How good are you at finding the formula for a number pattern ?
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.
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
To avoid losing think of another very well known game where the patterns of play are similar.
Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The winner is the player to take the last counter.
Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.
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?
Can you beat the computer in the challenging strategy game?
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.
Use Excel to explore multiplication of fractions.
These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.
Can you find a way to turn a rectangle into a square?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.
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?
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. . . .
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. . . .
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
Match pairs of cards so that they have equivalent ratios.
The interactive diagram has two labelled points, A and B. It is designed to be used with the problem "Cushion Ball"
Discover a handy way to describe reorderings and solve our anagram in the process.
Can you give the coordinates of the vertices of the fifth point in the patterm on this 3D grid?
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
A tool for generating random integers.
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. . . .
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
There are thirteen axes of rotational symmetry of a unit cube. Describe them all. What is the average length of the parts of the axes of symmetry which lie inside the cube?
This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.
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.
Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .
Practise your skills of proportional reasoning with this interactive haemocytometer.
A collection of our favourite pictorial problems, one for each day of Advent.
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.
Here is a chance to play a fractions version of the classic Countdown Game.
Can you discover whether this is a fair game?
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.
Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.
Match the cards of the same value.
There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .
Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.
A collection of resources to support work on Factors and Multiples at Secondary level.
This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!
Use Excel to practise adding and subtracting fractions.
Use an interactive Excel spreadsheet to explore number in this exciting game!
Use an interactive Excel spreadsheet to investigate factors and multiples.
Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?
A group of interactive resources to support work on percentages Key Stage 4.