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?

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

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

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

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

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

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

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?

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

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.

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?

Make a mobius band and investigate its properties.

Make a flower design using the same shape made out of different sizes of paper.

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

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

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

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

Surprise your friends with this magic square trick.

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

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

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?

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

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?

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

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?

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?

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

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

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

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?

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?

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

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

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

This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

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?

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?

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

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

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

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

This practical activity challenges you to create symmetrical designs by cutting a square into strips.