Two hands with two jobs
A clock face has the numbers 1 to 12 around it and two hands that turn from the middle. The short hand names the hour. The long hand counts the minutes.
Here the short hand points at 3 and the long hand points straight up at 12. When the long hand is on the 12, the time is exactly the hour, so this clock shows three o’clock. It is written 3:00: the hour, then a colon, then the minutes.
The short hand is on 3 and the long hand is on 12: three o’clock, 3:00.
The long hand counts in fives
The long hand goes once all the way round in one hour, and one hour is 60 minutes. The 12 numbers cut the way round into 12 equal steps, and each step is 5 minutes, because 12 fives are 60.
So count in fives from the 12, one five for each number the long hand has reached. On the 1 it is 5 minutes, on the 2 it is 10, and on the 3 it is 15. The time is 3:15, fifteen minutes past three. It is also called quarter past three, because the long hand has gone a quarter of the way round.
The long hand is on the 3, and three fives are 15: the time is 3:15.
Half past
When the long hand reaches the 6, it has counted six fives: 5, 10, 15, 20, 25, 30. That is 30 minutes, and the time is 3:30. The long hand has gone half of the way round, so 3:30 is also called half past three.
The long hand is on the 6: six fives are 30, so the time is 3:30, half past three.
The short hand moves too
While the long hand goes round, the short hand moves slowly from one number to the next. At 3:00 it points right at the 3. At 3:30 it is halfway between the 3 and the 4. At 3:45 it is nearly at the 4.
The hour is still 3 until the long hand comes back round to the 12. Only then does the short hand reach the 4, and the time becomes 4:00. So read the hour from the number the short hand has just passed, not the one it is coming up to.
At 3:45 the short hand is close to the 4, but it has not reached it, so the hour is still 3.
3:00 = 3 o'clock: the long hand is on 12 and the short hand points straight at 3
Set the clock to 3:45
Turning the long hand from 3:00 to 3:45 carries the short hand three quarters of the way from 3 toward 4. The numbers outside the rim are the minutes at each number.
Two ways to misread the numbers
The same number means different things to the two hands. The short hand on the 4 means 4 o’clock, but the long hand on the 4 means four fives, which is 20 minutes, not 4 minutes. With the short hand just past the 5 and the long hand on the 4, the time is 5:20.
The other mistake is reading the hour the short hand is coming up to. At 3:45 the short hand is near the 4, but the time is 3:45, not 4:45.
Worked example: The Minute Hand Turns Through Right Angles
Question The minute hand of a clock points to 12. Ben reads a book for 45 minutes, and the minute hand turns all that time. (a) How many right angles does the minute hand turn through? (b) How many degrees is that?
1.The minute hand goes once round the clock in 60 minutes. A full turn is 4 right angles, so one right angle takes 60 ÷ 4 = 15 minutes.
A full turn takes 60 minutes and is 4 right angles, so one right angle takes 60 ÷ 4 = 15 minutes. 2.In 15 minutes the hand turns from 12 to 3. That is one quarter turn, which is one right angle.
In 15 minutes the hand turns from 12 to 3: one quarter turn, which is one right angle. 3.Count in fifteens up to 45: 15, 30, 45. That is 3 lots of 15 minutes. (a) The minute hand turns through 3 right angles, from 12 round to 9.
(a) 15, 30, 45: the hand turns through 3 right angles, from 12 round to 9. 4.(b) One right angle is 90°. 3 right angles are 90° + 90° + 90° = 270°.
(b) 90° + 90° + 90° = 270°.
Answer: (a) 3 right angles; (b) 270°
Common mistakes
- Saying the hand turns through 9 right angles because it stops at the 9. The number on the clock face is not the number of right angles. Count the quarter turns: 12 to 3, 3 to 6, and 6 to 9.
- Thinking about the hour hand. In 45 minutes the hour hand moves less than the space between two numbers. The question asks about the minute hand, which turns through one right angle every 15 minutes.
More thousands, angles and time problems, worked step by step →