What is the greatest number of squares you can make by overlapping three squares?
These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Can you cut up a square in the way shown and make the pieces into a triangle?
A game in which players take it in turns to choose a number. Can you block your opponent?
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
Can you make the birds from the egg tangram?
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
Use the tangram pieces to make our pictures, or to design some of your own!
Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
How can you make an angle of 60 degrees by folding a sheet of paper twice?
The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.
You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.
Exploring and predicting folding, cutting and punching holes and making spirals.
Make a flower design using the same shape made out of different sizes of paper.
In this article for primary teachers, Fran describes her passion for paper folding as a springboard for mathematics.
Make a cube out of straws and have a go at this practical challenge.
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
A game to make and play based on the number line.
Here is a version of the game 'Happy Families' for you to make and play.
Which of the following cubes can be made from these nets?
Reasoning about the number of matches needed to build squares that share their sides.
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Delight your friends with this cunning trick! Can you explain how it works?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?
What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...
Can you visualise what shape this piece of paper will make when it is folded?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
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?
What shape is made when you fold using this crease pattern? Can you make a ring design?
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
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?
How many models can you find which obey these rules?
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?