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

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

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?

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

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

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?

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

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

Can you split each of the shapes below in half so that the two parts are exactly the same?

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

Make a mobius band and investigate its properties.

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.

Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

Follow these instructions to make a three-piece and/or seven-piece tangram.

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

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 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?

Using these kite and dart templates, you could try to recreate part of Penrose's famous tessellation or design one yourself.

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

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

Did you know mazes tell stories? Find out more about mazes and make one of your own.

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 see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?

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

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

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

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?

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?

Ideas for practical ways of representing data such as Venn and Carroll diagrams.

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

Follow these instructions to make a five-pointed snowflake from a square of paper.

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?

It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!

What do these two triangles have in common? How are they related?

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?

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.

Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?

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

Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.

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.

We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

For this activity which explores capacity, you will need to collect some bottles and jars.

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