First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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?

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!

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

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.

An interactive activity for one to experiment with a tricky tessellation

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

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

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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

Can you complete this jigsaw of the multiplication square?

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

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

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

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

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. . . .

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?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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?

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

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.

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 find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

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

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

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

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

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?

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!

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....?

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

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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?

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?

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

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.

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

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

Find out what a "fault-free" rectangle is and try to make some of your own.

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?

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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