Rule 90

Mathematics

CreativityImaginationBeauty

“…the wellsprings of mathematics lie not in utility and relevance, but creativity, imagination and an appreciation of the beauty of the subject.”

Interconnections

Baravelle Spirals

a = �

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change in attitude (mindset)

appreciation of the imagination, creativity and beauty inherent in maths

exploring/highlighting the interconnections between number, algebra and geometry

achieved through

achieved through

Year 7

Iteration

Tiling the Plane

Graph Theory

Golden Ratio

Year 8

Number Theory

Conic Sections

Topology

Game Theory

Year 7

Iteration

Tiling the Plane

Graph Theory

Golden Ratio

Year 8

Number Theory

Conic Sections

Topology

Game Theory

o baravelle spirals

o strange attractors

o seeds, orbits and iteration

o the butterfly effect

o sierpinski

o happy and sad numbers

o fractals

o fractals in 3 dimensions

o prisoners and escapers

o mandlebrot

o cellular automata

o game of life

activity: fractals in 3 dimensions

time: 1-2 lessons

resources: 3d fractals PP, fractal cuts 1, fractals cuts 2, menger sponge pdf

outcomes: volume; similarity; fractions; isometric drawing; series; generalising

teaching notes:

• fractal cuts - links well to work on sierpinski

• use paper in the ratio 1:2 to begin with

• work on volume and similarity follow

naturally

• menger sponge is a good piece of work to

follow on from fractal cuts – it is the 3

dimensional extension of the sierpinski

carpet and an approach to finding the

volume of the sponge in a similar manner to

finding the area of the carpet is beneficial

• the menger sponge has infinite surface area

and zero volume

• isometric drawings may be practised

• if the volume of the original cube is 1m3,

finding the volume of subsequent

iterations, and generalising, is a challenge as

well as providing good fraction practise

• volume = (20/27)n

• ~1950 students

• ~470 in 6th Form

• Very large, mainly

rural catchment

area in Suffolk

• 60% bussed in

• Ofsted April 2013

• Teaching school

• KS2 data suggests

students are at, or

slightly below,

national average

on arrival

• 3, 100 minute

lessons a day;

fortnightly

timetable

Causality

• students take the notes and do something with the

information the result of which is more imaginative

and creative than the standard approach

• students become independent thinkers with a deeper

understanding of content

• students become engaged in the content

• each notebook is a unique version of the content

• determines misconceptions

Advantages

Disadvantages• planning time

• what to include and what to exclude

• artifact rather working document?

“The moving power of mathematical invention is

not reasoning but imagination.”

Augustus de Morgan

change in attitude (mindset)

appreciation of the imagination, creativity and beauty inherent in maths

exploring/highlighting the interconnections between number, algebra and geometry

achieved through

achieved through

fluency

reason

solve problems

number

algebra

ratio and proportion

geometry and measures

probability and statistics

know, apply and understand