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?

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

Can you complete this jigsaw of the multiplication square?

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!

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?

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?

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

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

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?

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

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

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

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?

An environment which simulates working with Cuisenaire rods.

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

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

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

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

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?

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

Use the interactivities to complete these Venn diagrams.

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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?

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

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?

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

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

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

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

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

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

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?

An interactive activity for one to experiment with a tricky tessellation

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

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 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?

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.

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.

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?

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