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.

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

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

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

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

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?

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

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

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?

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

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?

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

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

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

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?

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

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

Make a mobius band and investigate its properties.

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

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

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

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

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

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

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!

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

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

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

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

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

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

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

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

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

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

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

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

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

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

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

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

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.

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

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?