Year 4 · Chapter 8

Year 4 Telling the Time and the 24-Hour Clock: worked examples and questions with answers

By the end of this chapter you will be able to

Read an analogue clock: o'clock, half past, quarter past, quarter to, and every five minutes, saying past or to
Read a clock to the nearest minute, on clocks with Arabic numbers, Roman numerals and no numbers, and place the hour hand correctly
Write times as digital times with am and pm, and on the 24-hour clock, and change between the three ways of writing time
Change between seconds and minutes, minutes and hours, hours and days, days and weeks, and years and months
Know how many days are in each month (the knuckle trick), and what a leap year is
Work out how long something takes, and find end and start times, by counting on, including across noon and midnight
Read bus, train, TV and school timetables, and work out journey times and waiting times

You should already know

Counting in fives and the 5 times table (Chapter 3)
Adding and subtracting numbers and borrowing across 60 (Chapter 2)
Roman numerals to 12 (Chapter 1)
Halves, quarters and fractions of an amount (Chapter 5)
Measures and converting units (Chapter 7)

Where this leads

Shapes, angles and symmetry: turns on a clock face (Chapter 9)
Statistics: time graphs and tables (Chapter 11)
Converting between units of time and timetables in Year 5
Time zones and speed in later years

National Curriculum for England, Key Stage 2 mathematics, Year 4. Content: Read, write and convert time between analogue and digital 12-hour and 24-hour clocks, Read analogue clocks to the nearest minute, using past and to, and Roman numeral clock faces, Convert between units of time: seconds, minutes, hours, days, weeks, months and years, Know the number of days in each month, and in a year and a leap year, Calculate durations of time, and find start and end times, including across noon and midnight, Read timetables and solve time problems, including journey and waiting times.

Printable worksheets. Every lesson in this chapter has a free worksheet and an answer sheet to download and print.

8.1 Telling the time: o'clock, half past, quarter past and quarter to: Worksheet (PDF) · Answers (PDF) · lesson page
8.2 Reading to the nearest minute, and clocks with Roman numerals: Worksheet (PDF) · Answers (PDF) · lesson page
8.3 Digital time: am, pm and the 24-hour clock: Worksheet (PDF) · Answers (PDF) · lesson page
8.4 Units of time: seconds, minutes, hours, days and weeks: Worksheet (PDF) · Answers (PDF) · lesson page
8.5 Months, years and the calendar: Worksheet (PDF) · Answers (PDF) · lesson page
8.6 How long does it take? Durations, start times and end times: Worksheet (PDF) · Answers (PDF) · lesson page
8.7 Timetables and time problems: Worksheet (PDF) · Answers (PDF) · lesson page
Check-up and SATs-style questions: Worksheet (PDF) · Answers (PDF) · lesson page

Exercise P Do you remember?

Non-calculator

FWork out 7 × 5.

Done

FWhat number is the Roman numeral VIII?

Done

FWork out 60 − 45.

Done

FWhat is a quarter of 60?

Done

FWork out 3 × 12.

Done

8.1

Telling the time: o'clock, half past, quarter past and quarter to

Year 4
Read analogue clocks, o'clock, half past, quarter past, quarter to, Five-minute past and to

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Telling the time: o'clock, half past, quarter past and quarter toComing soon

An analogue clock has a round face with two hands. The short, thick hand is the hour hand. It shows the hour. The long, thin hand is the minute hand. It shows the minutes. Around the edge there are 12 numbers and 60 tiny marks.

The hour hand (short, dark) is just past the 2. The minute hand (long, blue) points at the 4. The orange numbers outside count the minutes in fives: the 4 means 20 minutes.

The minute hand. The long hand goes all the way round the clock in 1 hour. 1 hour is 60 minutes. There are 12 numbers, so each number is 5 minutes after the one before. Count in fives: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60.

The hour hand. The short hand goes round once in 12 hours. It shows the hour. When the time is 2 o’clock, it points exactly at the 2. When the time is later than 2 o’clock, it has moved a little past the 2. We always say the hour it has passed.

