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Secondary Magazine - Issue 53: An idea for the classroom

This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 03 February 2010 by ncetm_administrator
Updated on 16 February 2010 by ncetm_administrator

Secondary Magazine Issue 53   blocks from the mean height of a tower problem

An idea for the classroom - multiple representations

A couple of years ago, I was working with a group of pupils on averages, in particular the mean. The pupils were pretty good at the ‘add them all up and divide by how many there are’ routine – they would have been even better if they had known the ‘Hey diddle diddle’ rhyme we talked about in Issue 48 – but when I asked them to make some sense of this routine I wasn’t convinced by the responses. I started another lesson by talking about things being fair – always a huge bone of contention in my house when I was a kid! If my brother was allowed sweets – I had to have the same number, if he had pocket money – I had to have the same amount. I went on to talk about my poor brother’s suffering now he has three children and introduced the concept of redistributing sweets (or whatever) to keep the total the same but make it ‘fair’. The pupils in my class were pretty happy about the concept and gradually began to tell me that they were finding the mean!

In an attempt to develop this idea a bit further, I recently used this multiple representation exercise. Pupils are getting used to doing this sort of activity so they were asked to ‘sort out’ the cards. Most cards were placed quite quickly, but there were a few problems which gave pupils some extension activities to do – they initially thought that I had made a mistake until I confirmed that this might generate a new set of cards! I feel that it is the creation of a new set of cards that really pushes their understanding a stage further and also gives pupils the opportunity to generate their own mathematics – a step towards becoming ‘independent’ in the functional sense?

I hope your pupils enjoy doing this activity – do tell us about your experiences. 

examples of multiple representations cards

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