Guess the measure of turns the minute hand of a clock makes in each of the following cases. The initial position of the minute hand is given. Draw the final position of the minute hand on the clock face. Discuss your reasoning in class.
When the minute hand moves by 15 minutes, it has made a ____ turn of the circle.
1/4 turn (or quarter turn)
When the minute hand moves by 30 minutes, it has made a ____ turn of the circle.
1/2 turn (or half turn)
When the minute hand moves by 45 minutes, it has made a ____ turn of the circle.
3/4 turn
When the minute hand has turned by 1/12 of a full turn, it has moved by ____ minutes.
5 minutes
When the minute hand has turned a full-circle, it has moved by ____ minutes.
60 minutes
When the minute hand has turned by 1/6 of a full turn, it has moved by ____ minutes.
10 minutes
When the minute hand has turned by 4/12 of a full turn, it has moved by ____ minutes.
20 minutes
Explanation
(a) 15 minutes out of 60 minutes = 15/60 = 1/4 of a full turn. (b) 30 minutes out of 60 minutes = 30/60 = 1/2 of a full turn. (c) 45 minutes out of 60 minutes = 45/60 = 3/4 of a full turn. (d) 1/12 of 60 minutes = 60 ÷ 12 = 5 minutes. (e) A full circle by the minute hand equals 60 minutes (one hour). (f) 1/6 of 60 minutes = 60 ÷ 6 = 10 minutes. (g) 4/12 = 1/3 of 60 minutes = 60 ÷ 3 = 20 minutes.