Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

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

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

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?

Mathmo is a revision tool for post-16 mathematics. It's great installed as a smartphone app, but it works well in pads and desktops and notebooks too. Give yourself a mathematical workout!

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Here is a chance to play a version of the classic Countdown Game.

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

Can you work through these direct proofs, using our interactive proof sorters?

Use the interactivities to complete these Venn diagrams.

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

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Can you locate these values on this interactive logarithmic scale?

Can you work out which spinners were used to generate the frequency charts?

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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.

Have you seen this way of doing multiplication ?

How good are you at finding the formula for a number pattern ?

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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

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

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

An environment that simulates a protractor carrying a right- angled triangle of unit hypotenuse.

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Can you complete this jigsaw of the multiplication square?

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

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

A game in which players take it in turns to choose a number. Can you block your opponent?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Sort the houses in my street into different groups. Can you do it in any other ways?

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

Find the frequency distribution for ordinary English, and use it to help you crack the code.

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.