What type of mathematics questions could inflame the imagination of eleven plus candidates? At some stage children will enjoy the reassurance of a set of mechanical exercises –while at other times they will enjoy the challenge of problems.
A gap year student travelled, as a tourist, 50% of his journey by car; 25% by train; 12.5% by ship; 10% on horseback; and the rest, 5 kilometres, on foot.
1. What percentage did the tourist travel on foot?
2. What distance did the tourist travel altogether?
3. What distance did he travel by car?
4. What distance did he travel by train?
5. What distance did he travel (a) by ship (b) on horseback?
Do we concentrate on the question or do we take the opportunity of discussing the pros and cons of the gap year and talk about our own experiences? Is there time in the eleven plus year to make digressions? Do we try to impress the child with stories of strange foods and fleas in unlikely places?
At what stage of the eleven plus approach should we expect the eleven plus child to say: “I know – I will add up all the percentages”? Is this question suitable for a very bright Year 4 child or for an eleven plus candidate just before the examinations?
How quickly can we expect a child’s mind to see the relationship between the percentage travelled on foot and the distance on covered on foot – then work out how to translate this information across the whole question?
5. (a) 25km, (b) 20km.
Our eleven plus children have to know about fractions, decimals, percentages and how to manipulate numbers. Without this knowledge the gap year question above would remain shrouded in mystery and frustration. Perhaps we expect too much of some eleven plus children yet others will relish the challenge of a juicy problem. You could, for example, ask your child to solve the problem set by Augustus de Morgan:
Great fleas have little fleas upon their backs to bite them
And little fleas have lesser fleas, and so ad infinitum.