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1 Tandi Clausen-May Teaching Maths to Pupils with Different Learning Styles London: Paul Chapman, 2005 Click the mouse. Click the mouse only when you seeClick the mouse. Otherwise you will miss some of the dynamic bits. Angles 3 – Angles inside a straight-sided shape (The internal angles of a polygon)

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2 Click the mouse to move the pointer through the angles inside the triangle. When you move through the angles inside a straight- sided shape, what angle do you turn through? Click the mouse.

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3 The pointer started like this… Click the mouse to move the pointer through the angles inside the triangle again. … but it finished like this!

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4 The pointer started like this… … but it finished like this! Click the mouse.

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5 So the pointer has turned through a half turn! The angles inside a triangle add up to a half turn. Click the mouse.

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6 What happens to the angles inside the triangle if you break one side to make a quadrilateral? Click the mouse to break one side of the triangle Click the mouse.

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7 These two angles got larger… …and there is a new angle here. Click the mouse.

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8 Click the mouse to move the pointer through the angles inside the quadrilateral. When you move through the angles inside a quadrilateral, what angle do you turn through? Click the mouse.

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9 The pointer started like this… … and it finished like this as well! Click the mouse.

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10 Click the mouse to move the pointer through the angles inside the quadrilateral again. Click the mouse.

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11 So the pointer has turned through a whole turn! The angles inside a quadrilateral add up to a whole turn. Click the mouse.

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12 If you close the quadrilateral back into a triangle…. Click the mouse to close the quadrilateral …the new angle gets bigger and bigger… …until it is a straight angle. Click the mouse.

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13 The straight angle is here, on one side of the triangle. Click the mouse to watch the new angle grow back into a straight angle again. In a sense, you could say that a triangle is a quadrilateral with one straight angle! Click the mouse.

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14 There is an extra straight angle in this triangle, so it is a kind of quadrilateral. Click the mouse to move the pointer through the angles inside thequadrilateral with one straight angle. Click the mouse.

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15 We start with a triangle, whose internal angles add up to a half turn. In the triangle, the pointer turned through a half turn, like this: Click the mouse to move the pointer through the angles inside the triangle. Click the mouse.

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16 We start with a triangle, whose internal angles add up to a half turn. In the triangle, the pointer turned through a half turn, like this: So the internal angles of a triangle add up to a half turn. Click the mouse.

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17 Click the mouse to move the pointer through the angles inside thequadrilateral with one straight angle. Now we add one straight angle, to make a quadrilateral with one straight angle. Now we have added an extra half turn. So the internal angles of a quadrilateral add up to a whole turn. Click the mouse.

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18 Click the mouse to move the pointer through the angles inside thepentagon with two straight angles. Now we could add another straight angle, to make a pentagon with two straight angles! Now we have added another half turn. So the internal angles of a pentagon add up to one and a half turns. Click the mouse.

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19 n - 2 ? Every time we add a new straight angle to one side of the polygon, we add another half turn to the sum of the internal angles. Number of sides 3 (triangle) Number of half turns 1 4 (quadrilateral)2 5 (pentagon)3 n Click the mouse when you are ready.

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