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

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Prove Pythagoras' Theorem using enlargements and scale factors.

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

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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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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.

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

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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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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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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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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?

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

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

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

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

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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?

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Use Excel to explore multiplication of fractions.

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Have a go at this version of John Conway's game. Do you have any good strategies for winning?

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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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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An Excel spreadsheet with an investigation.

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Use Excel to practise adding and subtracting fractions.

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Use an interactive Excel spreadsheet to investigate factors and multiples.

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Use an Excel spreadsheet to explore long multiplication.

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

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

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Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?

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

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Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

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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?

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

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Can you find triangles on a 9-point circle? Can you work out their angles?

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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?

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