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

**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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To celebrate the traditional gym membership peak associated with the New Year, here are some muscles whose names have mathematical associations. As you read, see if you can match the muscle to the image in this picture:

**SCALENE:** a set of three (or occasionally four) muscles in each side of the neck, so named as they are all of different lengths.

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__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?

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__WHERE MATHS MEETS GEOGRAPHY__

**1) COUNTING SHEEP:** Wales is famous for its sheep, but **are there more sheep or more people in Wales?** Have a guess, answer later on!

**2)**** VI****SIT THE STEEP****EST STREET IN THE WORLD!! **with a calf-busting gradient of

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### SINGLE USE PLASTICS FROM ONE TO A TRILLION –

### GET READY FOR SOME HUGE HUGE NUMBERS!

**ONE:**

This is a one litre bottle of water.

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## 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:

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!

# 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!!).

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__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.

**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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__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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# DISSECTIONS OF AN OCTAGON

**OCTAGON-INTO-QUADRILATERALS**

**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:

- 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?
- What fraction of the red-and-white octagon has been shaded red? (and can you prove it?)

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