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Telling time

Measurement · level 2, lesson 4 of 6

A question to start

A day has 24 hours. But look at a clock: it has only 12 numbers. Where did the other 12 hours go?

And here is a second puzzle. At half past 3, where does the short hand point? Many people draw it pointing straight at the 3. But it does not! It points halfway between 3 and 4.

Both puzzles have the same answer: the hands of a clock are always moving, round and round, and they tell a story about how much of the day has gone by. In this lesson you will learn to read that story, on round clocks and on digital ones.

The idea

Hours and minutes

We cut a day into smaller pieces of time.

  • A day is cut into 24 hours.
  • An hour is cut into 60 minutes.
  • A minute is cut into 60 seconds.

Some benchmarks: a second is about as long as it takes to say "one elephant". A minute is about half the time you should spend brushing your teeth (about 2 minutes). An hour is about as long as two cartoon episodes, or a long walk in the park.

The clock face

A round clock with hands is called an analogue clock (say "ANN-a-log").

  • The short hand is the hour hand. It shows the hour.
  • The long hand is the minute hand. It shows the minutes.
  • Both hands always turn the same way, the way we call clockwise: from 12 to 1 to 2, round to 12 again.

The minute hand goes all the way round once in one hour (60 minutes). The hour hand is much slower: it goes all the way round once in 12 hours.

So now the first puzzle. In one day the hour hand goes round twice: once from midnight to the middle of the day, and once again from the middle of the day to midnight. 12 hours and 12 more hours make 24 hours. The clock uses its 12 numbers twice! We say a.m. for the hours before the middle of the day (the morning) and p.m. for the hours after it (afternoon, evening and night). So 7 a.m. is breakfast time, and 7 p.m. is evening.

O'clock

When the minute hand points straight up at 12, it is the start of an hour. We say o'clock. The hour hand points straight at the hour.

Half past, quarter past, quarter to

Here are four times between 3 o'clock and 4 o'clock.

1 2 3 4 5 6 7 8 9 10 11 12 3 o'clock 1 2 3 4 5 6 7 8 9 10 11 12 quarter past 3 1 2 3 4 5 6 7 8 9 10 11 12 half past 3 1 2 3 4 5 6 7 8 9 10 11 12 quarter to 4

Think of the clock face as a round pizza cut into 4 equal slices, with cuts at 12, 3, 6 and 9. Each slice is a quarter of the clock, so each slice is a quarter of an hour.

  • Quarter past 3: the minute hand has gone one quarter of the way round, to the 3. It is 15 minutes after 3 o'clock.
  • Half past 3: the minute hand has gone halfway round, to the 6. It is 30 minutes after 3 o'clock.
  • Quarter to 4: the minute hand is at the 9. Only one quarter is left until 4 o'clock. It is 15 minutes before 4 o'clock, which is 45 minutes after 3.

Why is a quarter 15 minutes? A whole hour is 60 minutes. Cut 60 into 4 equal parts: 15, 15, 15 and 15, which makes 60. And half an hour is two quarters: 15 and 15 is 30 minutes.

Where the hour hand really points

Now the second puzzle. The hour hand does not jump from 3 to 4 at 4 o'clock. It creeps along slowly the whole hour, as the minute hand goes round.

1 2 3 4 5 6 7 8 9 10 11 12 3:00 1 2 3 4 5 6 7 8 9 10 11 12 3:30 1 2 3 4 5 6 7 8 9 10 11 12 3:45
  • At 3:00 it points at the 3.
  • At half past 3, half the hour has gone, so it is halfway from 3 to 4.
  • At quarter to 4, three quarters of the hour have gone, so it is nearly at 4.

This is a great clue. If the hour hand is between 3 and 4, the hour is still 3 (it has not reached 4 yet). Always read the number the hour hand has just passed.

Five-minute steps

The minute hand does not only stop at 12, 3, 6 and 9. Look at the big clock below. The numbers on the outside show the minutes.

1 2 3 4 5 6 7 8 9 10 11 12 0 5 10 15 20 25 30 35 40 45 50 55

Between one number and the next there are 5 small spaces, so each number is 5 more minutes. So when the minute hand points at a number, count by 5s from the 12.

  • At 1, it is 5 minutes past. At 2, 10 minutes. At 3, 15 minutes. At 4, 20 minutes. At 5, 25 minutes.

On this clock, the hour hand has passed 7 and the minute hand points at 5. It is 25 minutes past 7, written 7:25.

Each tiny mark is 1 minute. There are 60 of them all the way round, which is why one trip of the minute hand is 60 minutes.

"Past" and "to"

People say times in two ways.

