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.

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

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

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

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

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

Can you complete this jigsaw of the multiplication square?

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?

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.

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!

These interactive dominoes can be dragged around the screen.

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

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?

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?

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

Can you fit the tangram pieces into the outline of Little Fung at the table?

Can you fit the tangram pieces into the outline of this telephone?

An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.

Can you fit the tangram pieces into the outlines of these people?

Can you fit the tangram pieces into the outlines of these clocks?

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

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

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

What is the greatest number of squares you can make by overlapping three squares?

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?

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

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?

Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?

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.

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

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

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 Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?

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

Exchange the positions of the two sets of counters in the least possible number of moves

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!

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.

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

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.