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?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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?
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?
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!
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
If you have only four weights, where could you place them in order to balance this equaliser?
Choose a symbol to put into the number sentence.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
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 all the different ways of lining up these Cuisenaire rods?
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.
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?
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?
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....?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Can you complete this jigsaw of the multiplication square?
Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
A card pairing game involving knowledge of simple ratio.
A generic circular pegboard resource.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Exchange the positions of the two sets of counters in the least possible number of moves
An interactive activity for one to experiment with a tricky tessellation
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.
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. . . .
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Use the interactivity or play this dice game yourself. How could you make it fair?
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?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Try out the lottery that is played in a far-away land. What is the chance of winning?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
A simulation of target archery practice
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
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?
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
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?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
A train building game for 2 players.
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?
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
Board Block game for two. Can you stop your partner from being able to make a shape on the board?