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.

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?

Can you explain the strategy for winning this game with any target?

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

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?

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

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 can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.

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

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

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?

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

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.

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

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!

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. . . .

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

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.

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

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

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

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

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....?

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

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

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

Can you find all the different triangles on these peg boards, and find their angles?

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?

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

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

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

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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

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

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

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?

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

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.

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

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

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 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.

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.