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

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

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

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?

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

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?

Can you hang weights in the right place to make the equaliser balance?

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

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?

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

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!

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

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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

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.

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?

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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?

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

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.

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

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

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

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?

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

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.

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?

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.

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

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....?

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 fit the tangram pieces into the outline of this telephone?

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.

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

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

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

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

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?

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