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
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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.
Use Excel to explore multiplication of fractions.
Use an Excel spreadsheet to explore long multiplication.
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. . . .
Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Can you discover whether this is a fair game?
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 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?
To avoid losing think of another very well known game where the patterns of play are similar.
A collection of resources to support work on Factors and Multiples at Secondary level.
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 investigate the effect of translations around a number grid.
Use an interactive Excel spreadsheet to explore number in this exciting game!
A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.
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.
Can you explain the strategy for winning this game with any target?
Use Excel to practise adding and subtracting fractions.
An Excel spreadsheet with an investigation.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Use an interactive Excel spreadsheet to investigate factors and multiples.
How good are you at finding the formula for a number pattern ?
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?
How good are you at estimating angles?
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?
Here is a chance to play a fractions version of the classic Countdown Game.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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. . . .
Here is a chance to play a version of the classic Countdown Game.
An animation that helps you understand the game of Nim.
It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?
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.
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.
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?
Can you beat the computer in the challenging strategy game?
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. . . .
A game in which players take it in turns to choose a number. Can you block your opponent?
A group of interactive resources to support work on percentages Key Stage 4.
P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?
The interactive diagram has two labelled points, A and B. It is designed to be used with the problem "Cushion Ball"
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?
Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?
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?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
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?
This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?