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Mathematical Challenge Week Four

25 November 2015

This week’s challenge looks at a problem used to develop students understanding of averages and in particular, the mean average by playing with numbers. It’s a very good problem aimed at around the Year 7 age and goes like this:

  • Maths Challenge Week Four

I have a large supply of 3kg and 8kg weights.

Two 8 kg and three 3kg weights have a mean weight of 6kg. Can you show me how?

Can you find other combinations of 3kg and 8kg weights whose mean weight is a whole number of kg?

·         What's the smallest?

·         What's the largest?

·         Can you make all the whole numbers in between?

If you’ve worked all that out (and you can make all the whole numbers in between!), then what happens if I change the starting weights?

·         What if you have a different pair of weights (for example 2kg and 7kg)?

·         Which whole numbers is it possible to have as the mean weight now?

The beginning of this problem might seem simple – and it is a great way to get students to think about what averages really mean (forgive the pun), but you’ll see in the end there’s some really good reasoning skills which students can apply as well.

If you can solve the above questions, please do forward your answers by emailing me m-brown@bisspuxi.com">here. 

Martin Brown, Head of Mathematics