Telling time to the nearest five minutes
The long hand of a clock points at the 4. Why does that mean twenty minutes and not four, and how do you read, write and draw a time like that?
Where you are 13 in Time and money
When you reach for it
Most times in a day are not on the hour or the half hour. A piano lesson starts at twenty past four. Story time at the library starts at five past ten. In Telling time a child read a clock only when the long minute hand pointed at 12 (o’clock) or at 6 (half past). This lesson lets the minute hand point at any of the twelve numbers, and reads the time to five minutes.
The key is one fact about the face. The long hand passes a number every five minutes, so the minutes are found by counting the numbers by fives: “five, ten, fifteen, twenty”. That count is counting by fives, which the child already knows, put to a new use.
The lesson runs over three days:
- Part 1: reading the minute hand by counting fives, and writing the time as 4{:}20.
- Part 2: where the hour hand sits between two numbers, and which hour to read from it.
- Part 3: drawing the hands for a time, and the names quarter past and quarter to.
A geared teaching clock, where turning the minute hand moves the hour hand along with it, is the best thing to have on hand. Turn it slowly and let the child count as the long hand passes each number.
The procedure
Part 1: Counting the minute hand by fives
The marks around the face. Look closely at a clock face. Besides the twelve numbers, there are small marks all the way around the rim, 60 of them. The minute hand moves from one small mark to the next in one minute. One whole turn passes all 60 marks, and one whole turn is one hour, which is why an hour has 60 minutes (Units of time).
Five marks from number to number. Between one number and the next there are always five small marks, so the minute hand takes five minutes to go from any number to the next one. Starting at 12, it reaches 1 after 5 minutes, 2 after 10 minutes, 3 after 15 minutes, and so on. Counting the numbers by fives counts the minutes, because each step of “five, ten, fifteen” stands for one whole gap of five marks. This is the whole reason the count works: equal gaps, five minutes each, counted in jumps of five.
| Minute hand on | Minutes after the hour | Minute hand on | Minutes after the hour |
|---|---|---|---|
| 12 | 0 | 6 | 30 |
| 1 | 5 | 7 | 35 |
| 2 | 10 | 8 | 40 |
| 3 | 15 | 9 | 45 |
| 4 | 20 | 10 | 50 |
| 5 | 25 | 11 | 55 |
The table is a skip count, not a list to memorize. A child points at each number in turn and says the next count. Two landmarks make long counts shorter. The 6 is half past, 30 minutes, which the child knows from Telling time, so for the 8 they can start at 30 and go on: “thirty-five, forty”. The 12 is 0 minutes, or a full 60 minutes, which means a new hour is starting.
Notice the two jobs of a number on the face. Read against the hour hand, the 4 means the hour 4. Read against the minute hand, the same 4 means 20 minutes, because the minute hand has passed four gaps of five. The numbers are printed for the hour hand; the minute hand has to be counted.
The hour, a first look. The hour hand works as it did in Telling time: the hour is the number it has most recently passed going clockwise. In Part 1 the hour hand is never close to the next number, so this is easy to see. Part 2 looks at the cases where it is hard.
Writing the time. A digital clock and a written time show the hour, a colon, and then the minutes, the same way Telling time wrote 4{:}30. Twenty minutes after 4 o’clock is written
and read “four twenty”, or “twenty past four”, or “twenty minutes after four”. All three name the same time.
The minutes always take two digits. When the minute hand is on 1, five minutes have passed, and the time is written 4{:}05, read “four oh five”. The 0 holds the tens place, so the two digits after the colon are read together as one number of minutes (Place value). Writing 4{:}5 would look like fifty minutes to anyone who reads the digits as tens and ones.
Part 2: Where the hour hand sits
The hour hand moves the whole time. While the minute hand makes one full turn, the hour hand moves from one number to the next, slowly and steadily. So at ten past the hour, the hour hand has gone a little of the way. At half past it is halfway. At ten to the next hour it is most of the way there.
Which hour to read. The hour is the number the hour hand has passed, not the number it is nearest to. At 1{:}50 in the picture, the hour hand is very close to 2, but it has not reached 2, so the hour is still 1. The hour changes to 2 only at the moment the minute hand comes back up to 12; that is what “2 o’clock” means.
Let the minute hand settle it. When the hour hand is so close to a number that it is hard to tell which side it is on, the minute hand decides. The two hands always agree:
- Minute hand between 12 and 6 (less than 30 minutes): the hour hand is less than halfway to the next number. It has just passed the hour.
- Minute hand between 6 and 12 (more than 30 minutes): the hour hand is more than halfway to the next number, and close to it, but the hour has not changed yet.
So if the minute hand points at 11 and the hour hand looks as if it is on 8, it is really just short of 8, and the time is 7{:}55. If the minute hand points at 1 and the hour hand looks as if it is on 8, it is just past 8, and the time is 8{:}05.
