Telling time
A clock face has two hands and twelve numbers. How do you read the time from it, and how do you write that time the way a digital clock shows it?
Where you are 13 in Time and money
When you reach for it
Children hear times all day long. School starts at 8 o’clock, lunch is at half past 11, the bus comes at 3. A time is only useful if everyone reads it the same way from a clock, and there are two kinds of clock to read. An analog clock has a round face with the numbers 1 to 12 and two hands that turn. A digital clock, like the one on a microwave or many alarm clocks, shows the time in digits, such as 7{:}30.
This lesson teaches reading and writing a time to the hour and to the half hour on both kinds of clock. It runs over four days:
- Part 1: the clock face, the two hands and what each one counts, and times on the hour (“o’clock”).
- Part 2: half past the hour, and why the hour hand sits halfway between two numbers.
- Part 3: digital clocks, and writing a time as 3{:}00 or 7{:}30.
- Part 4: matching an analog clock to a digital one, and drawing the hands for a time.
The whole lesson rests on one fact: the two hands turn together, at different speeds, so where one of them points tells you where the other one must be. A real clock is the best thing to have on hand, ideally a geared teaching clock where turning the minute hand moves the hour hand along with it. A paper plate with two paper hands works, but its hands move on their own, so the adult has to keep the hour hand honest.
The procedure
Part 1: The clock face and the hour
The face. The numbers 1 to 12 run around the circle, with 12 at the top and 6 at the bottom. Read them in the direction the hands turn, which is called clockwise after the clock itself: from 12 to 1 to 2 and on around to 12 again.
Two hands, two jobs. The hour hand is the short one. It tells which hour it is. The minute hand is the long one. It tells how far into that hour we are. A good way for a child to remember: the short word, hour, goes with the short hand. On most clocks the hour hand is also thicker. Some clocks have a third, very thin hand that sweeps around quickly; it counts seconds and can be ignored here.
How they move together. The minute hand goes all the way around the face once in one hour. In that same hour the hour hand moves only from one number to the next. So the minute hand is the fast one and the hour hand is the slow one, and they never stop moving. Turn the minute hand of a geared clock slowly once around and let the child watch the hour hand creep along to the next number. That one demonstration is worth more than any explanation.
On the hour. When the minute hand points straight up at 12, a new hour is just beginning, and the hour hand points exactly at a number. That number is the hour. In the picture the hour hand points at 4 and the minute hand at 12, so it is 4 o’clock. “O’clock” is short for “of the clock”, and it is said only when the minute hand is on 12.
So reading a time on the hour takes two looks. First the minute hand: is it on 12? Then it is something o’clock. Then the hour hand: which number does it point at? That number names the hour. The order matters, because the minute hand tells you what kind of time it is before the hour hand tells you which one.
Part 2: Half past the hour
Half a turn of the minute hand. Start at an o’clock time, with the minute hand on 12. Turn the minute hand around until it points straight down at 6. It has gone through exactly half of the circle: 12 to 6 on one side, and 6 back up to 12 on the other side, are the two equal halves of the face.
A whole turn of the minute hand is one hour, so half a turn is half an hour. The two halves are equal shares of one whole, which is exactly what makes them halves (see Equal shares and naming the whole and Equal shares and naming the whole). When the minute hand points at 6, the time is half past the hour.
Where the hour hand is at half past. The hour hand has been moving the whole time the minute hand turned. In a full hour it goes from one number to the next, so in half an hour it goes half of the way. At half past, the hour hand points halfway between two numbers.
Look at the three clocks. At 4 o’clock the hour hand points at 4. At half past 4 the minute hand has made half a turn, and the hour hand has gone half of the way from 4 to 5. At 5 o’clock the minute hand is back on 12 and the hour hand has arrived at 5.
Which hour is it? At half past, the hour hand sits between two numbers, so it does not point at the hour the way it does at o’clock. The hour is the number the hour hand has just passed, the one it is moving away from, not the one it is moving toward. Between 4 and 5 it has passed 4 and not yet reached 5, so the time is half past 4. Half past 4 is still in the 4 o’clock hour; the 5 o’clock hour has not begun.
Going clockwise, the number just passed is the one before the hour hand. Near the top of the clock this needs care. Between 12 and 1, the number just passed is 12, so the time is half past 12. Example 4 works through it.
Part 3: Digital clocks and writing the time
A digital clock shows no hands at all. It shows two numbers with a colon between them.
