1. Lucy Sayce-Browne lucy.sayce-browne@reading.gov.uk 25 October 2012
Maths and 2 Veg
Lucy Sayce-Browne
25 October 2012

2. Part of a balanced diet.
What would be your five a day?
Actually the maths is already out there. You get at least 5 a day but its about noticing it. Raising awareness. You don’t have to create the maths, just the opportunity to notice it. “Ooh look! Maths!”

3. Ooh look! Maths! Link also to stories in today’s press. Music.
Objects on tables. Where is the maths? Return to this later.

4. Where to find the maths? Numbers.....big numbers
Stan’s Café:
Big numbers.
How much blood in the world – read excerpt from Innumeracy p14 (unfortunately American units)
Millions and billions:
Million seconds = 11 days, billion seconds = 32 years
How far would £1m stretch in pound coins? £1bn?
Could you fit a £1m into a suitcase? An articulated lorry? £1bn?
Stan’s cafe display for school based on all the children in school – use kidney/butter beans.

5. Where else to find the maths?
Measures
Innate ability to compare things. Multiplicative relationship (comparing height to parent) more useful than additive.

6. Relationships If dark green is 2* tall, which rod is 1*? 2 1 1½
Looking for multiplicative relationships. More fun to do this with your body.
Find something in the room that is the same/bigger/smaller than the length of your foot? 1 1½

7. If I am 2* tall, what can I find that is 1*?
Find something in the room that is half the height of you? How would you work this out? String?

8. Comparing measures within your own body – rich source of relationships
Comparing measures within your own body – rich source of relationships. (Golden ratio – return to).
Creating a body graph using armpit to fingertips and height to armpit. Stickers on the wall. Would also work with thumb and index finger on axes.
Making different isosceles triangles by standing with legs apart. Leading into locus (Tummy button always directly above the apex and equal distance from outstretched fingertips.)
More locus – angels in the snow.
Using leaves to make a graph of length vs width.
Nb Tape measure is a number line. Might prefer to use red/white rod for younger children (encouraging approximation to nearest 10cm) or any other non-standard measure.

9. Where else to find the maths?
Measures
Non-standard measures
Using non-standard measures:
Foot – Julius caesar?
Bushels, pecks, megalithic yard, fathoms, nautical miles etc etc (Book: The Measure of Albion)
Milk measurer
Metre stick in Paris.

11. When measures go wrong When measures go wrong.
Space probe to Mars that missed as not using the same measurements.
Think how carefully the 23 mile skydiver must have had to calculate for a successful drop.

12. Where else to find the maths?
Golden ratio
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
21 ÷ 13 = 1.615
34 ÷ 21 = 1.619
55 ÷ 34 = 1.618
89 ÷ 55 = 1.618
Continuation of fibonacci sequence.
Division to golden ratio
Occurence in nature – body ratios, growth of trees, breeding rabbits, petals on flowers

13. http://www. maths. surrey. ac. uk/hosted-sites/R
Rabbits breeding: Continue sequence 1,1,2,3,5,
Division to find phi.
Folding golden rectangle to make golden spiral. Use pair of fibonacci numbers to form rectangle. Higher pair better.
Nautilus, fir cones, pineapples, flower petals etc.
Body ratios
Art: Mondrian, da Vinci etc
Architecture: windows, Parthenon

14. Image of sunflower and fir cone. Aha! One of the veg!

15. Golden rectangle: all fold to give beginning of golden spiral.

16. Folding a golden rectangle.

17. Image of nautilus. Nb doesn’t work! Don’t believe everything you read.

18. Where else to find the maths?
Symmetry
Spotting patterns, noticing what is the same and what is different.
Dance, leaves.
Self similarity – following a rule. Creating snowflake pictures.
Self similarity in nature – fractals.

19. The Mandelbrot set http://neave.com/fractal/
Named after Benoit Mandelbrot, born in Poland in 1924 but moved to France as a child. First named ‘fractals’.

20. Fractals in nature

21. Where else to find the maths?
Music:
rhythm - note values, tempo, time signatures, cross rhythms
melody - pitch, numbering/labelling notes, notation, scales
harmony – chords, scales,
musical instruments –frequency of notes produced from tubes, strings, skins etc
songs about maths
Include singing rounds.
Positive links to learning music and effect on overall achievement. Patterns?

22. Notes: The Musical Scale
Pythagoras;
Noted sounds made by blacksmith’s hammer on the anvil
Explored ratios of different notes.
Halving the length of a string gives a note an octave higher. 2/1
The next simplest ratio gives a fifth. 3/2
Nb not everyone using our western 8 notes scale. Actually ours is 7 major notes and 12 semitone. Why 7 and 12?
Chinese = pentatonic (5), others have 31 or even 53.

24. Intervals in the scale …..(ratios courtesy of Pythagoras)
An octave spans 8 notes (2:1)
C D E F G A B C
One note difference e.g. C D E (9:8)
Doh, a Deer
A third e.g. C – E (5:4)
Once in Royal David’s City
A fourth e.g. C – F (4:3)
Amazing Grace
A fifth e.g. C – G (3:2)
Twinkle Twinkle Little Star
An octave, C – C
Somewhere over the rainbow
Nb now use equal temperament scale so can transpose. All these intervals are slightly different. Do need to use different tuning if playin ge.g. Baroque music. This is why its more suited to stringed instruments which have more variable tuning than a piano.

26. Frequencies of notes
Pure musical notes produce a longitudinal wave of movement in the air particles which our eardrums can detect. How frequently the wave of movement hits our eardrum denotes the pitch of the note that we hear. More frequent hits leads to a higher sounding note.
Frequency is measured in hertz, waves per second.
Shorter strings vibrate more quickly producing a higher frequency and therefore a higher note.
Middle C has a frequency of about 262 Hertz in other words, 262 pockets of higher air pressure pound against your ear each second. Therefore one pocket strikes your ear every seconds.

27. Chords or “Why do some notes sound better together”

28. What we can hear Species Range (Hz) Turtle 20–1,000 Goldfish 100–2,000
Frog 100–3,000
Pigeon 200–10,000
Sparrow 250–12,000
Human 20–20,000
Chimpanzee ,000
Rabbit 300–45,000
Dog 50–46,000
Cat 30–50,000
Guinea pig 150–50,000
Rat 1,000–60,000
Mouse 1,000–100,000
Bat 3,000–120,000
Dolphin 1,000–130,000
Why chimpanzees don’t do drum and bass!

29. Tempo
To show how fast a piece should be played a little “equation” is used:
e.g. this means that there
are 90 crochet beats
in a minute
= 90
How does this compare with your normal walking pace?
How can you use a watch which shows seconds to work
out what 90 beats per minute feels like?

30. Note values US ENGLISH Semibreve Minim Crochet Quaver Semi-quaver
Rich source of fractions.

31. Rhythms from other cultures
El Zaffa (Egypt, wedding march)
Chiftitelli (Turkey, belly dancing)
Eve bell pattern (Africa)
Takada drumming (Africa)

32. 4 beat rhythms
Clapping rhythms.xlsx

33. Making sure your class are well fed
What will be your 5-a-day?
nb link to lettuce – hyperbolic planes. Example of crocheting in the hyperbolic plane on TED.
Return to objects on the tables and find the maths. Write on a post-it.
Move to other tables and see what others have written.
Share favourites.

34. Next steps
As a result of today’s session, what will you do differently:
Tomorrow....
Next month....
Forever.