This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

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

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

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.

What is the greatest number of squares you can make by overlapping three squares?

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 ...

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

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

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?

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

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

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

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!

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

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

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?

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

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

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

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?

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?

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?

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

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

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

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

Can you each work out what shape you have part of on your card? What will the rest of it look like?

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.

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?

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

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

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

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?

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

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

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

Surprise your friends with this magic square trick.

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

Make a mobius band and investigate its properties.

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.

Reasoning about the number of matches needed to build squares that share their sides.

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?