Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

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?

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

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.

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

These pictures show squares split into halves. Can you find other ways?

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

You have a set of the digits from 0 – 9. Can you arrange these in the 5 boxes to make two-digit numbers as close to the targets as possible?

An activity making various patterns with 2 x 1 rectangular tiles.

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 make the birds from the egg tangram?

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?

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?

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

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?

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

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

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

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.

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

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?

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?

Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?

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

Explore the triangles that can be made with seven sticks of the same length.

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?

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

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.

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

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 outline of this junk?

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

In this activity focusing on capacity, you will need a collection of different jars and bottles.

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.

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?

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

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

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

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

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

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 outlines of the chairs?

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

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

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?