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...
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
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
To avoid losing think of another very well known game where the patterns of play are similar.
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Can you discover whether this is a fair game?
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?
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.
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. . . .
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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 explain the strategy for winning this game with any target?
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?
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, 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.
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
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 put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
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 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.
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Can you find a way to turn a rectangle into a square?
Prove Pythagoras' Theorem using enlargements and scale factors.
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 find triangles on a 9-point circle? Can you work out their angles?
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.
Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?
An animation that helps you understand the game of Nim.
Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.
This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.
A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?
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. . . .
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?
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?
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.
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
Here is a chance to play a fractions version of the classic Countdown Game.
A tool for generating random integers.
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...
Here is a chance to play a version of the classic Countdown Game.
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.
How good are you at finding the formula for a number pattern ?
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?
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?
This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.
Match the cards of the same value.
Can you beat the computer in the challenging strategy game?
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.