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

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?

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?

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

Use the interactivity to sort these numbers into sets. Can you give each set a name?

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

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

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

A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.

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

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

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

Can you fit the tangram pieces into the outline of this telephone?

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

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?

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

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

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?

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.

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

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 put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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?

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.

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!

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

Take it in turns to make a triangle on the pegboard. Can you block your opponent?

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

Exchange the positions of the two sets of counters in the least possible number of moves

How many different rhythms can you make by putting two drums on the wheel?

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.

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.

An interactive activity for one to experiment with a tricky tessellation

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

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

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

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?

Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?

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

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

These interactive dominoes can be dragged around the screen.

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?

You'll need two dice to play this game against a partner. Will Incey Wincey make it to the top of the drain pipe or the bottom of the drain pipe first?