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

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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

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

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Use Excel to explore multiplication of fractions.

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What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

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Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.

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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?

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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. . . .

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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.

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

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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.

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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.

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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. . . .

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

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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. . . .

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Use Excel to investigate the effect of translations around a number grid.

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A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.

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Use an Excel spreadsheet to explore long multiplication.

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Use an interactive Excel spreadsheet to investigate factors and multiples.

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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?

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

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Use Excel to practise adding and subtracting fractions.

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An Excel spreadsheet with an investigation.

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Use an interactive Excel spreadsheet to explore number in this exciting game!

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

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

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Prove Pythagoras' Theorem using enlargements and scale factors.

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In this game you are challenged to gain more columns of lily pads than your opponent.

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

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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. . . .

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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?

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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. . . .

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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.

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Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.

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

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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.

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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. . . .

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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?

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

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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?

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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.

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

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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?

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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?

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The interactive diagram has two labelled points, A and B. It is designed to be used with the problem "Cushion Ball"

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Can you find the pairs that represent the same amount of money?

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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?