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

Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

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?

Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?

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

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.

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?

Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

Find the frequency distribution for ordinary English, and use it to help you crack the code.

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.

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

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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?

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

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?

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

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

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

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

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!

Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.

An interactive activity for one to experiment with a tricky tessellation

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.

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. . . .

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

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?

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

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 make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

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.

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

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.

Use Excel to explore multiplication of fractions.

Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...

These interactive dominoes can be dragged around the screen.

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

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.