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

These interactive dominoes can be dragged around the screen.

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

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....?

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?

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?

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

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?

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

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

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

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

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 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.

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

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?

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

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

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?

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

Practise your number bonds whilst improving your memory in this matching pairs game.

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?

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

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

Can you complete this jigsaw of the multiplication square?

Practise your tables skills and try to beat your previous best score in this interactive game.

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?

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?

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

Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

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?

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

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

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

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

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

A train building game for two players. Can you be the one to complete the train?