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!

Can you work out what is wrong with the cogs on a UK 2 pound coin?

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.

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.

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

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

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.

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

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?

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 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?

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

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

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?

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?

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.

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.

Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?

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?

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.

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

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?

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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

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?

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?

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

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.

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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

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

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?

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. . . .

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. . . .

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?

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

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.

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

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?

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

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