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.

Are these statements always true, sometimes true or never true?

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

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

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?

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

Use the information on these cards to draw the shape that is being described.

How many possible necklaces can you find? And how do you know you've found them all?

Can you make a spiral for yourself? Explore some different ways to create your own spiral pattern and explore differences between different spirals.

This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles.

This problem shows that the external angles of an irregular hexagon add to a circle.

This ladybird is taking a walk round a triangle. Can you see how much he has turned when he gets back to where he started?

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

This problem explores the shapes and symmetries in some national flags.

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

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?

Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?

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?

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.

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

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

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

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

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?

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

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.

This task requires learners to explain and help others, asking and answering questions.

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

A task which depends on members of the group working collaboratively to reach a single goal.

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

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

What can you see? What do you notice? What questions can you ask?

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

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

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.

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

Can you describe the journey to each of the six places on these maps? How would you turn at each junction?

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

How much do you have to turn these dials by in order to unlock the safes?

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

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

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?

Use the clues about the symmetrical properties of these letters to place them on the grid.

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?