Four special times in the hour: 7 o’clock (minute hand on 12), quarter past 7 (on 3), half past 7 (on 6) and quarter to 8 (on 9).

Special times. A whole clock face is 60 minutes. Half of it is 30 minutes, so the minute hand at the 6 means half past. A quarter of it is 15 minutes, so the minute hand at the 3 means quarter past, and at the 9 it means quarter to the next hour (15 minutes to go).

Past and to. In the first half hour, the minute hand is on the right-hand side. We say how many minutes past the hour it is. In the second half hour, the minute hand is on the left-hand side. We say how many minutes are left to the next hour.

Blue half = past. Orange half = to. On the left: 20 minutes past 3 (“twenty past three”). On the right: the minute hand is on the 8, so it is 40 minutes past 3. There are 20 minutes left to 4 o’clock, so we also say “twenty to four”.

Key ideas

The short, thick hand is the hour hand. The long, thin hand is the minute hand.
The minute hand: each number is 5 minutes. Count in fives from the 12. Each tiny mark is 1 minute.
Minute hand on 12: o’clock. On 3: quarter past. On 6: half past. On 9: quarter to.
Right-hand side of the clock: past. Left-hand side: to the next hour.
For “to” times, take the minutes away from 60 (40 minutes past = 20 minutes to), and say the next hour.
Use the hour the short hand has passed.

Worked example 8.1.1

What time does the clock show? Write the time in words.

Key words. An analogue clock has a round face with two hands. The short, thick hour hand shows the hour. The long, thin minute hand shows the minutes. Past means after the hour. To means before the next hour.

Method. Look at the hour hand first, then the minute hand. Count the minutes in fives, then say the time.

Look at the short hand (the hour hand). It tells us the hour. Use the last number it has passed.
The short hand points exactly at 5. The hour is 5.
Look at the long hand (the minute hand). It tells us the minutes. Count in fives from the 12, then count single marks.
The long hand points straight up at 12. That is 0 minutes past the hour.
Say the time. On the hour we say o'clock.
The minute hand is on the 12, so we say five o'clock.

Check. In numbers this is 5:00. ✓

Watch out. Do not mix up the two hands. The short, thick hand shows the hour. The long, thin hand shows the minutes.

Worked example 8.1.2

What time does the clock show? Write the time in words.

Method. Look at the hour hand first, then the minute hand. Count the minutes in fives, then say the time.

Look at the short hand (the hour hand). It tells us the hour. Use the last number it has passed.
The short hand is between 8 and 9. It has passed 8 but has not reached 9, so the hour is 8.
Look at the long hand (the minute hand). It tells us the minutes. Count in fives from the 12, then count single marks.
The long hand points at 6. Count in fives: 5, 10, 15, 20, 25, 30.
6 × 5 = 30 minutes
Say the time. Use the minutes to say past or to, and the hour from step 1.
30 minutes is half of an hour (60 ÷ 2 = 30). So it is half past eight.

Check. In numbers this is 8:30. ✓

Watch out. Do not mix up the two hands. The short, thick hand shows the hour. The long, thin hand shows the minutes.

Worked example 8.1.3

What time does the clock show? Write the time in words.

Method. Look at the hour hand first, then the minute hand. Count the minutes in fives, then say the time.

Look at the short hand (the hour hand). It tells us the hour. Use the last number it has passed.
The short hand is between 2 and 3. It has passed 2 but has not reached 3, so the hour is 2.
Look at the long hand (the minute hand). It tells us the minutes. Count in fives from the 12, then count single marks.
The long hand points at 3. Count in fives: 5, 10, 15.
3 × 5 = 15 minutes
Say the time. Use the minutes to say past or to, and the hour from step 1.
15 minutes is a quarter of an hour (60 ÷ 4 = 15). So it is quarter past two.

Check. In numbers this is 2:15. ✓

Watch out. Do not mix up the two hands. The short, thick hand shows the hour. The long, thin hand shows the minutes.

Worked example 8.1.4

What time does the clock show? Write the time in words.