After twelve comes one. Going clockwise, the number after 12 is 1. A few minutes after 12 o’clock, the hour hand is just past 12, and the hour is 12: the time is 12{:}10, not 1{:}10. Close to the end of that hour the hour hand is almost on 1, and the time is still 12 something.
Read the minute hand first. For this reason a clock is read in the same order every time. Look at the minute hand and count by fives. That tells you how far through the hour it is, which tells you where the hour hand should be. Then read the hour hand.
Part 3: Drawing the hands, and quarter hours
Drawing the hands for a time. To draw 10{:}25 on a blank face, each hand goes in its own place, minute hand first because it depends only on the minutes.
The minute hand points at the number the count of fives reaches. Count “five, ten, fifteen, twenty, twenty-five” around the face, one number per count, and stop at the fifth number, 5. Draw the hand long, clearly longer than the hour hand.
The hour hand starts from the hour, 10, and goes toward the next number, 11, as far as the minute hand has gone around. The minute hand on 5 has not reached 6, less than half of its turn, so the hour hand goes a little less than halfway from 10 to 11. Draw it short. The hour hand does not need to be placed exactly; it needs to be on the right side of halfway and clearly past the hour, so that the clock reads back as the time that was asked for.
A drawn clock is checked by reading it back as in Parts 1 and 2.
Quarters of an hour. The numbers 3, 6 and 9, with 12, cut the face into four equal parts, the fourths of a circle from Equal shares and naming the whole. A fourth is also called a quarter. One quarter of the minute hand’s turn, from 12 to 3, is 15 minutes: count “five, ten, fifteen”.
That gives three times their own names:
| Minute hand on | Minutes after the hour | Written | Said |
|---|---|---|---|
| 3 | 15 | 5{:}15 | quarter past 5 |
| 6 | 30 | 5{:}30 | half past 5 |
| 9 | 45 | 5{:}45 | quarter to 6 |
Quarter past means a quarter of an hour after the hour. Half past is the old name from Telling time. Quarter to looks ahead. At 9 the minute hand has a quarter of its turn left, from 9 back up to 12, which is 15 minutes (“five, ten, fifteen” again). So 5{:}45 is 15 minutes before 6 o’clock, and it is called a quarter to 6. The hour in the words is the next hour, even though the digital clock still shows 5. The digital clock always counts the minutes after the hour that has passed; “quarter to” counts the minutes left before the hour that is coming. Both describe the same clock.
Worked examples
Read each problem aloud with the child and, if you can, set the time on a real clock. Examples 1 and 2 go with Part 1, Examples 3 and 4 with Part 2, and Examples 5 to 7 with Part 3.
The piano lesson
Tolkyn’s piano lesson starts when the clock on the teacher’s wall looks like this. What time does the lesson start? Write it as a digital clock would show it.
Start with the minute hand, the long one. It points at 4. Count the numbers by fives from 12: 1 is “five”, 2 is “ten”, 3 is “fifteen”, 4 is “twenty”. So 20 minutes have passed since the hour began.
Now the hour hand, the short one. It is a little past 4 and has not reached 5, so the hour is 4. That agrees with the minute hand: 20 minutes is less than half an hour, so the hour hand should be less than halfway from 4 to 5, and it is.
The lesson starts at twenty past four, written
The two hands both point near the 4, but they say different things: the short hand says the hour 4, the long hand says 20 minutes.
Story time at the library
Story time at the public library starts when the library clock looks like this. Write the time.
The minute hand points at 1. It has gone one gap of five marks past 12, so 5 minutes have passed. The hour hand is just past 10, so the hour is 10.
The minutes take two digits, so 5 minutes is written 05, and story time starts at
read “ten oh five”, or “five past ten”. The 0 matters: the two digits after the colon are read together as one number, and 05 is five minutes, while the 5 alone in the tens place would look like fifty.
Almost eight
Kawehi finishes playing her piece at the piano lesson and looks at the clock. What time is it?
The minute hand comes first. It points at 11. Counting all the way around is long, so start from a landmark: 9 is 45, then 10 is 50 and 11 is 55. So 55 minutes have passed since the hour began.
The hour hand is almost on 8. Is the hour 8? No. 55 minutes is nearly a whole hour but not quite, so the hour hand has gone nearly all of the way to the next number but has not reached it. It is just short of 8, and the number it has passed is 7. The hour is 7.
In five more minutes the minute hand will reach 12, the hour hand will reach 8, and it will be 8{:}00. Until then, it is still the hour of 7. The time can also be said “five to eight”: 5 minutes before 8 o’clock.
Two clocks near nine
Snezhana looks at the library clock when she arrives (clock A) and again later (clock B). On both clocks the hour hand is close to 9. What time does each clock show?
