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?

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

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?

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

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?

Can you fit the tangram pieces into the outline of this telephone?

Can you fit the tangram pieces into the outline of Little Fung at the table?

Can you fit the tangram pieces into the outline of Little Ming playing the board game?

Can you fit the tangram pieces into the outline of this junk?

Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?

Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?

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?

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?

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

If you'd like to know more about Primary Maths Masterclasses, this is the package to read! Find out about current groups in your region or how to set up your own.

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

Can you fit the tangram pieces into the outlines of these people?

Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?

Can you fit the tangram pieces into the outlines of the workmen?

Can you fit the tangram pieces into the outline of these rabbits?

Can you fit the tangram pieces into the outline of the telescope and microscope?

Can you fit the tangram pieces into the outline of this plaque design?

Can you fit the tangram pieces into the outline of this goat and giraffe?

Can you fit the tangram pieces into the outlines of the candle and sundial?

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

Can you fit the tangram pieces into the outlines of these clocks?

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

Can you fit the tangram pieces into the outline of the child walking home from school?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

Can you fit the tangram pieces into the outlines of the chairs?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

Can you make the birds from the egg tangram?

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

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 is a simple paper-folding activity that gives an intriguing result which you can then investigate further.

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

How can you make a curve from straight strips of paper?

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

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

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

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.

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

The challenge for you is to make a string of six (or more!) graded cubes.