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Students will be able to: explore congruence of a plane shape when rotating the shape about a centre of rotation determine the ‘order of rotation’ in shapes with rotational symmetry.

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Q1. Explain the difference between translation and reflection. Q2. Describe the translation of the following triangles (red to blue).

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In your notebook, draw the arrow below and its reflection.

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A rotation turns a figure about a fixed point, called the centre of rotation. A rotation is specified by: the centre of rotation the angle of rotation the direction of rotation (clockwise or anti-clockwise).

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Identify how far the triangles below (black to grey) have rotated in a clockwise and anticlockwise direction.

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Rotating a simple shape Provide students with cardboard from a discarded box (or other source), scissors and a pen/pencil. Instruct students to cut out a simple triangle (roughly 20 cm across) and approximate the middle with a small dot. Working on a flat surface, place the sharp end of their pencil on the dot and rotate the shape. Move the pencil to a corner or edge of the shape and rotate again.

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Does the cut-out change shape when it is rotated? (No) If the cut-out is rotated 90 o which of the two centres of rotation would produce the largest arc? (the rotation point near the corner/edge) How could a larger rotation arc be produced? (by moving the centre of rotation further away from the shape) If the shape was rotated 270 o in a clockwise direction, could the rotation be described in another way? ( Yes: 90 o in an anti-clockwise direction.)

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An image rotated 90 o in an anti-clockwise direction would need to be rotated by what amount in a clockwise direction to be in the same place? (360 o – 90 o = 270 o ; also accept the answer: – 270 o.)

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Direct students to cut out an equilateral triangle accurately from the cardboard previously used. Have them locate the centre of the triangle and mark it. Place the shape on a clean sheet of paper and trace around it. Leave the shape in place on the paper. With pencils firmly on the centre point of the triangle, rotate the shape and note the number of times that the cardboard exactly covers the tracing.

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How many times did the cut-out triangle exactly cover the traced triangle? (three) Would you expect the same answer for an isosceles or scalene triangle? Explain your thinking. (No: their shape will only be covered once in a full rotation.) Rotate a cut-out of an isosceles or scalene triangle on the board to verify your expectation. If a shape can be rotated about its centre point and cover its exact shape within 360 o, then the shape is said to have ‘rotational symmetry’. The number of times that this occurs corresponds to the ‘order of rotation’.

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