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

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

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?

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

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?

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?

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?

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

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

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

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

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?

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

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

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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?

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

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?

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

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?

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.

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?

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?

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

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

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

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

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

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

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

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?

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

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?

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?

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?

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

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

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

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