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

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

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

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

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

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

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.

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

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

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

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 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. . . .

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?

A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand. . . .

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.

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

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.

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 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?

Can you work out which spinners were used to generate the frequency charts?

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.

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?

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. . . .

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

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

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?

To avoid losing think of another very well known game where the patterns of play are similar.

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?

Discs are flipped in the air. You win if all the faces show the same colour. What is the probability of winning?

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

This is an interactivity in which you have to sort the steps in the completion of the square into the correct order to prove the formula for the solutions of quadratic equations.

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.

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

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?

How good are you at finding the formula for a number pattern ?

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

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

Prove Pythagoras' Theorem using enlargements and scale factors.

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.

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?

Use this animation to experiment with lotteries. Choose how many balls to match, how many are in the carousel, and how many draws to make at once.

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.

A simple spinner that is equally likely to land on Red or Black. Useful if tossing a coin, dropping it, and rummaging about on the floor have lost their appeal. Needs a modern browser; if IE then at. . . .

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?