Use the number weights to find different ways of balancing the equaliser.

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

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

An environment which simulates working with Cuisenaire rods.

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

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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

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

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

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

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

Can you find all the different ways of lining up these Cuisenaire rods?

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

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

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

Use the interactivity to move Mr Pearson and his dog. Can you move him so that the graph shows a curve?

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 complete this jigsaw of the multiplication square?

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

Can you create a story that would describe the movement of the man shown on these graphs? Use the interactivity to try out our ideas.

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....?

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

What happens when you try and fit the triomino pieces into these two grids?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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

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

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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?

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

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

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 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?

Stop the Clock game for an adult and child. How can you make sure you always win this game?

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?

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

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?

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

A game for two or more players that uses a knowledge of measuring tools. Spin the spinner and identify which jobs can be done with the measuring tool shown.

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

Try out the lottery that is played in a far-away land. What is the chance of winning?

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?

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

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