Musings on substitution

How do you teach algebraic substitution? It occurred to me this week as I was introducing it to a mid-low ability class that you can make an analogy with sporting substitutions. This may be something you know already and totally obvious; (I am often slow to catch on to these ideas!) but if you haven’t heard this one before, read on!

Get three kids to stand in a line at the front of the class each holding up a mini whiteboard. On the first whiteboard (on the left) write ‘a’, the next write ‘+’, then ‘6’. You then ‘make a substitution’, swapping a number on a new mini whiteboard for the letter ‘a’. The kid holding the ‘a’ sits down and a new kid holding the number gets up. You have ‘substituted the letter with a number’. You can link it to sports substitution with the ‘one off, one on’ analogy. Rather than holding a board up showing the numbers of the players being substituted, as in sport, you can hold a mini whiteboard up with ‘a = 5’ and get the kids to learn this means the ‘a’ comes off and the ‘5’ goes on….

You can take this anaology as far as you like, but I did find that the algebra-phobic kids I used it with seemed to get the idea of what substitution is all about. One to have up your sleeve…

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2 Responses

  1. Hope Gerson says:

    I’ve done something like this with simplification. For instance x^4 can be substituted for xxxx. I did it as a whole class activity. I think a demonstration would have gone better. But it was definitely fun.

  2. Bryony says:

    I have done something similar and played a you tube clip from a football match. I play dumb and ask if i am losing can i take the goalie off and put 6 strikers on in his place to get them to stress importance of equivalent substitution

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