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

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?

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

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

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.

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

A collection of resources to support work on Factors and Multiples at Secondary level.

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?

An interactive activity for one to experiment with a tricky tessellation

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

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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.

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.

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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

Can you complete this jigsaw of the multiplication square?

Can you beat the computer in the challenging strategy game?

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

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

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?

Can you explain the strategy for winning this game with any target?

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

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

A game in which players take it in turns to choose a number. Can you block your opponent?

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

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

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

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

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

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

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?

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?

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

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 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?

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?

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?

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

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

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?