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

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?

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

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

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?

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

Here is a chance to play a version of the classic Countdown Game.

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

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

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.

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

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

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

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.

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

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?

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

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

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

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

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

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

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

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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.

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?

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?

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!

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

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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

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

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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?

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

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

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

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

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

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.

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

An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .

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

An interactive activity for one to experiment with a tricky tessellation

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