Two and Three Piece Dissection PuzzlesAuthor(s): Peter RansomSource: Mathematics in School, Vol. 31, No. 4, Dissection Puzzles Special Issue (Sep., 2002), p. 2Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30212195 .

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Twvo and Three piece Dissection Puzzles

by Peter Ransom

Some of my favourite dissections are described in what follows, and the ways in which I use them with my classes. I find these lessons (or parts of lessons) are popular as pupils all experience some degree of success.

Early in Year 7 I start shape work with a two-piece dissection. This gives me an opportunity to see how well pupils follow instructions, how accurate they are at measuring, how systematic they are and the state of their shape vocabulary. The two-piece dissection is made from a square with a cut being made from one vertex to the midpoint of a side.

For all attainers I give them a square piece of card from which they produce the two pieces. This means that they all work with a standard size square (with right angles!). Getting them to draw their own square can come later - it spoils it for low attainers if they struggle early on to get a reasonable start.

Using the two pieces of card I ask them to put the pieces together along sides that are the same length to make as many different shapes as they can, drawing and naming them (if they can) in their books. This is a useful exercise on seeing how systematic they are and what shape names they know. For a plenary I get them to put their shapes on the OHP in turn until all the possibilities have been found (and named).

I've found it useful for demonstration purposes to cut the two pieces from an old cake board as these are thick and generally covered in shiny paper. I can then attach the pieces to the board with Blutack, and pupils can move them round to get different shapes.

In year 8 I revisit this work with the three-piece dissection. This is the same as the two-piece with an extra bit cut off by joining the vertex shown to the midpoint of the side shown, stopping at the existing cut. A diagram makes it clear.

First of all we talk about each piece.

What are they called? Can you be more specific? Where are there right angles? Which sides are equal?

Then they draw and name the shapes they get by putting two or three pieces together along equal sides (or non-equal sides for the more ambitious).

There are many dissections that can be used in similar ways, but by keeping the number of pieces low and simple to make more time can be spent in exploring the shapes made.

The puzzle books by Botermans, Delft and Slocum contain hundreds of dissection puzzles that can be easily made from card and provide a rich source of tangram-type dissection puzzles. A word of warning, however - don't pick them up unless you have some time to spare! They are so intriguing that they are very hard to put down!

References

Delft, Pieter van and Botermans, Jack 1978 Creative Puzzles of the World, Cassell, London, ISBN 0-304-30300-3.

Slocum, Jerry and Botermans, Jack 1987 Puzzles Old and New: How to Make and Solve Them, Thorsons, Wellingborough, ISBN 1-85336-018-X.

Slocum, Jerry and Botermans, Jack 1994 The Book oflngenious and Diabolical Puzzles, Random House, New York, ISBN 0-8129-2153-4.

School Mathematics Project 2000 SMP Interact Book 1, CUP, Cambridge, ISBN 0-521-77795-X.

Keywords: Using and applying; Shape and space; Vocabulary.

Author Peter Ransom, The Mountbatten School and Language College, Whitenap Lane, Romsey SO51 5SY. e-mail: p_ransom@hotmail.com

2 Mathematics in School, September 2002 The MA web site www.m-a.org.uk

This content downloaded from 131.170.6.51 on Tue, 8 Oct 2013 12:26:01 PMAll use subject to JSTOR Terms and Conditions