The curriculum
Investigating alternate approaches to the teaching of algebra such as the use of Algebra Tiles needs to be given serious consideration.
A good reference for further reading is the materials provided by National Centre for the Excellence in teaching Mathematics as is the audio extract.
I particular like to introduce algebra to a group of learners, and more importantly the need for algebra, by using polygons. This is a very limited version of the conversation with a class along the lines of (and I tend to use the word shape rather than polygon at this point).
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I have been given this shape, holding up the triangle.
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What is the shape called and what do we know about it (asking about it’s properties), ie recalling previously learnt facts. |
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What shall we call the area of shape |
Eventually after lots of suggestions we settle on “t” |
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Right Hand
Left Hand |
Then I show the follow in two hands. What is the area of this shape (right hand and this one (left hand) before putting them together t+t … ie 2t |
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We then investigate the areas of other shapes such as the ones opposite and showing that the area of the parallelogram “p” is 2t |
Forming expression and simplifying |
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Then we move into exploring other shapes and combining shapes to get expressions such as p + t.
This process can go on for a while getting ever more complex. |
Forming expression and simplifying where appropriate |
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Each pair (group) of learners would be given a set of card cut outs of the polygons and asked to make 6 shapes (drawings) with their associated expressions.
The expressions are then passed to a different group for them to make the shapes – this results in some discussion as there can be different interpretations. |
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Eventually, I show them the shape opposite and say the area is “h”, but get from them that h = 6t (sometimes having to overlay some triangles to demonstrate- depends on the class).
At this point I say the area of the hexagon is 60 cm2, so what is the are o the triangle, the parallelogram etc.
As a final step (again depending on the class), I might say I made a mistake with the area of the hexagon it was actually 120 cm2 and get the class to tell me the areas of the other shapes. |
This begins the process of forming and solving equations |
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Plastic polygons can be purchased relatively cheaply – for example from
Or
https://www.learningresources.co.uk/power-polygonstm-set-of-450 |
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