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

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

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

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

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?

These interactive dominoes can be dragged around the screen.

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

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....?

How many right angles can you make using two sticks?

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.

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.

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

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

Can you sort these triangles into three different families and explain how you did it?

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?

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?

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?

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

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?

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

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!

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

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?

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

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

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?

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

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

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

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

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?

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

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

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

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