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?

Can you complete this jigsaw of the multiplication square?

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

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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!

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

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

An environment which simulates working with Cuisenaire rods.

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?

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing 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?

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

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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

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

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

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

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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

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?

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?

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

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

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

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.

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

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.

An interactive activity for one to experiment with a tricky tessellation

A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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

What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

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

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

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

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

Try out the lottery that is played in a far-away land. What is the chance of winning?

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?

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