Method. Look at the hour hand first, then the minute hand. Count the minutes in fives, then say the time.

Look at the short hand (the hour hand). It tells us the hour. Use the last number it has passed.
The short hand is between 10 and 11. It has passed 10 but has not reached 11, so the hour is 10.
Look at the long hand (the minute hand). It tells us the minutes. Count in fives from the 12, then count single marks.
The long hand points at 9. Count in fives: 5, 10, 15, 20, 25, 30, 35, 40, 45.
9 × 5 = 45 minutes
Say the time. Use the minutes to say past or to, and the hour from step 1.
45 minutes past is the same as 15 minutes to the next hour (60 − 45 = 15). The next hour is 11. So it is quarter to eleven.

Check. In numbers this is 10:45. ✓

Watch out. Use the hour the short hand has passed, even when the minute hand is nearly round to the next hour.

Worked example 8.1.5

What time does the clock show? Write the time in words.

Method. Look at the hour hand first, then the minute hand. Count the minutes in fives, then say the time.

Look at the short hand (the hour hand). It tells us the hour. Use the last number it has passed.
The short hand is between 3 and 4. It has passed 3 but has not reached 4, so the hour is 3.
Look at the long hand (the minute hand). It tells us the minutes. Count in fives from the 12, then count single marks.
The long hand points at 4. Count in fives: 5, 10, 15, 20.
4 × 5 = 20 minutes
Say the time. Use the minutes to say past or to, and the hour from step 1.
The minute hand is on the right-hand side, so we say past.
20 minutes after 3: twenty past three

Check. In numbers this is 3:20. ✓

Watch out. Do not mix up the two hands. The short, thick hand shows the hour. The long, thin hand shows the minutes.

Worked example 8.1.6

What time does the clock show? Write the time in words, using to.

Method. Look at the hour hand first, then the minute hand. Count the minutes in fives, then say the time.

Look at the short hand (the hour hand). It tells us the hour. Use the last number it has passed.
The short hand is between 6 and 7. It has passed 6 but has not reached 7, so the hour is 6.
Look at the long hand (the minute hand). It tells us the minutes. Count in fives from the 12, then count single marks.
The long hand points at 8. Count in fives: 5, 10, 15, 20, 25, 30, 35, 40.
8 × 5 = 40 minutes
Say the time. Use the minutes to say past or to, and the hour from step 1.
The minute hand is on the left-hand side, so we say to. We count the minutes to the next hour.
60 − 40 = 20 minutes to 7.
twenty to seven

Check. In numbers this is 6:40. ✓

Watch out. Use the hour the short hand has passed, even when the minute hand is nearly round to the next hour.

Worked example 8.1.7

Write the time shown on the clock in numbers (digital time).

Method. The short hand gives the hour and the long hand gives the minutes. Write them with a colon between.

Look at the short hand (the hour hand). It tells us the hour. Use the last number it has passed.
The short hand is between 9 and 10. It has passed 9 but has not reached 10, so the hour is 9.
Look at the long hand (the minute hand). It tells us the minutes. Count in fives from the 12, then count single marks.
The long hand points at 11. Count in fives: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55.
11 × 5 = 55 minutes
Write the time in numbers. A digital time is the hour, a colon, then the minutes. The minutes always have two digits.
hour 9, minutes 55 → 9:55

Check. In words this is five to ten. ✓

Watch out. Use the hour the short hand has passed, even when the minute hand is nearly round to the next hour.

Worked example 8.1.8

Which clock shows ten to four? Write the letter.

ABCD

Method. Work out where both hands should be. Then check each clock.

Say the time we want: ten to four = 3:50. We need the hour and the minutes in numbers.
3:50
Find where the minute hand should point. The long hand shows the minutes.
The minute hand points at the 10 (10 × 5 = 50 minutes).
Find where the hour hand should be. The short hand shows the hour.
The hour hand is between 3 and 4 (it has passed 3).
Check each clock. Read each clock. The right one has both hands in the right places.
A: shows 10:15 × not a match
B: shows 3:10 × not a match
C: shows 3:50 ✓
D: shows 4:50 × not a match
Choose the clock.
C

Check. Clock C has the minute hand at 50 minutes and the hour hand past 3. ✓

Watch out. A clock with the hands the wrong way round (short hand for minutes) shows a different time.

