This booklet is a compilation of ideas from Bexley’s Mad Maths Conference 2005.

The conference drew together the talents of Johnny

Ball, Rob Eastaway, Mr Numbervator and Hattie Maths, showing just how much fun learning about maths can be and also how important maths is in our everyday lives. I have included an explanation of the maths behind each activity and how it could be used with pupils.

Maths Magic or the Magic of Maths?Maths may not be magic, but you can do some magical things with maths!

In science we often start with an intriguing demonstration to get kids hooked, such as using a statically charged balloon to make a pupil’s hair stand on end. The learning comes when pupils ask, “how does it work?”

With the activities in this booklet you will soon find the pupils doing algebra without you mentioning the word formula once, developing higher order thinking skills along the way.

The Maths Around UsFrom historical stories to investigations in science, from music and dance to geographical enquiry; cross-curricular opportunities help demonstrate the appliance and importance of mathematics in the world around us.

Challenging, Testing and CreatingMuch of maths is based on rules, systems and patterns. True investigation is not about spotting patterns but explaining and reasoning the maths behind them. Many of the activities here encourage pupils to investigate, explore and reason.

You will soon find pupils creating their own versions – now that’s creative maths!

Darren Ellsum, Primary Mathematics ConsultantBexley Primary Team Ext 4391

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The Power To Read Your Mind

Get a giant dice and ask a pupil to throw it in the air and catch it. Ask them to hold it up and concentrate on the number they are looking at. As if by magic you will be able to read their mind and tell them the number they can see.

The opposite sides of a dice always add up to 7

Such activities are a fun way of introducing algebra.

In this case N + X = 7 with N being the side you can see and X the one the pupil is concentrating on.

You don’t have to use letters like n and x to explore these, you can use more pupil friendly shapes, blobs or names like Fred.

Think Of A Number, Any Number…

”Think of a number…double it…add ten…halve your answer…take away the number you first thought of”. Is your answer 5?

Call your start number X and track the process through. You will soon see how this will always lead to 5.

When they are used to tracking processes in this way your class will soon want to create their own foolproof “think-of-a-number tricks”, learning about algebra along the way!

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Try it with this one:

Think of a number between 1 and 10Multiply this number by two.Add 5.Multiply the answer by 50.If you have already had your birthday this year, add 1755, otherwise add 1754.Now subtract the four-digit year that you were born.

The first digit in the answer will be the first number you thought of and the last two digits your age.

The algebra behind this one is quite difficult. However testing out whether it works for all numbers 1 to 10 will give a purpose to a lot of calculation! Does it work for numbers over 10?

NB - If the year is 2006 add 1756/1755 and so on.

Repeating Digits

Pick a number between 1 and 9 (call it N). On a calculator multiply it (in any order) by 3, 7, 11, 13, 37. The answer will always be NNNNNN.

3, 7, 11, 13 and 37 are the factors of 111,111.

This activity helps to reinforce that the order of multiplication doesn’t make any difference.

What are the factors of 111, 1,111 and 11,111…? Will the trick work with these numbers using their factors?

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Ancient Greek Death Ray

Legend has it that in 500BC a Greek city was defended from an attacking Roman naval fleet when Archimedes directed soldiers to polish their shields and arrange themselves in the foothills above the bay. The sun’s rays were reflected as a powerful beam that set the attacking wooden ships alight.

This story from history shows maths in action. The key to the plan is effective use of angles.

Get the pupils to draw diagrams showing how this may have worked.

Modern technology often relies on angles (eg Satellite communications). Where else can we see angles in action?

Four Against One

Take two canes and a length of rope. Get four pupils to hold the ends of the canes with the canes set one metre apart. Wrap the rope around the two canes in an under and over fashion, do this four times.

Get another pupil the take both ends of the rope. The challenge is for the four holding the canes to stop them being pulled together.

This creates a simple pulley that increases pulling power by a ratio of approximately 4:1 . Get the pupils to explore the relationship between the distance pulled and how much this closes the gap between the two canes. What happens if you wrap the rope only 3 times or increase it to 5 times?

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Magic Square

Write on a piece of paper the number 14 and put in an envelope.Ask a pupil to circle any number on the grid. Cross out the other numbers in its row and column. Get them to circle another number and repeat the crossing out for the row and column. Do the same for two more numbers. Add up the 4-circled numbers and reveal the number in the envelope.

Because of the crossing out rules you will always end up with only one number from each row and column. This is a special type of magic square and the remaining numbers will always give the same agreed total.

Get the class to create their own alternative magic squares for this trick. There is a lot of maths just in creating them!

First decide what ‘magic’ number you would like. Suppose it is 20. You can now choose a square grid of any size. Around the edges of the squares, put numbers that add up to 20. For example:

4 3 1

2

7

3

Fill in the squares in the table by adding the number above the column to the number by the row (so the top left here is 2+4=6). Then rub out the numbers around the outside of the grid. What’s left is the magic square.

Less able pupils may stick to simple numbers or a smaller grid (eg 3x3) More able pupils can extend the grid, use larger numbers or even decimals or fractions.

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7 5 4 63 1 0 24 2 1 36 4 3 5

The Ice Cream TrickOn an OHP put

STRAWBERRY ICE CREAMVANILLA ICE CREAMRASPBERRY ICE CREAMCHOC ICE

Ask the children if they think they know which is the odd one out. You may get lots of interesting answers, but remind them we are thinking mathematically.

Flip the OHP over HORIZONTALLY. You will see that CHOC ICE can still be read, while all the other ice creams are “messed up”.

This is a way of introducing horizontal symmetry. Get the children to explore which other letters have horizontal symmetry. You can then develop the activity into whole words.

