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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?

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Can you sort these triangles into three different families and explain how you did it?

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

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How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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

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

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Take it in turns to make a triangle on the pegboard. Can you block your opponent?

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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?

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

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Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

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

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Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

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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?

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Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

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In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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Try to picture these buildings of cubes in your head. Can you make them to check whether you had imagined them correctly?

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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?

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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?

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How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

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Here are shadows of some 3D shapes. What shapes could have made them?

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

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Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?

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Complete the squares - but be warned some are trickier than they look!

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This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

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This activity focuses on similarities and differences between shapes.

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My dice has inky marks on each face. Can you find the route it has taken? What does each face look like?

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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.

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Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

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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?

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How many faces can you see when you arrange these three cubes in different ways?

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Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.