Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Here is a version of the game 'Happy Families' for you to make and play.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
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?
Can you make the birds from the egg tangram?
A game in which players take it in turns to choose a number. Can you block your opponent?
Delight your friends with this cunning trick! Can you explain how it works?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
A game to make and play based on the number line.
Factors and Multiples game for an adult and child. How can you make sure you win this game?
These practical challenges are all about making a 'tray' and covering it with paper.
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?
Use the tangram pieces to make our pictures, or to design some of your own!
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?
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?
Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
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?
Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
How many models can you find which obey these rules?
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?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?
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?
How is it possible to predict the card?
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
What is the greatest number of squares you can make by overlapping three squares?
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?
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?
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?
Make a flower design using the same shape made out of different sizes of paper.
Reasoning about the number of matches needed to build squares that share their sides.
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.
I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades?
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?
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
Can you deduce the pattern that has been used to lay out these bottle tops?
In this article for primary teachers, Fran describes her passion for paper folding as a springboard for mathematics.
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
I start with a red, a blue, a green and a yellow marble. I can trade any of my marbles for three others, one of each colour. Can I end up with exactly two marbles of each colour?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?