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

Can you put these shapes in order of size? Start with the smallest.

You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?

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

Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?

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

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?

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

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

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

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

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

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

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

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.

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

Surprise your friends with this magic square trick.

Make a mobius band and investigate its properties.

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

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

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

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?

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

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?

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

In this activity focusing on capacity, you will need a collection of different jars and bottles.

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

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

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?

Explore the triangles that can be made with seven sticks of the same length.

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

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?

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?

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

An activity making various patterns with 2 x 1 rectangular tiles.

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

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?

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!

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

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

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?

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