Worked example 8.1.9

Write “twenty-five to nine” in numbers.

Method. For “past” the hour stays. For “to” count back from the next hour: the hour is one less.

Find how many minutes are left to the next hour. “To” means before the next hour.
25 to 9: 25 minutes before 9
Take the 25 minutes away from 60 to get the minutes past 8. The hour before 9 is 8.
60 − 25 = 35
The time is 8:35 = 8:35
Check by saying it back.
8:35 is twenty-five to nine.

Check. 8:35 in words is twenty-five to nine. ✓

Watch out. “To 9” times are in the hour before 9. Quarter to 9 is 8:45, not 9:45.

Watch out

Count in fives, and use “to” after the 6. When the minute hand is on the 8, the time is not “eight past”. The 8 means 8 × 5 = 40 minutes. 40 minutes past 3 is 20 minutes to 4. Also, for “to” times the hour you say is the next hour, but the short hand is still just before it.

8.2

Reading to the nearest minute, and clocks with Roman numerals

Year 4
Read clocks to the nearest minute, Roman numeral clock faces, The hour hand between numbers

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Reading to the nearest minute, and clocks with Roman numeralsComing soon

Between one number and the next on a clock face there are 5 small gaps. Each small gap is 1 minute. So we can read the time to the nearest minute.

How to read the minutes. Look at the minute hand. Find the last number it has passed. Count in fives to that number. Then count on the small marks.

The minute hand has passed the 4 (that is 20 minutes). It is then 3 small marks further on. 20 + 3 = 23 minutes. The time is 4:23, or 23 minutes past 4.

Past or to? If the minute hand is on the right-hand side (up to 30 minutes), say how many minutes past. If it is on the left-hand side, say how many minutes are left to the next hour. To find the minutes to the next hour take the minutes away from 60. At 7:47, 60 − 47 = 13, so it is 13 minutes to 8.

Where is the hour hand? The hour hand moves slowly all the time. Halfway through the hour it is halfway between two numbers. Just before the next hour it is nearly at the next number, but the hour is still the smaller number.

Left: 5:55. The hour hand is nearly at the 6 but has not reached it, so the hour is 5. Right: 6:05. The hour hand has just passed the 6, so the hour is 6.

Roman numeral clocks. Some clocks use Roman numerals instead of 1 to 12. You read the hands in just the same way. The minute hand counts in fives from the XII.

I = 1 II = 2 III = 3 IV = 4 V = 5 VI = 6 VII = 7 VIII = 8 IX = 9 X = 10 XI = 11 XII = 12

Some clocks write 4 as IIII instead of IV. It still means 4. On a clock face with no numbers at all, use the long marks: the top is 12, the right is 3, the bottom is 6 and the left is 9.

Roman numeral clocks. Left: the minute hand is on VII (35 minutes) but one small mark back, so 34 minutes: 7:34. Middle: 2:18. Right: this clock uses IIII for 4. The minute hand is just past II, so 5:12.

Key ideas

Each number on the clock is 5 minutes. Each small mark is 1 minute.
To read the minutes: count in fives to the last number passed, then count on the small marks.
Up to 30 minutes say past. After 30 minutes, take the minutes from 60 and say to the next hour.
The hour is the number the short hand has passed. At 5:55 the hour hand is nearly at 6, but the hour is 5.
Roman numerals: I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII. The XII is at the top. Read the hands the same way.

Worked example 8.2.1

Read the clock to the nearest minute. Write the time as minutes past or to.

Method. Find the hour and the minutes. If the minutes are 30 or fewer say past. If they are more than 30, work out how many minutes are left to the next hour.