Clock A: the minute hand points at 10. From the landmark 6 at 30: 35, 40, 45, 50. So 50 minutes have passed. Fifty minutes is more than half an hour, so the hour hand must be more than halfway to the next number, close to it. That means the hour hand is just before 9, and the hour it has passed is 8. Clock A shows
Clock B: the minute hand points at 2, so 10 minutes have passed. Ten minutes is only a little of the hour, so the hour hand has only just left a number. It is just past 9, and the hour is 9. Clock B shows
The two hour hands look almost the same. The minute hands are what tell them apart: one says “nearly the end of an hour”, the other “just after the start of one”.
Drawing two forty
Snezhana’s piano practice starts at 2{:}40. Draw the hands on a blank clock.
Minute hand first. The minutes are 40. Count by fives, one number for each count: “five, ten, fifteen, twenty, twenty-five, thirty, thirty-five, forty”. The eighth count lands on 8, so the minute hand points at 8. A shorter way: 6 is 30, then 7 is 35 and 8 is 40. Draw it long.
Hour hand next. The hour is 2, so the hour hand starts from 2 and goes toward 3. The minute hand on 8 is past 6, more than halfway around, so the hour hand is more than halfway from 2 to 3. In fact the minute hand has gone eight of the twelve gaps, two thirds of its turn, so the hour hand has gone two thirds of the way from 2 to 3. Draw it short.
Check by reading it back: the minute hand on 8 is 40 minutes, and the hour hand has passed 2 but not 3, so the clock reads 2{:}40.
Quarter past eleven
Tolkyn’s next piano lesson begins at quarter past 11. Write the time as a digital clock shows it, and say where the hands go.
Quarter past means a quarter of an hour after 11 o’clock. A quarter of the minute hand’s turn is from 12 to 3, “five, ten, fifteen”, so a quarter of an hour is 15 minutes. The time is
The minute hand points at 3. The hour hand has gone a quarter of the way from 11 toward 12: the minute hand has done one quarter of its turn, and the hour hand does the same share of its trip to the next number.
Quarter to one
The library closes for lunch at quarter to 1. Write the time as a digital clock shows it.
Quarter to 1 means a quarter of an hour, 15 minutes, before 1 o’clock. The minute hand must be 15 minutes short of 12: counting back “five, ten, fifteen” from 12 passes 11 and 10 and lands on 9. So the minute hand points at 9.
The minute hand on 9 is 45 minutes after the hour (6 is 30, then 35, 40, 45). Which hour has passed? The next hour is 1, and the hour before 1, going clockwise, is 12. So the time is
not 1{:}45. The digital clock counts minutes after the hour that has passed, which is 12. The hour hand agrees: it is three quarters of the way from 12 to 1, past 12 and not yet at 1.
Boundaries
- Only times on a five. This lesson reads the clock when the minute hand points exactly at a number. A real minute hand moves every minute, so it is often between two numbers. Counting the small marks reads it to the exact minute, a later step. To the nearest five minutes, read the number the minute hand is closest to: a hand one mark past 7 is about 35 minutes. A hand just before 12 is nearest to 0 minutes of the next hour, so a time a minute or two before 8 o’clock is, to the nearest five minutes, 8{:}00.
- The hour hand points at a number only on the hour. At every other time it is between two numbers, and the hour is the one it has passed going clockwise, however close it is to the next.
- “Quarter to” names the next hour. 12{:}45 is quarter to 1, and 5{:}45 is quarter to 6. “Quarter past” and “half past” name the hour that has passed. After 12 the next hour is 1, not 13, on a twelve hour face; some digital clocks count on past 12 (Twenty four hour time and crossing midnight).
- The face does not say morning or afternoon. The hands go around twice a day, so 4{:}20 could be in the morning or the afternoon. That label is the next lesson, morning and afternoon times.
- A time is a moment, not a length. 4{:}20 says when the piano lesson starts, not how long it lasts. How long from one time to another is Elapsed time.
Where this goes next
The clock face now reads every time to five minutes. The next step labels the half of the day, in morning and afternoon, so that 7{:}55 before school and 7{:}55 after dinner can be told apart. Counting the small marks one by one then reads the clock to the exact minute.
Once two times can be read, the question “how long from this one to that one?” becomes Elapsed time, and counting by fives around the face is one of its first tools. The quarters of an hour are the same fourths of a circle as in Equal shares and naming the whole, and minutes take their place among seconds, hours and days in Units of time.
Exercises
Count the minutes (Part 1)
Use the clocks for Exercises 1 to 4. Write the time each clock shows.
- Clock A
- Clock B
- Clock C
- Clock D
- The minute hand points at 9. How many minutes have passed since the hour began?
- A digital clock shows 9{:}35. Which number does the minute hand point at?