The number before the colon is the hour. The digits after the colon are the minutes: how many minutes have gone by since the hour began. There are 60 minutes in an hour (see Units of time), so half an hour is 30 minutes. That is why half past 4 shows as 4{:}30. On the hour no minutes have gone by yet, so the minutes show as 00, and 4 o’clock shows as 4{:}00.
Children in this lesson do not need to count minutes. At this stage only two endings appear after the colon, and each matches one position of the minute hand:
| After the colon | The minute hand points at | Say it as |
|---|---|---|
| 00 | 12 | o’clock |
| 30 | 6 | half past |
The minutes always take two digits, even when the number of minutes is zero. Writing 4{:}0 or just 4 is not how a clock shows it, and later, when the minutes are 5, the clock shows 4{:}05, with a 0 holding the first place, so that the two digits after the colon are always read together as one number (Place value).
Read 7{:}30 aloud as “seven thirty” or as “half past seven”. Both name the same time. Read 3{:}00 as “three o’clock”; “three hundred” is not a time.
Writing a time means doing this in reverse: write the hour, then a colon, then 00 for o’clock or 30 for half past.
Part 4: Matching and drawing
Analog to digital. To match an analog clock with a digital time, read the analog clock as in Parts 1 and 2 and write it as in Part 3. The minute hand decides the digits after the colon: on 12 it is 00, on 6 it is 30. The hour hand decides the number before the colon.
Digital to analog. To draw the hands for a time on a blank face, each hand goes in its own place, and they are drawn in this order for a reason:
The minute hand goes first, because it depends only on the minutes. For \,{:}00 it points straight up at 12; for \,{:}30 it points straight down at 6. Draw it long, nearly reaching the numbers.
The hour hand goes second, and it depends on both numbers. For an o’clock time it points exactly at the hour. For a half past time it points halfway between the hour and the next number clockwise, because the hour hand has gone half of the way to the next hour. Draw it short, so no one can mix the two up.
A drawn clock can be checked by reading it back. If it reads as the time that was asked for, it is right. A clock whose minute hand is on 6 and whose hour hand points exactly at a number cannot happen on a real clock: the hour hand never waits on a number while the minute hand goes half way around.
Worked examples
Examples 1 and 2 go with Part 1, Examples 3 and 4 with Part 2, Examples 5 and 6 with Part 3, and Examples 7 and 8 with Part 4.
Three o’clock on the alarm clock
Taimi wakes up from a nap and looks at the alarm clock by her bed. What time is it? Say it, and write it as a digital clock would show it.
Look at the minute hand first. The long hand points straight up at 12, so a new hour has just begun: it is something o’clock.
Now the hour hand. The short hand points exactly at 3. So it is 3 o’clock.
No minutes have gone by since the hour began, so a digital clock shows the minutes as 00:
The 12 under the long hand is not part of the answer. The long hand never names the hour. Its job is to say how far into the hour we are, and pointing at 12 means “not at all yet”.
Both hands on twelve
Lyyli sees the classroom wall clock with both hands pointing straight up. What time is it?
The minute hand is on 12, so it is something o’clock. The hour hand is on 12 too, so the hour is 12. It is 12 o’clock, written
When both hands point the same way, the short hand lies on top of the long one and only the end of the long hand shows past it. Both hands are there; they simply overlap. At 12 o’clock the hour has two digits, so the digital clock shows two digits before the colon as well as two after it.
Half past seven
Reading time in Unto’s class starts when the classroom wall clock looks like this. What time does reading start? Write it as a digital clock would show it.
The minute hand points straight down at 6. It has gone half of the way around from 12, so half an hour has passed since the hour began. The time is half past some hour.
The hour hand is between 7 and 8, halfway. It has passed 7 and has not reached 8, so the hour is 7. Reading starts at half past 7.
Half an hour is 30 minutes, so a digital clock shows
which is read “seven thirty”. The hour hand sitting halfway agrees with the minute hand: half an hour has passed, so the hour hand has done half of its trip from 7 to 8.
Half past, near the top of the clock
On both clocks the minute hand points at 6. What time does each one show?
On both clocks the minute hand is on 6, so both show half past some hour. Only the hour hands differ, so read each hour hand and ask which number it has just passed, going clockwise.
Clock A. The hour hand is halfway between 11 and 12. Going clockwise it has passed 11 and is on its way to 12. The time is half past 11, or 11{:}30. It is not half past 12: the 12 o’clock hour starts only when the hour hand reaches 12.
