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

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?

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.

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

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

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

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

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

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?

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?

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?

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....?

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?

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.

Can you put these shapes in order of size? Start with the smallest.

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

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?

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

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

Complete the squares - but be warned some are trickier than they look!

Use the interactivity or play this dice game yourself. How could you make it fair?

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?

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?

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

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

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?

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

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.

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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 people?

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

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

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?

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