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Secondary Magazine - Issue 118: It Stands to Reason

Created on 14 January 2015 by ncetm_administrator
Updated on 02 February 2015 by ncetm_administrator


Secondary Magazine Issue 118'Le Penseur' by Juanedc (adapted), some rights reserved

It Stands to Reason
Pythagoras' Theorem

In this regular feature, an element of the mathematics curriculum is chosen and we collate for you some teaching ideas and resources that we think will help your pupils develop their reasoning skills. If you’d like to suggest a future topic, please do so to info@ncetm.org.uk or @NCETMsecondary.

How do you introduce Pythagoras’ Theorem to your pupils? Most adults remember something about a square and that word beginning with h, but few can demonstrate complete mastery of the concept. Other adults know that having a loop of rope with 12 equally spaced knots can be used to find a right angle if it is arranged to make a triangle with sides 3, 4 and 5 … though I’ve never met anyone who has such a carefully knotted rope to hand when it’s needed …

You may like to introduce the ideas of Pythagoras using the NRICH task Tilted Squares. Pupils are encouraged to work systematically to find the areas of squares as they progressively ‘tilt’ on a square grid:

By considering how to describe the ‘tilt’ mathematically, the right angle triangle of which these squares are the ‘square on the hypotenuse’ can be made evident, and this helps pupils to suggest an appropriate connection. To complement this task, you could show a tiling pattern that is based on the theorem:

There are a number of dissections that can demonstrate Pythagoras’ Theorem; that of Perigal is on his gravestone! For some pupils, this video clip reaches the parts of their brain that other demonstrations fail to do.

However, pupils need to have deep conceptual understanding of the generality of the theorem: dissections and tiling patterns show a specific example each time. Dynamic Geometry is a good tool for demonstrations which reinforce generality. From this, pupils can develop for themselves a proof of Pythagoras’ Theorem. Pythagoras Proofs suggests alternative ways of deriving a proof, which can be scaffolded appropriately so that all pupils can access them.

Following on:

Image credit
Page header by Juanedc (adapted), some rights reserved



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03 February 2015 12:28
Marvellous - a great story. Thank you.
By RobertWilne
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02 February 2015 18:56
You state at the start of this article that you have never met anyone with a carefully knotted rope to hand. Can I say that whilst with VSO as a volunteer maths teacher, I had the students outside with trusty rope knotted at 5, 12, 13m in order to carefully mark out the football, netball and volleyball pitches. Application of geometry to measure land as originally intended.
By stevemabvuto
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