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 make five differently sized squares from the tangram pieces?

Can you split each of the shapes below in half so that the two parts are exactly the same?

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

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?

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

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

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

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?

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

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

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?

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

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

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?

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

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.

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

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

Can you describe a piece of paper clearly enough for your partner to know which piece it is?

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

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

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

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?

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

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?

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 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?

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

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

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

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

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

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?

This practical activity challenges you to create symmetrical designs by cutting a square into strips.

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

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?

For this activity which explores capacity, you will need to collect some bottles and jars.

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.

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

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

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

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