me a fraction between One third and One half. How did you do it? Is it closer to One third or One half? How do you know? Talk me through how you would increase or decrease a price of £12 by, for example, 15%.

Can you do it in a different way? How would you find the multiplier for different percentage increases/decreases?

The answer to a percentage increase question is £10.

Make up an easy question.

Make up a difficult question.

What if pupils find this a barrier?

Use Year 8 multiplicative relationships mini-pack - Acrobat pdf document (203Kb), which includes innovative ideas to help pupils distinguish whether variables are in proportion or not. There is an analysis of progression in visual images used to develop links between fractions and ratios and so move pupils to multiplicative thinking.

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