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?

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

Work out how to light up the single light. What's the rule?

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?

Use the interactivities to complete these Venn diagrams.

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

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?

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

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

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?

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

Play this well-known game against the computer where each player is equally likely to choose scissors, paper or rock. Why not try the variations too?

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

These interactive dominoes can be dragged around the screen.

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

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

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

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!

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?

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

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?

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

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

Can you complete this jigsaw of the multiplication square?

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

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?

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

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

Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?

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?

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

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

Use the information about Sally and her brother to find out how many children there are in the Brown family.

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

How many different rhythms can you make by putting two drums on the wheel?

An interactive activity for one to experiment with a tricky tessellation