Clock B. The hour hand is halfway between 12 and 1. Going clockwise the number just passed is 12, even though 12 is a bigger number than 1. The time is half past 12, or 12{:}30.
The face goes 11, 12, 1 around the top, so “the number before” the hour hand is not always the smaller of the two numbers. It is the one the hand has come from. Turning a geared clock slowly from 11 o’clock through 12 o’clock to 1 o’clock and stopping at each half past makes this easy to see.
Reading the microwave clock
The clock on the microwave shows this. Say the time two ways.
The number before the colon is 9, so the hour is 9. The digits after the colon are 30: thirty minutes, half an hour, have passed since 9 o’clock. So the time is nine thirty, which is the same as half past 9.
On an analog clock at this moment, the minute hand would point at 6 and the hour hand would sit halfway between 9 and 10.
Writing a time down
Lyyli sets her alarm clock for 6 o’clock. Later, the alarm is moved to half past 6. Write each time as a digital clock would show it.
SolutionFor 6 o’clock the hour is 6 and no minutes have passed, so the minutes are 00. Write the hour, a colon and the minutes:
For half past 6 the hour is still 6, because half past 6 comes before 7 o’clock. Half an hour is 30 minutes:
The two times share the 6 before the colon. They differ only after it, and the digits after the colon are what tell o’clock from half past.
Matching analog and digital
Match the times 5{:}30, 6{:}00 and 6{:}30 with clocks A, B and C.
Sort by the minute hand first. Clock C has its minute hand on 12, so it is the only o’clock time, and its hour hand points at 6: clock C is 6{:}00.
Clocks A and B both have the minute hand on 6, so both are half past, and only the hour hand can tell them apart. On clock A the hour hand is between 6 and 7. It has passed 6, so A is half past 6, which is 6{:}30. On clock B the hour hand is between 5 and 6. It has passed 5, so B is half past 5, which is 5{:}30.
| Clock | Minute hand | Hour hand | Time |
|---|---|---|---|
| A | 6 | between 6 and 7 | 6{:}30 |
| B | 6 | between 5 and 6 | 5{:}30 |
| C | 12 | on 6 | 6{:}00 |
All three clocks have the hour hand touching or close to 6, which is why this match takes care. The question that settles it is whether the hour hand is right on 6, has just left it, or has not yet reached it.
Drawing the hands for half past eight
Draw the hands on a blank clock to show 8{:}30.
Start with the minute hand, since it depends only on the minutes. The minutes are 30, half an hour, so the minute hand points straight down at 6. Draw it long.
Then the hour hand. The hour is 8, and half an hour has passed since 8 o’clock, so the hour hand has gone half of the way from 8 toward 9. Draw it short, pointing halfway between 8 and 9.
Check by reading it back: the minute hand on 6 says half past, and the hour hand has just passed 8, so the clock reads half past 8, which is 8{:}30.
If the hour hand were drawn pointing exactly at 8, the clock would show a time that never happens, since the hour hand has always moved on from 8 by the time the minute hand reaches 6.
Boundaries
- Only hours and half hours, for now. This lesson reads a clock only when the minute hand is on 12 or on 6. Anywhere else, the minutes are some other number, and reading them needs counting around the face by fives, which comes in telling time to five minutes.
- The hour hand points at the hour only on the hour. At every other time it sits between two numbers, and the hour is the number it has just passed going clockwise. At half past it is exactly halfway.
- The face shows only 12 hours. The hands go around twice each day, so a clock reading 7{:}00 could be morning or evening. The clock alone cannot say which; morning and afternoon times add the label that does.
- Some clocks are built differently. Some faces show only some of the numbers, or none, and some digital clocks count the hours of the day all the way up to 23 (Twenty four hour time and crossing midnight). The two hands, and the hour before the colon, work the same way on every one of them.
- A time is not an amount of time. 7{:}30 names a moment. How long something lasts, such as from 7{:}00 to 7{:}30, is Elapsed time, a separate question.
Where this goes next
The minute hand on 6 means 30 minutes because half of 60 is 30. The other positions of the minute hand come next: counting by fives around the face, one five for each number, reads any time to five minutes, and quarter past and quarter to split the face into fourths, as Equal shares and naming the whole split a circle. That is telling time to five minutes, and counting by fives is in counting by twos, fives, threes and fours.
Times then get labels for the half of the day, in morning and afternoon, and finding how long something lasts, from a start time to an end time, becomes Elapsed time. Hours, minutes and seconds take their place among days, weeks and years in Units of time.
