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House of Maths School Workshops Primary & Secondary in Dorset & South - WHAT’S SPECIAL ABOUT THE NUMBER ELEVEN?

TIMES TABLE SECRETS, CUBE NETS, OCTAHEDRA, PALINDROMES AND ALTERNATING DIGIT SUMS: LET’S HEAR IT FOR NUMBER ELEVEN!

Eleven Medley

NETFLIX:  the Producers of instant cult TV series “Stranger Things” clearly appreciate the wonder of the number Eleven: they even (or should that be “oddly”) named the series’ main character “Eleven”.

CUBE NETS: there are eleven distinct nets of cubes.

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House of Maths School Workshops Primary & Secondary in Dorset & South - THE CAR WHEEL GAMES (RECEPTION TO YEAR 6)

COUNTING AND SYMMETRY GAMES FOR RECEPTION TO YEAR 6

THE “WHAT” GAMES?? the strips of metal joining the hub (centre) of a wheel to its rim (edge) are called the spokes. Have you tried to count the number of spokes on a car wheel?  How good is your counting? What other patterns can you find in the wheels?

SAFETY RULES:

  • Do not attempt to count the spokes on a moving car. Only count the spokes if it is parked.
  • Small children should hold an adult’s hands.
  • Ask permission if there is someone sat inside the car you want to count. Explain that you are playing a maths game and that their car has really cool wheels!

GAME 1- COUNT THE SPOKES:  Some car wheels have 5 spokes, some have 7, some have more. Find some cars and count the number of spokes.

GAME 2– COLLECT THE SET: how many different numbers can you find? Here are wheels with every number of spokes from 4 up to 16. I can’t find 17!! – can you?

Car Wheels from 4 to 18

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House of Maths School Workshops Primary & Secondary in Dorset & South - BRITAIN’S GOT TALENT RUNNER-UP 2019 IS A MATHEMAGICIAN!

A Mathemagical Sleight of Hand:

Last night saw the live final of TV Talent Show Britain’s Got Talent. The evening’s second most popular act “X” was a masked magician, presumably named “X” in homage to his love of the algebraic symbol used to represent the unknown. Viewers of a mathematical persuasion will have noticed that runner-up “X”‘s big magic trick of the evening used not sleight of hand, but rather sleight of mathematics. The voting general public were impressed enough to make X the evening’s runner-up, losing out only to octogenarian singer Colin Thackeray.

The magical effect:

Here’s a photo of the act in progress:

Britain's Got Talent 2019

The mathemagician can now demonstrate “mind-control” as follows:

Start at any circle
Move left or right to the nearest square.
Move up or down to the nearest circle.
Move diagonally to the nearest square.
Move left or right to the nearest circle.

Are you now on HOPE? Yes, I thought so!

I’ll not spoil your fun – see if you can work out for yourself how this trick works!

 

 

House of Maths School Workshops Primary & Secondary in Dorset & South - STAR POLYGONS

Star Polygons: an introduction

Star polygons are beautiful mathematical objects, a juxtaposition of maths and art. They’re also really easy to make: as an example here is a {5,2} Star Polygon. The first number tells us to start with 5 points (“vertices” or in the singular “vertex“) in a circle. It’s convenient to number them 0, 1, 2, 3, 4. (You can label them 1, 2, 3, 4, 5 if you prefer). The second number tells us which points to connect: you count on 2 places each time. So start at 0, join to 2, then 4, then 1, 3 and finally back to 0: the star is complete! Note that arithmetic behaves quite unusually when creating a star polygon: for example 4+2=1. Mathematicians call this modular arithmetic and it crops up all over the place, most obviously on clocks (e.g. 10 o’clock + 5 hours = 3 o’clock!!).

Star Polygon {5,2}

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House of Maths School Workshops Primary & Secondary in Dorset & South - CIRCULAR REASONING: TOP TIPS FOR USING A COMPASS

DO’S AND DON’TS WITH A COMPASS

LEVEL: UP TO GCSE

1. “A PAIR OF COMPASSES”: does not mean you should use two of them! Same comment applies to wearing a pairs of trousers or glasses.

Compass pair of compasses

2.  USE A TEENY WEENY PENCIL: Long pencils get stuck against your hand and prevent the compass moving properly, but a tiny stubby pencil can stay in the compass without getting entangled in your pencil case. If you snap a small piece off the end of another pencil and resharpen the end your Mum will probably not notice. I’ve been using the same compass pencil for years, and it still has plenty of length left.

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House of Maths School Workshops Primary & Secondary in Dorset & South - TRIANGULAR NUMBERS AND PYTHAGOREAN TRIPLES – A SURPRISING RELATIONSHIP

A SURPRISING FORMULA FOR GENERATING PYTHAGOREAN TRIPLES

A Pythagorean Triple is a set of three positive integers (whole numbers) that satisfy Pythagoras’ Theorem $a^2+b^2=c^2$, such as {3, 4, 5} or {5, 12, 13} or {28, 45, 53}. It’s easy to see that there are infinitely many such triples: one way is to take multiples of the well-known {3, 4, 5} triple; multiplying each number by 2 or 3 etc we find that {6, 8, 10} or {9, 12, 15} etc also satisfy $a^2+b^2=c^2$. A more interesting way to generate infinitely many Pythagorean Triples is as follows:

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House of Maths School Workshops Primary & Secondary in Dorset & South - FUN WITH OCTAGONS

DISSECTIONS OF AN OCTAGON

octagon from quadrilaterals dissection

OCTAGON-INTO-QUADRILATERALS

octagon half shaded

WHAT FRACTION IS SHADED RED?

“Geometry” is a posh word for “shapes”. Here are two fun geometry puzzles for you, inspired by a question form the UK Mathematics Trust Challenge. Anyone can play, even non-mathematicians:

  1. The first octagon has been cut into four congruent (same size, same shape) quadrilaterals (four sides). Can you figure a way to dissect the octagon into four congruent pentagons (five sides)? How about into four congruent hexagons (six sides) – or even heptagons and beyond?
  2. What fraction of the red-and-white octagon has been shaded red? (and can you prove it?)

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