@MEIConference #MEIConf2019
#MEIConf2019
The GeoGebra files can be accessed from
https://www.geogebra.org/m/chqrh8uk
For more on dissections see session F2 at
http://mei.org.uk/conference12
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Divide an 11 by 11 square into five rectangles in a different
way using the dimensions 1,2,3,4,5,6,7,8,9,10 once each.
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Cutting up squares:
Enrichment material for KS3 and KS4
How can you cut a 6 by 6 square into two pieces
which can be rearranged to make a 9 by 4
rectangle? Can you dissect a square into triangles
that are all acute angled? In this session, we’ll look
at problems which provide enrichment material for
Key Stage 3 and Key Stage 4 students across a
wide range of attainment levels.
Pythagoras Circle theorems Regular polygons
Area of parallelogram Linear equations
Proof and reasoning Percentages Constructions
#MEIConf2019
#MEIConf2019
Jigsaws
All shapes of one specified type
#MEIConf2019
How many squares is it possible to divide a square into?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
#MEIConf2019
7,10,13,16, …6,9,12,15,… 8,11,14,17,…
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …
#MEIConf2019
Mrs Perkins’s Quilt – smallest number of co-prime
squares into which an n by n square can be dissected
10 squares 8 squares
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#MEIConf2019
Splitting squares (or rectangles) into
different sized squares
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9 piece
jigsaw
32
33
2 2 2 2 2 2 2 2 21 4 7 8 9 10 14 15 18 1056 32 33
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#MEIConf2019
#MEIConf2019
#MEIConf2019
#MEIConf2019
A square
#MEIConf2019
#MEIConf2019
2 2 2 2 2 24 25 491 2 3 ... 23 24
6
270
2
1
1 2 1
6
n
r
n n nr
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2 2 2 2 2 2 2 2 8 9 171 2 3 4 5 6 7 8 204
6
204100% 90.7%
225
2
2
14 196
15 225
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1240 of 1296 squares needed, so a 95.68% filling
2 2 2 2 2 2
2 2
15 16 311 2 3 ... 13 14 15 1240
6
35 1240 36
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1240 of 1296 squares needed, so a 95.68% filling
#MEIConf2019
2 2 2 2 2 2
2 2
23 24 471 2 3 ... 21 22 23 4324
6
65 4324 66
4324100% 99.27%
4356
#MEIConf2019
4324100%
4356
99.27%
#MEIConf2019
Cutting up squares:
Enrichment material for KS3 and KS4
How can you cut a 6 by 6 square into two pieces
which can be rearranged to make a 9 by 4
rectangle? Can you dissect a square into
triangles that are all acute angled? In this
session we’ll look at problems which provide
enrichment material for KS3 and KS4 students
across a wide range of attainment levels.
#MEIConf2019
#MEIConf2019
#MEIConf2019
#MEIConf2019
#MEIConf2019
Jigsaws
#MEIConf2019
Cutting up squares:
Enrichment material for KS3 and KS4
How can you cut a 6 by 6 square into two
pieces which can be rearranged to make a 9 by
4 rectangle? Can you dissect a square into
triangles that are all acute angled? In this session
we’ll look at problems which provide enrichment
material for KS3 and KS4 students across a wide
range of attainment levels.
#MEIConf2019
#MEIConf2019
#MEIConf2019
#MEIConf2019
#MEIConf2019
#MEIConf2019
#MEIConf2019
Looking for squares in a tessellation of Greek crosses
#MEIConf2019
Looking for squares in a tessellation of Greek crosses
#MEIConf2019
1 square → 5 pieces → 2 squares,
(edge lengths l and 2l)
#MEIConf2019
#MEIConf2019
#MEIConf2019
#MEIConf2019
#MEIConf2019
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We also pioneer the development of innovative
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