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?

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

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

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....?

These interactive dominoes can be dragged around the screen.

Can you complete this jigsaw of the multiplication square?

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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

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?

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

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.

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

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

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

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

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

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?

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?

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

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

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

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

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?

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?

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?

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?

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

Play this well-known game against the computer where each player is equally likely to choose scissors, paper or rock. Why not try the variations too?

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.

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 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

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

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.

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

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

Board Block game for two. Can you stop your partner from being able to make a shape on the board?

Calculate the fractional amounts of money to match pairs of cards with the same value.

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?

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

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

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

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. . . .