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.

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

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?

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.

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

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

Make a mobius band and investigate its properties.

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

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

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 ...

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

Exploring and predicting folding, cutting and punching holes and making spirals.

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

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

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

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

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?

Surprise your friends with this magic square trick.

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

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!

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

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

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

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?

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

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

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

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

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?

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

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.

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

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

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

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

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

How many models can you find which obey these rules?

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