Find out what a "fault-free" rectangle is and try to make some of your own.

An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.

An environment which simulates working with Cuisenaire rods.

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.

Can you explain the strategy for winning this game with any target?

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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?

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

Can you find all the different ways of lining up these Cuisenaire rods?

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

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?

Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

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

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

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?

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?

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

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?

This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.

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

Practise your diamond mining skills and your x,y coordination in this homage to Pacman.

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.

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

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.

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.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

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. . . .

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?

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

Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

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.

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

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?

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....?

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?

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 fit the tangram pieces into the outlines of the chairs?

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

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

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

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.

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Can you fit the tangram pieces into the outline of the child walking home from school?

Can you fit the tangram pieces into the outline of this telephone?

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.

Can you fit the tangram pieces into the outline of Little Fung at the table?