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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
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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
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