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?
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?
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?
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?
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?
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...
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?
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?
Symmetric Tangles
Age 14 to 16
The tangles created by the twists and turns of the Conway rope trick are surprisingly symmetrical. Here's why!
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?
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.
Impossible Triangles?
Age 16 to 18
Challenge Level
Which of these triangular jigsaws are impossible to finish?
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.
Speedy Summations
Age 16 to 18
Challenge Level
Watch the video to see how to add together an arithmetic sequence of numbers efficiently.
Slick Summing
Age 14 to 16
Challenge Level
Watch the video to see how Charlie works out the sum. Can you adapt his method?
Modular Origami Polyhedra
Age 7 to 16
Challenge Level
These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.
Kingsfield School - Building on Rich Starting Points
Age 5 to 18
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.
Drawing Celtic Knots
Age 11 to 14
Challenge Level
Here is a chance to create some Celtic knots and explore the mathematics behind them.
Turning the Place Over
Age 11 to 18
Challenge Level
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?
How Many?
Age 5 to 7
Challenge Level
This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?
Jo Boaler Explains Complex Instruction
Age 5 to 18
Challenge Level
A video clip of Jo Boaler talking about Complex Instruction.
Dotty Six
Age 5 to 11
Challenge Level
Dotty Six is a simple dice game that you can adapt in many ways.
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?
Take One Example
Age 5 to 11
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.
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?
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!
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?
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.
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?
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?
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?
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?
Totality
Age 5 to 11
Challenge Level
This is an adding game for two players. Can you be the first to reach the target?
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?
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?
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?
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.
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.
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?
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?
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?
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?
Sorted
Age 14 to 18
Challenge Level
How can you quickly sort a suit of cards in order from Ace to King?
Perimeter Possibilities
Age 11 to 14
Challenge Level
I'm thinking of a rectangle with an area of 24. What could its perimeter be?
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.
Tasks Promoting Inquirylive
Age 11 to 18
Challenge Level
Video for teachers of a talk given by Dan Meyer in Cambridge in March 2013.
Strange Bank Account
Age 11 to 14
Challenge Level
Imagine a very strange bank account where you are only allowed to do two things...
Up, Down, Flying Around
Age 11 to 14
Challenge Level
Play this game to learn about adding and subtracting positive and negative numbers
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?
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?
Rhombuses from Diagonals
Age 11 to 16
Take a look at the video showing rhombuses and their diagonals...
Areas on a Grid
Age 11 to 16
Take a look at the video showing areas of different shapes on dotty grids...
Sketching Graphs - Transformations
Age 16 to 18
Challenge Level
If you can sketch y=f(x), there are several related functions you can also sketch...
Subtraction Surprise
Age 7 to 14
Challenge Level
Try out some calculations. Are you surprised by the results?
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?
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?
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?
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...
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?
Vanishing Roots
Age 14 to 18
If $y=x^2-6x+c$, and we vary $c$, what happens to the roots when $c>9$?
Pouring Problem
Age 7 to 11
Challenge Level
What do you think is going to happen in this video clip? Are you surprised?
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?
Tumbling Down
Age 7 to 11
Challenge Level
Watch this animation. What do you see? Can you explain why this happens?
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?
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?
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?
Surprising Split
Age 7 to 11
Challenge Level
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
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?
NRICH is part of the family of activities in the Millennium Mathematics Project.