video

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Modular origami polyhedra

These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.

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Turning the place over

As part of Liverpool08 European Capital of Culture there were a huge number of events and displays. One of the art installations was called "Turning the Place Over". Can you find our how it works?

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Jo Boaler explains complex instruction

A video clip of Jo Boaler talking about Complex Instruction.

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Tasks promoting inquiry

Video for teachers of a talk given by Dan Meyer in Cambridge in March 2013.

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Sketching graphs - transformations

If you can sketch y=f(x), there are several related functions you can also sketch...

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Introductory video

An introductory video to the Probability and Evidence collection

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Maths for parents 2017

Resources from Charlie's and Fran's 2017 Madingley course for parents.

article

Take one example

This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.

article

Kingsfield School - building on rich starting points

Alf and Tracy explain how the Kingsfield School maths department use common tasks to encourage all students to think mathematically about key areas in the curriculum.

problem

Strike it out

Age

5 to 11

Challenge level

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

problem

Dotty six

Age

5 to 11

Challenge level

Dotty Six is a simple dice game that you can adapt in many ways.

problem

All change

Age

5 to 7

Challenge level

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

problem

Eightness of eight

Age

5 to 7

Challenge level

What do you see as you watch this video? Can you create a similar video for the number 12?

problem

Nim-7

Age

5 to 11

Challenge level

Can you work out how to win this game of Nim? Does it matter if you go first or second?

problem

Totality

Age

5 to 11

Challenge level

This is an adding game for two players. Can you be the first to reach the target?

problem

Unexpected ordering

Age

5 to 7

Challenge level

Watch the video of Fran re-ordering these number cards. What do you notice? Try it for yourself. What happens?

problem

Subtraction slip

Age

5 to 7

Challenge level

Can you spot the mistake in this video? How would you work out the answer to this calculation?

game

Strike it out for two

Age

5 to 11

Challenge level

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

game

Dotty six for two

Age

5 to 11

Challenge level

Dotty Six game for an adult and child. Will you be the first to have three sixes in a straight line?

project

How many?

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

problem

Air nets

Age

7 to 18

Challenge level

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

problem

Subtraction surprise

Age

7 to 14

Challenge level

Try out some calculations. Are you surprised by the results?

problem

Bryony's triangle

Age

7 to 11

Challenge level

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

problem

Tumbling down

Age

7 to 11

Challenge level

Watch this animation. What do you see? Can you explain why this happens?

problem

Surprising split

Age

7 to 11

Challenge level

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

game

James's code challenge

Age

7 to 18

Challenge level

The Enigma Project's James Grime has created a video code challenge. Watch it here!

project

Helicopters

Design and test a paper helicopter. What is the best design?

problem

Roll over the dice

Age

7 to 11

Challenge level

Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?

problem

Pouring problem

Age

7 to 11

Challenge level

What do you think is going to happen in this video clip? Are you surprised?

problem

Bundles of cubes

Age

7 to 11

Challenge level

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

problem

Truth or lie

Age

7 to 11

Challenge level

Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?

game

Daisy

Age

7 to 11

Challenge level

In this game for two players, take it in turns to shade one petal, or two petals next to each other. Is it better to go first or second?

problem

Method in multiplying madness?

Age

7 to 14

Challenge level

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

problem

Counting cards

Age

7 to 11

Challenge level

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

problem

Drawing rhombuses

Age

11 to 16

Take a look at the video showing rhombuses drawn on dotty grids...

problem

Rhombuses from diagonals

Age

11 to 16

Take a look at the video showing rhombuses and their diagonals...

problem

Areas on a grid

Age

11 to 16

Take a look at the video showing areas of different shapes on dotty grids...

problem

Drawing squares

Age

11 to 16

Take a look at the video showing squares drawn on dotty grids...

problem

Squares from diagonals

Age

11 to 16

Take a look at the video showing squares and their diagonals...

problem

Sociable cards

Age

11 to 14

Challenge level

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

problem

Summing consecutive numbers

Age

11 to 14

Challenge level

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

problem

Constructing triangles

Age

11 to 14

Challenge level

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

problem

Perimeter possibilities

Age

11 to 14

Challenge level

I'm thinking of a rectangle with an area of 24. What could its perimeter be?

problem

Frogs

Age

11 to 14

Challenge level

How many moves does it take to swap over some red and blue frogs? Do you have a method?

problem

The best card trick?

Age

11 to 16

Challenge level

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

problem

Strange bank account

Age

11 to 14

Challenge level

Imagine a very strange bank account where you are only allowed to do two things...

game

Favourite

Up, down, flying around

Age

11 to 14

Challenge level

Play this game to learn about adding and subtracting positive and negative numbers

problem

Ace, two, three...

Age

11 to 14

Challenge level

Can you picture how to order the cards to reproduce Charlie's card trick for yourself?

problem

Drawing Celtic knots

Age

11 to 14

Challenge level

Here is a chance to create some Celtic knots and explore the mathematics behind them.

problem

Always a multiple?

Age

11 to 14

Challenge level

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

$How Risky \is my diet?$

problem

How risky is my diet?

Age

11 to 16

Challenge level

Newspapers said that eating a bacon sandwich every day raises the risk of bowel cancer by 20%. Should you be concerned?

problem

Seven squares

Age

11 to 14

Challenge level

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

problem

Take three from five

Age

11 to 16

Challenge level

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

problem

Amazing card trick

Age

11 to 14

Challenge level

How is it possible to predict the card?

problem

Seven squares - group-worthy task

Age

11 to 14

Challenge level

Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?

problem

Twisting and turning

Age

11 to 14

Challenge level

Take a look at the video and try to find a sequence of moves that will untangle the ropes.

problem

Shopping basket

Age

11 to 16

Challenge level

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

article

Vanishing roots

If $y=x^2-6x+c$, and we vary $c$, what happens to the roots when $c>9$?

article

Symmetric tangles

The tangles created by the twists and turns of the Conway rope trick are surprisingly symmetrical. Here's why!

problem

Power countdown

Age

14 to 16

Challenge level

In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

problem

Factorising with multilink

Age

14 to 16

Challenge level

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

problem

Summing geometric progressions

Age

14 to 18

Challenge level

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

problem

Double trouble

Age

14 to 16

Challenge level

Simple additions can lead to intriguing results...

problem

Beelines

Age

14 to 16

Challenge level

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

problem

Sorted

Age

14 to 18

Challenge level

How can you quickly sort a suit of cards in order from Ace to King?

problem

A brief introduction to complex numbers

Age

14 to 18

Challenge level

In this problem, we define complex numbers and invite you to explore what happens when you add and multiply them.

problem

Statins and risk

Age

14 to 16

Challenge level

"Statins cut the risks of heart attacks and strokes by 40%"
Should the Professor take statins? Can you help him decide?

problem

Probability in court

Age

14 to 18

Challenge level

When you're on trial for murder, it can be crucial that the court understands probability...

problem

The ELISA test

Age

14 to 18

Challenge level

In 1% of cases, an HIV test gives a positive result for someone who is HIV negative. How likely is it that someone who tests positive has HIV?

problem

Painted cube

Age

14 to 16

Challenge level

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

problem

The invertible trefoil

Age

14 to 16

Challenge level

When is a knot invertible ?

problem

Cyclic quad jigsaw

Age

14 to 16

Challenge level

A picture is made by joining five small quadrilaterals together to make a large quadrilateral. Is it possible to draw a similar picture if all the small quadrilaterals are cyclic?