Tandi Clausen-May

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

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

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

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

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

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.

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

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

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

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

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

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.

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

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

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.

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.

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

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

19. 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 Number of half turns 3 (triangle) 1 4 (quadrilateral) 2 5 (pentagon) 3 n n - 2 ? Click the mouse when you are ready.