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?

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

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

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

Can you complete this jigsaw of the multiplication square?

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

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 right angles can you make using two sticks?

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?

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 work out how to balance this equaliser? You can put more than one weight on a hook.

These interactive dominoes can be dragged around the screen.

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

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

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

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

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

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

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

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?

Work out the fractions to match the cards with the same amount of money.

A game for 1 person to play on screen. Practise your number bonds whilst improving your memory

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

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?

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

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?

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.

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.

A game for two people that can be played with pencils and paper. Combine your knowledge of coordinates with some strategic thinking.

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. . . .

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!

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

How many trains can you make which are the same length as Matt's, using rods that are identical?

Use the interactivity or play this dice game yourself. How could you make it fair?

Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?

Train game for an adult and child. Who will be the first to make the train?

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

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?

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

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