3
Halves, thirds and fourths of a clock
Discover Mathematics P3: Term 2, Lessons 61–70
GoalFind halves, thirds and fourths of a clock face and of an hour.
New words
half hour · 30 minutes, half of 60 minutesquarter hour · 15 minutes, a fourth of an hourclock face · the round front of a clock with the numbers
Explanation
A clock face is a circle, and the minute hand goes all the way round in 1 hour, which is 60 minutes. When the minute hand goes from the 12 to the 6, it has gone half way round, so half an hour has passed: 60 ÷ 2 = 30 minutes. When it goes from the 12 to the 3, it has gone a fourth of the way: 60 ÷ 4 = 15 minutes. When it goes from the 12 to the 4, it has gone a third of the way: 60 ÷ 3 = 20 minutes. So half of an hour is 30 minutes, a third of an hour is 20 minutes and a fourth of an hour is 15 minutes.
| Part of an hour | Minutes |
|---|---|
| a half | 30 |
| a third | 20 |
| a fourth | 15 |
Worked examples
Half an hour. At 5:30 the minute hand points to the 6, half way round the clock face. 30 minutes is half of 60.
A fourth of an hour. At 5:15 the minute hand points to the 3. It has gone a fourth of the way round, because 4 × 15 = 60.
A third of an hour. At 5:20 the minute hand points to the 4. It has gone a third of the way round, because 3 × 20 = 60.
Class activity
Hour fractions. Ask someone to start a timer for 15 minutes, then 20 minutes, then 30 minutes. For each one, say what part of an hour it is. Draw each time on a clock face by shading the part the minute hand has travelled from the 12.
Practice
1
How many minutes are in 2 fourths of an hour?
A fourth of an hour is 15 minutes, so 2 fourths are 2 × 15 = 30 minutes. This is the same as half an hour.
2
How many minutes are in a third of an hour?
60 ÷ 3 = 20 minutes.
3
The minute hand has gone from the 12 to the 6. What fraction of an hour is this, and how many minutes?
It is half of an hour, which is 30 minutes. The time is 7:30.
4
Hana’s lesson starts at 9:00 and lasts half an hour. When does it end?
Half an hour is 30 minutes, so it ends at 9:30.
5
Omar plays football for 3 fourths of an hour. For how many minutes does he play?
A fourth of 60 minutes is 15 minutes, so 3 fourths are 3 × 15 = 45 minutes.