Watch it pass through 180º (at this moment the arrow will be pointing horizontally but right to left). Encourage them to watch the arrow pass through 90º (if AB is horizontal the arrow will be pointing straight up at this moment). Encourage them to do the turns slowly and watch the arrow complete the turns. In the second case, if p is 60º, q is 290º, and r is 50º, the total turn will be 400º.Įxamples such as the second one above may cause problems for the students. In the first case if p is 60º, q is 90º, and r is 50º, the total turn will be 20º. What is the total turn? If s is 60º and t is 70º the total turn will be 130º. You will see that in this case they are turning the back half of the arrow through the angle t. Slide the TM until the centre is at C, and turn the arrow through the angle t. They then turn the arrow through the angle s. In this case the students should set the TM to 0º with the arrow pointing to A, and with the centre at B. For instance, if s is 60º and t is 110º the total turn will be -50º. Here the total amount of turn will be negative. Try other similar examples until the students are confident with this situation. For example, if s is 60º and t is 50º the TM should be showing a total turn of 10º. This basically boils down to a turn of sº minus tº.
Now they turn the arrow until it points towards E. The arrow should still be pointing along the line from C to D. Now they slide the TM along the line BC until the centre is at C. The students turn the arrow until it points towards C (through the angle marked s). Set the TM to 0º and place the centre at B with the arrow pointing to A. Repeat this little exercise until the students understand how the TM can be used to sum 2 or more turns. They can read the total turn from the TM. Now continue the turn by turning the arrow to point to D. The students now turn the arrow so that it points to B. Initially the students should place the TM with the centre on C and the arrow (set to 0º) pointing to A. Issue each student with a piece of paper with 3 rays. Once the equipment is made the students need to learn how it can be used to measure the sum of two or more turns. They will need to trust you that this piece of equipment, and more importantly, the mathematical idea it helps us understand, is of particular importance, and it will eventually make some otherwise difficult ideas easy. This session is likely to appear somewhat pointless to the students. Give each of the students time to make their own TM. The circle should be approximately 6cm in diameter. A flat backed drawing pin (pointing upwards) could be used as the centre pin. The arrow needs to be able to rotate about its centre. The circle is calibrated with the angles from 0º to 360º in steps of 10º. The sort of stiff plastic used used in packaging works well. In this session (or in an introductory session) the students make the piece of equipment called a Turn Measurer (TM) and begin to use it for measuring amounts of turn.īoth the circle and the arrow need to be made of clear plastic.
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