Area of triangles

This task begins by asking learners to say which triangle looks the biggest.  There are inevitably different arguments here as to which one it is.  The challenge increases significantly when learners are asked which triangle has the bigger area.   For a class with sufficient basic algebraic skills, this can be a rewarding and engaging discussion.  Likely needing some teacher prompting.  For some, the general expressions may be too difficult to get to immediately, and instead specificity may be called for.  Assigning values for AC and AB and then exploring from there is very useful.  You may suggest the values for learners or ask them to generate values. Some may wish to speculate upon the length of CD or CE – this is clearly not imperative to solving the problem – but can make an interesting diversion for more able pupils. 

Credit:  @chrismcgrane84, inspired by Maths In Action S2-3

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