Exercises
Reading o’clock (Part 1)
Use the clocks for Exercises 1 to 4. For each clock, say the time and write it as a digital clock shows it.
- Clock A.
- Clock B.
- Clock C.
- Clock D.
- Unto looks at the classroom wall clock. The hour hand points at 2 and the minute hand points at 12. What time is it?
- At 8 o’clock, where does each hand point?
Half past (Part 2)
Use the clocks for Exercises 7 to 10. For each clock, say the time and write it as a digital clock shows it.
- Clock A.
- Clock B.
- Clock C.
- Clock D.
- At half past 2, between which two numbers does the hour hand point?
Digital clocks (Part 3)
- The microwave clock shows 10{:}30. Say the time in words.
- The microwave clock shows 5{:}00. Say the time in words.
- Write half past 1 the way a digital clock shows it.
- Write 11 o’clock the way a digital clock shows it.
- Lyyli’s alarm clock shows 3{:}30. Where do the hands of an analog clock point at that time?
Match and draw (Part 4)
Use the clocks for Exercises 17 to 19. The times are 2{:}30, 1{:}30 and 2{:}00.
- Which clock shows 2{:}00?
- Which clock shows 2{:}30?
- Which clock shows 1{:}30?
- On a blank clock, draw the hands for 9{:}00.
- On a blank clock, draw the hands for 10{:}30.
- On a blank clock, draw the hands for half past 3.
Explain
- Why does the minute hand point at 6 at half past every hour?
- A clock has its hour hand pointing exactly at 4 and its minute hand pointing at 6. Can a working clock ever look like this? Why or why not?
- While the hour hand moves from 3 to 4, how many times does the minute hand go all the way around? Which hand is faster?
Answers
- 5 o’clock, 5{:}00. The minute hand is on 12 and the hour hand points at 5.
- 11 o’clock, 11{:}00. The minute hand is on 12 and the hour hand points at 11.
- 9 o’clock, 9{:}00. The minute hand is on 12 and the hour hand points at 9.
- 1 o’clock, 1{:}00. The minute hand is on 12 and the hour hand points at 1.
- 2 o’clock, 2{:}00. The minute hand on 12 makes it o’clock, and the hour hand names the hour.
- The hour hand points at 8 and the minute hand points at 12. On the hour the minute hand is always on 12 and the hour hand points exactly at the hour.
- Half past 10, 10{:}30. The minute hand is on 6, and the hour hand has passed 10 but not reached 11.
- Half past 3, 3{:}30. The minute hand is on 6, and the hour hand has passed 3.
- Half past 1, 1{:}30. The minute hand is on 6, and the hour hand has passed 1.
- Half past 2, 2{:}30. The minute hand is on 6, and the hour hand has passed 2.
- Between 2 and 3, halfway. Half an hour after 2 o’clock the hour hand has gone half of the way from 2 to 3.
- Ten thirty, or half past 10. The hour is 10 and 30 minutes is half an hour.
- Five o’clock. The hour is 5 and the minutes are 00, so no minutes have passed.
- 1{:}30. The hour is 1, then a colon, then 30 for half past.
- 11{:}00. The hour is 11, then a colon, then 00 for o’clock.
- The minute hand points at 6 and the hour hand points halfway between 3 and 4. The 30 puts the minute hand on 6, and half an hour after 3 o’clock the hour hand is halfway to 4.
- Clock A. It is the only clock with the minute hand on 12, and its hour hand is on 2.
- Clock B. The minute hand is on 6 and the hour hand has just passed 2.
- Clock C. The minute hand is on 6 and the hour hand has just passed 1.
- The minute hand points straight up at 12 and the hour hand points exactly at 9.
- The minute hand points straight down at 6 and the hour hand points halfway between 10 and 11.
- The minute hand points at 6 and the hour hand points halfway between 3 and 4. Half past 3 is written 3{:}30.
- A whole turn of the minute hand is one hour. The 6 is straight across the face from the 12, so going from 12 to 6 is half a turn, and half a turn is half an hour. Half past means half an hour after the hour began, so the minute hand is always on 6.
- No. With the minute hand on 6, half an hour has passed since the hour began, and in that time the hour hand has moved halfway to the next number. So the hour hand must point between two numbers, not exactly at 4. A working clock at half past 4 has its hour hand halfway between 4 and 5.
- Once. The minute hand goes all the way around in one hour, and in that same hour the hour hand moves from one number to the next. So the minute hand is the faster hand.