A game in which players take it in turns to choose a number. Can you block your opponent?

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

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

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.

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

Can you fit the tangram pieces into the outline of Little Ming?

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

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 set the logic gates so that the number of bulbs which are on is the same as the number of switches which are on?

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

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.

Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?

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. . . .

An interactive activity for one to experiment with a tricky tessellation

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!

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

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.

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

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

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.

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?

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

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?

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

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

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

Find the frequency distribution for ordinary English, and use it to help you crack the code.

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

Use the interactivities to complete these Venn diagrams.

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

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

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

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

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.

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 explain the strategy for winning this game with any target?

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

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