Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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!

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

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?

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

Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?

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

Work out the fractions to match the cards with the same amount of money.

An interactive activity for one to experiment with a tricky tessellation

An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .

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.

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.

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?

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

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

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

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?

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?

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

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

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

Train game for an adult and child. Who will be the first to make the train?

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?

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?

Can you find all the different ways of lining up these Cuisenaire rods?

Can you work out what is wrong with the cogs on a UK 2 pound coin?

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

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

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

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.

Can you complete this jigsaw of the multiplication square?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Can you fit the tangram pieces into the outline of Granma T?

Can you use the interactive to complete the tangrams in the shape of butterflies?

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.

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

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

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!

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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

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