Can you work out what is wrong with the cogs on a UK 2 pound coin?
What is the greatest number of squares you can make by overlapping three squares?
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!
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?
What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
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?
What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.
Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
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?
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?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?
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....?
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 find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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.
Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?
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?
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?
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. . . .
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.
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!
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?
Work out the fractions to match the cards with the same amount of money.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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.
Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .
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 for 1 person to play on screen. Practise your number bonds whilst improving your memory
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. . . .
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?
Mo has left, but Meg is still experimenting. Use the interactivity to help you find out how she can alter her pouch of marbles and still keep the two pouches balanced.
A game for two people that can be played with pencils and paper. Combine your knowledge of coordinates with some strategic thinking.