page
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.
page
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?
page
Jo Boaler explains Complex Instruction
A video clip of Jo Boaler talking about Complex Instruction.
page
Tasks promoting inquiry
Video for teachers of a talk given by Dan Meyer in Cambridge in March 2013.
page
Sketching graphs - transformations
If you can sketch y=f(x), there are several related functions you can also sketch...
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.
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.
game
Strike it Out for Two
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
game
Dotty Six for Two
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
Favourite
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
Favourite
Dotty Six
Age
5 to 11
Challenge level
Dotty Six is a simple dice game that you can adapt in many ways.
problem
Favourite
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
Favourite
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
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
Favourite
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?
problem
Favourite
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
Favourite
Totality
Age
5 to 11
Challenge level
This is an adding game for two players. Can you be the first to reach the target?
game
James's Code Challenge
The Enigma Project's James Grime has created a video code challenge. Watch it here!
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
Favourite
Subtraction Surprise
Age
7 to 14
Challenge level
Try out some calculations. Are you surprised by the results?
problem
Favourite
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
Favourite
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
Daisy
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
Favourite
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
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
Favourite
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?
problem
Favourite
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
Areas on a grid
Take a look at the video showing areas of different shapes on dotty grids...
game
Favourite
Up, down, flying around
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
Favourite
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
Favourite
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
Favourite
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
Favourite
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
Favourite
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
Favourite
Strange Bank Account
Age
11 to 14
Challenge level
Imagine a very strange bank account where you are only allowed to do two things...
problem
Favourite
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
Favourite
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
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
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
Favourite
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...
problem
Favourite
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
Favourite
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
Favourite
Amazing Card Trick
Age
11 to 14
Challenge level
How is it possible to predict the card?
problem
Favourite
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
Symmetric Tangles
The tangles created by the twists and turns of the Conway rope
trick are surprisingly symmetrical. Here's why!
problem
Favourite
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
Favourite
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
Favourite
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
Favourite
Double Trouble
Age
14 to 16
Challenge level
Simple additions can lead to intriguing results...
problem
Favourite
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
Favourite
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
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?
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
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?
problem
Favourite
Angle Trisection
Age
14 to 16
Challenge level
It is impossible to trisect an angle using only ruler and compasses
but it can be done using a carpenter's square.
problem
Speedy summations
Age
16 to 18
Challenge level
Watch the video to see how to add together an arithmetic sequence of numbers efficiently.
problem
Favourite
Whirlyball
Age
16 to 18
Challenge level
Whirl a conker around in a horizontal circle on a piece of string.
What is the smallest angular speed with which it can whirl?
problem
Impossible triangles?
Age
16 to 18
Challenge level
Which of these triangular jigsaws are impossible to finish?