@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

#MEIConf2019

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.

#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

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

#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

#MEIConf2019

#MEIConf2019

Splitting squares (or rectangles) into

different sized squares

#MEIConf2019

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

#MEIConf2019

#MEIConf2019

#MEIConf2019

#MEIConf2019

#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

#MEIConf2019

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

#MEIConf2019

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

#MEIConf2019

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

One square into three congruent squares

#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

#MEIConf2019

#MEIConf2019

#MEIConf2019

#MEIConf2019

About MEI Registered charity committed to improving

mathematics education

Independent UK curriculum development body

We offer continuing professional development

courses, provide specialist tuition for students

and work with employers to enhance

mathematical skills in the workplace

We also pioneer the development of innovative

teaching and learning resources