Look at the short hand (the hour hand). It tells us the hour. Use the last number it has passed.
The short hand is between 7 and 8. It has passed 7 but has not reached 8, so the hour is 7.
Look at the long hand (the minute hand). It tells us the minutes. Count in fives from the 12, then count single marks.
The long hand has passed the 4 and is 3 small marks further on.
The 4 is 4 × 5 = 20 minutes. Now count on 3.
20 + 3 = 23 minutes
Say it with past or to. Up to 30 minutes we say past. After 30 minutes we count the minutes left to the next hour and say to.
23 minutes after 7: 23 minutes past 7

Check. In numbers this is 7:23. ✓

Watch out. Do not mix up the two hands. The short, thick hand shows the hour. The long, thin hand shows the minutes.

Worked example 8.2.2

Read the clock to the nearest minute. Write the time as minutes past or to.

Method. Find the hour and the minutes. If the minutes are 30 or fewer say past. If they are more than 30, work out how many minutes are left to the next hour.

Look at the short hand (the hour hand). It tells us the hour. Use the last number it has passed.
The short hand is between 4 and 5. It has passed 4 but has not reached 5, so the hour is 4.
Look at the long hand (the minute hand). It tells us the minutes. Count in fives from the 12, then count single marks.
The long hand has passed the 9 and is 2 small marks further on.
The 9 is 9 × 5 = 45 minutes. Now count on 2.
45 + 2 = 47 minutes
Say it with past or to. Up to 30 minutes we say past. After 30 minutes we count the minutes left to the next hour and say to.
60 − 47 = 13 minutes before 5: 13 minutes to 5

Check. In numbers this is 4:47. ✓

Watch out. Use the hour the short hand has passed, even when the minute hand is nearly round to the next hour.

Worked example 8.2.3

Write the time in numbers (digital time).

Method. The short hand gives the hour and the long hand gives the minutes. Write them with a colon between.

Look at the short hand (the hour hand). It tells us the hour. Use the last number it has passed.
The short hand is between 11 and 12. It has passed 11 but has not reached 12, so the hour is 11.
Look at the long hand (the minute hand). It tells us the minutes. Count in fives from the 12, then count single marks.
The long hand has passed the 1 and is 3 small marks further on.
The 1 is 1 × 5 = 5 minutes. Now count on 3.
5 + 3 = 8 minutes
Write the time in numbers. A digital time is the hour, a colon, then the minutes. The minutes always have two digits.
hour 11, minutes 08 → 11:08

Check. In words this is eight minutes past eleven. ✓

Watch out. Do not mix up the two hands. The short, thick hand shows the hour. The long, thin hand shows the minutes.

Worked example 8.2.4

Read the clock to the nearest minute. Write the time as minutes past or to.

Method. Find the hour and the minutes. If the minutes are 30 or fewer say past. If they are more than 30, work out how many minutes are left to the next hour.

Look at the short hand (the hour hand). It tells us the hour. Use the last number it has passed.
The short hand is between 2 and 3. It has passed 2 but has not reached 3, so the hour is 2.
Look at the long hand (the minute hand). It tells us the minutes. Count in fives from the 12, then count single marks.
The long hand has passed the 11 and is 3 small marks further on.
The 11 is 11 × 5 = 55 minutes. Now count on 3.
55 + 3 = 58 minutes
Say it with past or to. Up to 30 minutes we say past. After 30 minutes we count the minutes left to the next hour and say to.
60 − 58 = 2 minutes before 3: 2 minutes to 3

Check. In numbers this is 2:58. ✓

Watch out. Use the hour the short hand has passed, even when the minute hand is nearly round to the next hour.

Worked example 8.2.5

This clock has Roman numerals. Write the time in numbers (digital time).

Method. The short hand gives the hour and the long hand gives the minutes. Write them with a colon between.

Look at the short hand (the hour hand). It tells us the hour. Use the last number it has passed.
The short hand is between 9 and 10. It has passed 9 but has not reached 10, so the hour is 9.
Look at the long hand (the minute hand). It tells us the minutes. Count in fives from the 12, then count single marks.
The long hand has passed the 2 and is 2 small marks further on.
The 2 is 2 × 5 = 10 minutes. Now count on 2.
10 + 2 = 12 minutes
Write the time in numbers. A digital time is the hour, a colon, then the minutes. The minutes always have two digits.
hour 9, minutes 12 → 9:12

Check. In words this is twelve minutes past nine. ✓

Watch out. Do not mix up the two hands. The short, thick hand shows the hour. The long, thin hand shows the minutes.

