Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

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

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

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?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?

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

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 fit the tangram pieces into the outlines of these people?

Can you fit the tangram pieces into the outlines of the chairs?

Can you fit the tangram pieces into the outline of the child walking home from school?

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

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

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

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

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

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

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

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?

Move just three of the circles so that the triangle faces in the opposite direction.

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

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

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.

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

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.

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?

Stop the Clock game for an adult and child. How can you make sure you always win this game?

Use the interactivities to complete these Venn diagrams.

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....?

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 this telephone?

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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

How many trains can you make which are the same length as Matt's, using rods that are identical?

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

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