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

How many models can you find which obey these rules?

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

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

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

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.

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

Make a mobius band and investigate its properties.

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

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

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.

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?

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

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

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

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

Can you visualise what shape this piece of paper will make when it is folded?

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.

Surprise your friends with this magic square trick.

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

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

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

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

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?

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

What shape is made when you fold using this crease pattern? Can you make a ring design?

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

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?

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?

Can you cut up a square in the way shown and make the pieces into a triangle?

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

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.

A brief video looking at how you can sometimes use symmetry to distinguish knots. Can you use this idea to investigate the differences between the granny knot and the reef knot?

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

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

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?

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

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

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.

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

Make a cube out of straws and have a go at this practical challenge.

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?

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?