Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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

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.

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

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

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?

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

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

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.

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?

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

Can you complete this jigsaw of the multiplication square?

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

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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....?

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?

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.

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?

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

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?

Use the interactivities to complete these Venn diagrams.

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

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

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

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

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

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

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?

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

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

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

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

What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

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?

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

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

Exchange the positions of the two sets of counters in the least possible number of moves

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

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?

An interactive activity for one to experiment with a tricky tessellation

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

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.

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

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?