- It is 35 minutes after 8 o’clock. Write the time as a digital clock shows it.
- The minute hand points at 10. How many minutes have passed since the hour began?
Which hour? (Part 2)
Use the clocks for Exercises 9 to 12. Write the time each clock shows.
- Clock A
- Clock B
- Clock C
- Clock D
- The hour hand is a little past 6 and the minute hand points at 2. What time is it?
- The hour hand is a little before 1 and the minute hand points at 11. What time is it?
- The hour hand is almost on 4, just before it, and the minute hand points at 10. What time is it?
Drawing and quarter hours (Part 3)
- Say where each hand goes for 7{:}25.
- Say where each hand goes for 4{:}50.
- Write quarter past 3 as a digital clock shows it.
- Write quarter to 10 as a digital clock shows it.
- Say 2{:}45 using the word quarter.
- The library opens at 9{:}15. Say the time using the word quarter, and say where the minute hand points.
- The minute hand points at 9 and the hour hand is three quarters of the way from 6 to 7. Write the time, and say it using the word quarter.
Explain
- When the minute hand points at 4, why is the time 20 minutes after the hour and not 4 minutes?
- At 6{:}55 the hour hand is very close to 7. Why is the time not 7{:}55? Where would the hour hand be at 7{:}55?
- Why is 45 minutes after the hour called a quarter to the next hour?
Answers
- 3{:}25. The minute hand is on 5: “five, ten, fifteen, twenty, twenty-five”. The hour hand has passed 3 and is less than halfway to 4.
- 11{:}10. The minute hand is on 2, which is 10 minutes. The hour hand is a little past 11.
- 6{:}05. The minute hand is on 1, which is 5 minutes, written with two digits as 05. The hour hand is just past 6.
- 1{:}40. The minute hand is on 8: 6 is 30, then 35, 40. The hour hand has passed 1 and is more than halfway to 2.
- 45 minutes. Count “five, ten, fifteen, ...” and the ninth count is 45; or start at 6, 30, then 35, 40, 45.
- The 7. The minutes are 35: 6 is 30, and one more five reaches 7 at 35.
- 8{:}35. The hour is 8 and the minutes are 35.
- 50 minutes. From 6 at 30: 35, 40, 45, 50.
- 2{:}55. The minute hand on 11 is 55 minutes. The hour hand is almost on 3 but has not reached it, so the hour is 2.
- 12{:}05. The minute hand on 1 is 5 minutes. The hour hand has just passed 12, so the hour is 12.
- 10{:}50. The minute hand on 10 is 50 minutes. The hour hand is close to 11 but before it, so the hour is 10.
- 8{:}25. The minute hand on 5 is 25 minutes. The hour hand has passed 8 and is a little less than halfway to 9.
- 6{:}10. The minute hand on 2 is 10 minutes, and the hour hand has just passed 6.
- 12{:}55. The minute hand on 11 is 55 minutes. The hour hand has not reached 1, so the hour it has passed is 12.
- 3{:}50. The minute hand on 10 is 50 minutes. The hour hand has not reached 4, so the hour is 3.
- The minute hand points at 5, since “five, ten, fifteen, twenty, twenty-five” ends on the fifth number. The hour hand is between 7 and 8, a little less than halfway, because 25 minutes is a little less than half an hour.
- The minute hand points at 10, since 50 minutes is ten fives. The hour hand is most of the way from 4 to 5, close to 5 but not on it, because 50 minutes is most of an hour.
- 3{:}15. A quarter of an hour is 15 minutes, after 3 o’clock.
- 9{:}45. Quarter to 10 is 15 minutes before 10 o’clock, so the minute hand is on 9, which is 45 minutes after 9 o’clock.
- Quarter to 3. The minute hand is on 9, 15 minutes before the next hour, which is 3.
- Quarter past 9. The minute hand points at 3, because 15 minutes is three fives.
- 6{:}45, quarter to 7. The minute hand on 9 is 45 minutes, the hour hand has passed 6, and 15 minutes are left before 7 o’clock.
- The minute hand needs five minutes to go from one number to the next, because there are five small marks between them. On 4 it has gone four of those gaps, which is “five, ten, fifteen, twenty”, 20 minutes. Only the hour hand reads the numbers as they are printed.
- At 6{:}55 the minute hand is on 11: the hour is nearly over but 7 o’clock has not come, so the hour hand has not reached 7 and the hour is still 6. At 7{:}55 the hour hand would have passed 7 and be almost on 8, a whole number further around.
- At 45 minutes the minute hand is on 9. From 9 back up to 12 is three gaps, 15 minutes, and 15 minutes is a quarter of an hour, since 12, 3, 6 and 9 cut the face into four equal parts. So there is a quarter of an hour left before the next hour begins.