Practical Equations

It started, as usual, with difficulties in the classroom.  I have a set of quite simple equations on cards, to be matched to the appropriate solutions.  The learners did fine apart from the ones in which the variable, call it x, appeared on both sides.  And as usual for me I looked around for a suitable representation of x.  As it happens I have a number of empty Oxo boxes in the cupboard I keep for work on volumes (an Oxo cube is 2 by 2 by 2 centimetres, and so are my plastic cubes).  So I tried to display the equation using Oxo boxes to represent x.


It worked, after a fashion, and in the example above you can see we moved on to negative numbers.  But how do I roll this out to a whole class, without needing an enormous number of Oxo boxes?  I moved on to envelopes, with each envelop representing p, which was part of an exam question.  I’m afraid that was too much for one group, who could see no connection between my envelopes and the question before them on the exam.  Plus I don’t have that many envelopes to use as consumables.

So back to the cupboard and the tin of matches.  I bought these first for the typical patterns questions on GCSE – a simple number pattern illustrated by a matchstick question.  We’ve had some fun making our own.






We began with something simple, created by Shannon:



She set this for Salma, and then explained how to solve it, which was interesting in itself, demonstrating each move:





And finally she went to the board and gave us the symbolic version:





Then Salma made one for Shannon, which was not quite so complex:



And it was all so move involving and engaging than the usual book stuff.  Equally, professionals seem stuck in the written mode and refusing to consider practical experiences.  I’m not saying that my learners have had a better experience, but consider the version from the Standards Unit.  I’ve tried this in the classroom, having lovingly produced laminated versions, and the whole experience was a failure.

Image Image

From our positive matchsticks we progressed to negative matchsticks, and with numerous cubes of many colours we could use a range of letters to represent the variables – pink cubes for ‘p’ for example.  I enjoyed it, and I hope the learners did, and gained a little more insight into the mystery that can be algebra.

And a final thanks to Shannon.





About Colin Billett

Maths teacher, among other things. View all posts by Colin Billett

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