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

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.

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?

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.

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.

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

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.

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

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?

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.

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

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

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Use the number weights to find different ways of balancing the equaliser.

Can you hang weights in the right place to make the equaliser balance?

An environment which simulates working with Cuisenaire rods.

How many trains can you make which are the same length as Matt's, using rods that are identical?

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

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

Use the interactivity or play this dice game yourself. How could you make it fair?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

How many different triangles can you make on a circular pegboard that has nine pegs?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?