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

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.

Use the blue spot to help you move the yellow spot from one star to the other. How are the trails of the blue and yellow spots related?

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

Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.

A collection of our favourite pictorial problems, one for each day of Advent.

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.

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

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

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

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

Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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?

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

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.

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?

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

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

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

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

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?

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....?

Use the information about Sally and her brother to find out how many children there are in the Brown family.

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

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 the child walking home from school?

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

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.

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

Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

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

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

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

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

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?