  • In the first half of the hour (the minute hand on the right side of the clock), we say minutes past: "20 past 2".
  • In the second half (the left side), we often say minutes to the next hour: 2:40 is "20 to 3", because 20 more minutes makes 3 o'clock. Count backwards by 5s from the 12: at 11 it is 5 to, at 10 it is 10 to, at 9 quarter to, at 8 it is 20 to.

Digital clocks

A digital clock shows the time with numbers.

3:00 3:30 9:05

The number before the two dots is the hour. The number after the two dots is the minutes.

  • 3:00 is 3 o'clock.
  • 3:30 is "three thirty", which is half past 3.
  • 9:05 is "nine oh five", 5 minutes past 9. The minutes always have two digits, so 5 minutes is written 05.

Matching the two kinds: 3:15 is quarter past 3, 3:30 is half past 3, 3:45 is quarter to 4.

A day on Mars

Mars spins a little slower than Earth. A day on Mars, called a sol, lasts 24 hours, 39 minutes and 35 seconds. So an Earth clock does not fit Mars. Some rover teams have lived on "Mars time" for the first months of a mission, starting work about 40 minutes later each Earth day, so that they were awake during the rover's Mars daytime.

Worked examples

Example 1. Read three clocks.

1 2 3 4 5 6 7 8 9 10 11 12 clock A 1 2 3 4 5 6 7 8 9 10 11 12 clock B 1 2 3 4 5 6 7 8 9 10 11 12 clock C

Clock A. The minute hand is at 10. The hour hand is nearly at 9 (it has passed 8).

  1. Count by 5s to the 10: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. That is 50 minutes past 8.
  2. The hour hand has passed 8, so the hour is 8. The time is 8:50.
  3. In "to" words: from 10 to 12 is 2 more numbers, 10 more minutes. It is 10 to 9.

Clock B. The minute hand is at 4. The hour hand is a little past 2.

  1. Count by 5s to 4: 5, 10, 15, 20. That is 20 minutes.
  2. The time is 2:20, or 20 past 2.

Clock C. The minute hand is at 11. The hour hand is almost at 12.

  1. Count by 5s to 11: 55 minutes past 11, which is 11:55.
  2. One more number to 12 is 5 minutes. It is 5 to 12.

Example 2. Digital to words. Write 6:45 in words, and draw where the hands go.

  1. 45 minutes is three quarters of the hour. Only one quarter is left until 7.
  2. So 6:45 is quarter to 7.
  3. Minute hand on the 9. Hour hand three quarters of the way from 6 to 7, nearly at 7.

Example 3. One hour later. It is 4:30. What time will it be in one hour? In half an hour?

  1. In one hour the minute hand goes all the way round and comes back to the same place, at 6. The hour hand moves on one number. So it will be 5:30.
  2. In half an hour, the minute hand goes half way round, from 6 to 12. That is the start of the next hour: 5:00.

Try it

  1. Which hand shows the hours, the long one or the short one?
  2. The minute hand is on 12 and the hour hand is on 8. What time is it?
  3. The minute hand points at 6, and the hour hand is halfway between 10 and 11. What time is it?
  4. Where does the minute hand point at quarter past any hour? At quarter to?
  5. Write 7:15, 7:30 and 7:45 in words.
  6. The minute hand is at 8. How many minutes past the hour is it? How many minutes to the next hour?
  7. Jack's clock shows 5:55. He says, "It is nearly 5." What is his mistake?
  8. How many times does the minute hand go all the way round in one day? (Hint: once each hour.)
Answers
  1. The short hand shows the hours. The long one shows the minutes.
  2. 8 o'clock (8:00).
  3. Half past 10 (10:30). The hour hand has passed 10 but not reached 11, so the hour is 10.
  4. Quarter past: the minute hand is on the 3. Quarter to: on the 9.
  5. 7:15 is quarter past 7. 7:30 is half past 7. 7:45 is quarter to 8.
  6. Count by 5s to 8: 5, 10, 15, 20, 25, 30, 35, 40. It is 40 minutes past. From 8 to 12 is 4 more numbers, 20 minutes, so it is also 20 minutes to the next hour. Check: 40 and 20 make 60.
  7. 5:55 is 55 minutes past 5, so it is nearly 6, not nearly 5. It is 5 minutes to 6.
  8. Once each hour, and there are 24 hours in a day, so 24 times. (The hour hand goes round only twice.)

Common mistake

Reading the hour hand as the next number. At 2:50 the hour hand is very close to 3, but the hour is still 2. Read the number the hour hand has just passed.

Mixing up the hands. The long hand is the minutes. If you mix them up, 3:00 turns into "12:15". Look for the short one first.

Where it leads