By Matthew Delooze
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Extra resources for You Say She's A Virgin? The Fallacy of Live Earth London
4 5 6 What other possible situations are there? What impossible situations can you invent? © Colin Foster 2010 Resources for Teaching Mathematics 14–16 53 14 Connect Four Introduction Learners frequently write algebraic expressions in order to answer stated questions rather than because of a real desire to express something mathematical. This lesson aims to create a situation in which learners notice connections between different values, represented by letters, and then seek to express those connections in algebraic form.
Here, centres of enlargement will need to go at a(4n + 1 +(–1)r, 1 – 2r). What other generalizations are possible? Learners could try making wallpaper patterns by repeating an image in a pattern across the paper. Where do the centres of enlargement have to go to make the pattern work? Why? To make it easier Learners who find themselves getting confused could begin with a blank piece of 1 cm × 1 cm squared paper, draw a rectangle anywhere they like and any size they like (although not too big) and try to explore where they can place the centre of enlargement, and what scale factor they can use, so that the image will lie completely on the piece of paper.
List the centres of enlargement that you are using for each image brick. 35 To make it harder Learners who are confident with this task could vary the dimensions of the original brick. How does this affect the centres of enlargement needed? Can you generalize to an original brick with vertices (0, 0), (2a, 0), (2a, a) and (0, a)? Here, centres of enlargement will need to go at a(4n + 1 +(–1)r, 1 – 2r). What other generalizations are possible? Learners could try making wallpaper patterns by repeating an image in a pattern across the paper.