This problem is intended to get children to look really hard at something they will see many times in the next few months.

Investigate these hexagons drawn from different sized equilateral triangles.

The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

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

These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.

What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?

This interactivity allows you to sort logic blocks by dragging their images.

Here is a selection of different shapes. Can you work out which ones are triangles, and why?

Look at some of the patterns in the Olympic Opening ceremonies and see what shapes you can spot.

Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?

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

Shapes are added to other shapes. Can you see what is happening? What is the rule?

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?

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Can you help the children in Mrs Trimmer's class make different shapes out of a loop of string?

Find out what a "fault-free" rectangle is and try to make some of your own.

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

Look at the mathematics that is all around us - this circular window is a wonderful example.

Can you spot circles, spirals and other types of curves in these photos?

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

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

Use the isometric grid paper to find the different polygons.

How many trapeziums, of various sizes, are hidden in this picture?

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?

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

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

How can these shapes be cut in half to make two shapes the same shape and size? Can you find more than one way to do it?

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

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

Read about David Hilbert who proved that any polygon could be cut up into a certain number of pieces that could be put back together to form any other polygon of equal area.

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

This activity challenges you to make collections of shapes. Can you give your collection a name?

Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

What mathematical words can be used to describe this floor covering? How many different shapes can you see inside this photograph?

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?

The challenge is to produce elegant solutions. Elegance here implies simplicity. The focus is on rhombi, in particular those formed by jointing two equilateral triangles along an edge.

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

This article describes investigations that offer opportunities for children to think differently, and pose their own questions, about shapes.

This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.

Read all about the number pi and the mathematicians who have tried to find out its value as accurately as possible.

The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?

This article for pupils gives some examples of how circles have featured in people's lives for centuries.

A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?

'What Shape?' activity for adult and child. Can you ask good questions so you can work out which shape your partner has chosen?