don steward
mathematics teaching 10 ~ 16

Friday, 8 April 2016

generalising GCSE questions (3)

an interesting question from AQA asks students to consider the smallest portion in a ratio as the numbers all increase

not exactly the question but close enough

considering a similar question where the consecutive trios don't 'overlap':

students could be asked to look at various examples

 a generalisation emerges, the difference between the amounts is always 1 over something
where does the 'something' come from?

involving algebra is fairly demanding:

another set of trios where there is an overlap (as in the original question)

what happens to the middle portion for this case?

so what must happen to the largest portion?

Dominic Franklin at Radclyffe School suggests an LCM approach rather than involving fractions:

I saw the solution to this type of problem as one of finding an LCM between the total “shares” of each set of ratios. So in the original question:

5: 6: 7 = 18 parts
7: 8: 9 = 24 parts

The LCM of these numbers is 72, so I need to scale both up, so we get:

20 : 24 : 28
21 : 24 : 27

We can see that the Rob has increased from 20 to 21.

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