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

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

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?

Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?

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

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?

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

Can you lay out the pictures of the drinks in the way described by the clue cards?

Can you make five differently sized squares from the tangram pieces?

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

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

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

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

Surprise your friends with this magic square trick.

Make a mobius band and investigate its properties.

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

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

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?

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.

These pictures show squares split into halves. Can you find other ways?

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?

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?

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

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?

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

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

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

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

Can you make the birds from the egg tangram?

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!

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

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

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

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?

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

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 work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

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?

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

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

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

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

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?

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