An environment that enables you to investigate tessellations of regular polygons

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.

Can you find triangles on a 9-point circle? Can you work out their angles?

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

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

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?

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?

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

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.

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?

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

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

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

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

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?

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?

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?

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. . . .

An interactive activity for one to experiment with a tricky tessellation

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.

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?

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.

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

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

Use Excel to explore multiplication of fractions.

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.

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

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

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?

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.

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

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.

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.

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 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.

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

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.

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. . . .

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

Can you beat the computer in the challenging strategy game?

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

Here is a chance to play a fractions version of the classic Countdown Game.

A game in which players take it in turns to choose a number. Can you block your opponent?

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

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

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.

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