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 interactivities to complete these Venn diagrams.

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

Can you complete this jigsaw of the multiplication square?

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

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

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?

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?

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?

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

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

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

These interactive dominoes can be dragged around the screen.

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

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

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

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

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 everybody knows. You can play with a friend or online. If you play correctly you never lose!

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?

An interactive activity for one to experiment with a tricky tessellation

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?

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....?

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?

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.

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?

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.

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

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!

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

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

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

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

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

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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

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

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

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?

Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?

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

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.