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.

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 ...

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

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

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

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Here are some short problems for you to try. Talk to your friends about how you work them out.

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.

Look at the changes in results on some of the athletics track events at the Olympic Games in 1908 and 1948. Compare the results for 2012.

Look at some of the results from the Olympic Games in the past. How do you compare if you try some similar activities?

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

Looking at the 2012 Olympic Medal table, can you see how the data is organised? Could the results be presented differently to give another nation the top place?

This problem explores the range of events in a sports day and which ones are the most popular and attract the most entries.

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

This activity is based on data in the book 'If the World Were a Village'. How will you represent your chosen data for maximum effect?

Take a look at these data collected by children in 1986 as part of the Domesday Project. What do they tell you? What do you think about the way they are presented?

Have a look at this data from the RSPB 2011 Birdwatch. What can you say about the data?

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

Class 5 were looking at the first letter of each of their names. They created different charts to show this information. Can you work out which member of the class was away on that day?

This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

Can you put these mixed-up times in order? You could arrange them in a circle.

Can you put these times on the clocks in order? You might like to arrange them in a circle.

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Dotty Six is a simple dice game that you can adapt in many ways.

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

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?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

What statements can you make about the car that passes the school gates at 11am on Monday? How will you come up with statements and test your ideas?

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 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.

The challenge for you is to make a string of six (or more!) graded cubes.

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

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

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?