Factors and Multiples game for an adult and child. How can you make sure you win this game?

A game in which players take it in turns to choose a number. Can you block your opponent?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Use the tangram pieces to make our pictures, or to design some of your own!

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Here is a version of the game 'Happy Families' for you to make and play.

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

A game to make and play based on the number line.

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

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?

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?

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?

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?

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.

Can you make the birds from the egg tangram?

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

Delight your friends with this cunning trick! Can you explain how it works?

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?

Surprise your friends with this magic square trick.

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?

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

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?

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?

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?

These practical challenges are all about making a 'tray' and covering it with paper.

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.

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

Exploring and predicting folding, cutting and punching holes and making spirals.

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 many models can you find which obey these rules?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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?

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?

Can you each work out the number on your card? What do you notice? How could you sort the cards?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

Here are some ideas to try in the classroom for using counters to investigate number patterns.

Which of the following cubes can be made from these nets?

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

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 make an angle of 60 degrees by folding a sheet of paper twice?

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?

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!