How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

Can you complete this jigsaw of the multiplication square?

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....?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Use the interactivities to complete these Venn diagrams.

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?

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

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?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

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

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

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

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?

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?

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

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

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

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

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 find all the different ways of lining up these Cuisenaire rods?

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?

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 1 to 8 into the circles so that the four calculations are correct?

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?

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. . . .

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

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

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.

Exchange the positions of the two sets of counters in the least possible number of moves

An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.

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!

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

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

How many different triangles can you make on a circular pegboard that has nine pegs?

Can you find all the different triangles on these peg boards, and find their angles?

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?

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

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?

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?

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

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