Using an OHP sheet is a novel and simple way of testing symmetry without pupils struggling with mirrors.

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Bubbles Everywhere!

Get a length of string/rope. Dip into the bubble mixture ensuring your hands are fully wet up to your knuckles. Make a hoop with the rope and throw a bubble. Increase the length of the rope and throw again. With practice you can use up to 2 or 3m of rope.

The maths here is in getting the pupils to talk about the properties of the shapes made.

Explore the relationship between the length of rope and the circumference of the sphere that it makes. This will of course be a very general link as you wont be able to measure the bubbles!

Change the rope shape from a hoop to a square, rectangle or triangle. What 3d bubbles do these create? Can the children predict?

To make great bubbles; mix 1 part glycerine, 1 part good quality washing up liquid and between 10 and 20 parts water according to strength required. Make sure the surface of the bubble mixture is free from foam.

Prism Bubbles

Get the pupils to make prisms out of plastic straws or connecting strips. Dip your 3D shapes into a bubble mixture so that they are completely immersed. Lift them out gently. You will get different results if you return the frame to the mixture, but this time only put them half way in before removing them. With practice you will get prisms within prisms.

Both making the frameworks and using them to create 3d bubbles gets pupils thinking about the structure and properties of prisms.

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Even Numbers

Make 6 cards with a number on the front and the back in this pattern (1,6) (3,8) (7,12) (9,14) (11,16) (13,18)Ask 6 pupils to come out and hold the cards. Ask the pupils to spin the cards around until you shout STOP. You will be able to tell them whether the number on the back is higher or lower than the one on the front. Secondly you will be able to tell them the actual number.

This one is all about spotting the 2 rules. Your pupils may even work it out before the end of the trick.

The even numbers are always higher than the odd.The difference between the two numbers is always five.

Get the pupils to create more cards using these same rules OR create their own rule for a similar trick.

Factor Fun

Think of a three-digit number (ABC) and write it twice on a calculator (ABCABC). If you now divide this by 7 then 11 and then 13, the answer will be ABC. Eg think of the number 469. Write it twice, 469469. Divide it by 7, 11 then 13 and you get back to 469.

7 x 11 x 13 = 1001 In effect you are dividing ABCABC by 1001. That has to bring it back to ABC. This reinforces distributive law.

Odd Numbers

Make 5 cards with a number written on the front and the back following this pattern (1,2) (3,4) (5,6) (7,8) (9,10).

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Ask 5 children to come out and hold the cards. With your back turned, ask them to spin the cards around until you shout STOP. Ask someone to tell you how many odd numbers there are. Mentally take the number of odd numbers from 30, this will be the total of the numbers facing the audience.

The maths behind this one is quite hard.It may be better to get the pupils to test the rule gathering evidence along the way. This will get pupils thinking and recording logically.

Eg No Odd : All Even 2+4+6+8+10 = 30- 0 = 291st Odd : Rest Even 1+4+6+8+10 = 30 – 1 = 292nd Odd: Rest Even 2+3+6+8+10 = 30 – 1 = 29

The Hidden Maths In Dance! Get the pupils to create a movement sequence or dance, discussing the maths along the way.

Music, movement and dance are full of maths! In order for a dance to feel and look right the sequences must reflect the number of beats in the bar. Sequences can then built around multiples of beats. Getting pupils to work in pairs to create symmetrical and asymmetrical movements, moving through levels and rotating through given degrees all reinforce work in their maths lessons. By wearing numbered t-shirts/bibs you can get them to create a dance around number sequences.

The maths should be age-related and at times challenging.

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Tie A Knot Without Letting Go

Ask a child to fold their arms with one hand poking above their arms and the other poking out below. Put each end of the ribbon or scarf in each hand. Holding the ends firmly ask them to open their arms with a wiggle and a knot to appear.

This trick relies on quite complicated topology.

Ask the pupils if the ribbon looks shorter. Has it really shortened in length or is it just taking up less space? Is there a difference?

Topology is sometimes called “rubber sheet geometry” and is a branch of mathematics that studies the properties of objects that remain unchanged when the object is twisted, distorted, squashed or stretched without it being cut or torn.

Even simple topology gets pupils talking, thinking and reasoning.

Lay a length of ribbon on a table and pull it tight. Now rearrange the ribbon in a wiggle. What has changed and what has remained the same?

Get the pupils to “push over” an oblong into a parallelogram and explore which properties change and which remain unchanged.

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Magic 11

It is easy to multiply TU x 1143 x 11 = 473 4 + 3 = 7 pNow place that between the 4 and the 3 to make 473So 52 x 11 must be 572 as 7 = 5 + 2

This is all down to place value.If you show it vertically you can see how it works more clearly. You may need to remind the pupils that addition is commutative:

43 x 10 = 430 43 x 1 = 43 473

But does it always work? What about 91 x 11 the answer is not 9101

91 x 10 = 91091 x 1 = 91 1001

When the sum of the T and U is over 10 the rule changes.Eg 85 x 11 (8+5 = 13)Add one onto the T to make 9 then place the 3 between this and the 5 making 935).

Maths Is Everywhere!Set up a general knowledge quiz where all the answers

are numbers or shapes.

A quiz such as this reinforces that maths is part of our everyday lives.

Get the pupils to imagine what would happen if numbers suddenly disappeared. What chaos would be caused?

Pupils could write stories or plays around “The day they stole numbers”.

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Acknowledgements:Johnny Ball - www.johnnyball.co.uk Rob Eastaway - www.robeastway.comIsaac Anoon - mr_numbervator@hotmail.com Sue Brown www.hattiemaths.com

Darren EllsumBexley Primary Team

© London Borough of Bexley 2005

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