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

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

Twenty four games for the run-up to Christmas.

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

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

Move just three of the circles so that the triangle faces in the opposite direction.

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

Use the interactivity to sort these numbers into sets. Can you give each set a name?

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

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

Can you complete this jigsaw of the multiplication square?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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?

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

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

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

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?

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

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

If you have only four weights, where could you place them in order to balance this equaliser?

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

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

These interactive dominoes can be dragged around the screen.

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

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

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?

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

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

How many right angles can you make using two sticks?

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

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?

An environment which simulates working with Cuisenaire rods.

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

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

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?

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.

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?