TOPIC 9: Rotation – Sample Activity

Context

Nyimu village is found deep in the valley and the residents have always failed to determine when to leave their gardens in the evening to prepare supper. They have actually always taken their lunch and left the gardens very late because they have no watches to tell the time. In an attempt to assist the residents of Nyimu village, Penelope designed a clock with only one rotating hand that rotates 5 times in one hour.

Support Material

The clock can be set to start and stop. Work in the garden starts at 7:00 am, lunch time is 1:00 pm and time to leave the gardens in Nyimu village is 6:00 pm.

Resource

Knowledge of rotation and numerical concepts.

Task

Design a manual that can best be understood by the users of Penelope’s clock while telling the time for lunch and the time to leave the gardens.

Topic Summary

In this topic, you have learnt that:

• the number of times a plane figure fits onto itself and looks the same as the original in one complete turn (through 360°) is called the order of rotational symmetry of the plane figure.
• rotation in a plane takes place about a fixed point called the centre of rotation. Every other point except the centre of rotation moves on the arc of a circle.
• a figure which is being rotated is called an object while the figure formed after rotation is an image.
• the angle between the line joining the corresponding points of the object and the image to the centre of rotation is the angle of rotation.
• the centre of rotation is obtained by finding the point of intersection of the mediators of lines joining a pair of two corresponding points on the object and the image.
• in a rotation, every line segment on the object turns through the same angle of rotation.
• the object and its images are directly congruent. They are the same shape and size.
• the distances between the centre of rotation and vertices of objects are equal to the distances between the centre of rotation and corresponding vertices of image.
• the centre of rotation is the only fixed point which does not change in position. All the other points on the object change in position during a rotation.
• with reference to a clock, clockwise rotation is a rotation towards the right and anticlockwise rotation is a rotation towards the left.
• the angle of rotation clockwise is negative while that anticlockwise is positive.
• a turn is a rotation through an angle of 360°. Thus, a positive quarter-turn means a rotation through +90° or rotation through 90° anticlockwise, a negative half-turn is a rotation through -180° or rotation through 180° clockwise e.t.c.