Worked example 8.2.6

This clock has Roman numerals. Write the time as minutes past or to.

Method. Find the hour and the minutes. If the minutes are 30 or fewer say past. If they are more than 30, work out how many minutes are left to the next hour.

Look at the short hand (the hour hand). It tells us the hour. Use the last number it has passed.
The short hand is between 10 and 11. It has passed 10 but has not reached 11, so the hour is 10.
Look at the long hand (the minute hand). It tells us the minutes. Count in fives from the 12, then count single marks.
The long hand has passed the 7 and is 2 small marks further on.
The 7 is 7 × 5 = 35 minutes. Now count on 2.
35 + 2 = 37 minutes
Say it with past or to. Up to 30 minutes we say past. After 30 minutes we count the minutes left to the next hour and say to.
60 − 37 = 23 minutes before 11: 23 minutes to 11

Check. In numbers this is 10:37. ✓

Watch out. Use the hour the short hand has passed, even when the minute hand is nearly round to the next hour.

Worked example 8.2.7

This clock only has the numbers 12, 3, 6 and 9. Write the time in numbers.

Method. The short hand gives the hour and the long hand gives the minutes. Write them with a colon between.

Look at the short hand (the hour hand). It tells us the hour. Use the last number it has passed.
The short hand is between 8 and 9. It has passed 8 but has not reached 9, so the hour is 8.
Look at the long hand (the minute hand). It tells us the minutes. Count in fives from the 12, then count single marks.
The long hand has passed the 3 and is 4 small marks further on.
The 3 is 3 × 5 = 15 minutes. Now count on 4.
15 + 4 = 19 minutes
Write the time in numbers. A digital time is the hour, a colon, then the minutes. The minutes always have two digits.
hour 8, minutes 19 → 8:19

Check. In words this is nineteen minutes past eight. ✓

Watch out. Do not mix up the two hands. The short, thick hand shows the hour. The long, thin hand shows the minutes.

Worked example 8.2.8

Why does this clock show 5:55 and not 6:55?

Method. The hour hand and the minute hand must agree. Look at the minute hand first.

Read the minute hand. The minute hand points at the 11. Count in fives: 5, 10, ... 55.
11 × 5 = 55 minutes
Think about the hour hand. It is nearly at the 6, but not quite there. At 55 minutes past the hour the hour hand is almost at the next number.
The hour hand has passed the 5 but not reached the 6.
Find the hour. The hour is the number the short hand has passed.
The hour is 5.
Write the time.
The time is 5:55, which is 5 minutes to 6. It is not 6:55.

Check. 5:55 is only 5 minutes before 6 o’clock, so the hour hand is nearly on the 6. ✓

Watch out. Do not say the hour hand has reached the 6 until it is exactly on it.

Worked example 8.2.9

Which clock shows 6:37? Write the letter.

ABCD

Method. Work out where both hands should be. Then check each clock.

Say the time we want: 6:37. We need the hour and the minutes in numbers.
6:37
Find where the minute hand should point. The long hand shows the minutes.
The minute hand is 2 small marks after the 7 (35 + 2 = 37 minutes).
Find where the hour hand should be. The short hand shows the hour.
The hour hand is between 6 and 7 (it has passed 6).
Check each clock. Read each clock. The right one has both hands in the right places.
A: shows 6:37 ✓
B: shows 6:23 × not a match
C: shows 7:32 × not a match
D: shows 5:37 × not a match
Choose the clock.
A

Check. Clock A has the minute hand at 37 minutes and the hour hand past 6. ✓

Watch out. A clock with the hands the wrong way round (short hand for minutes) shows a different time.

Watch out

Count carefully from the last number. Do not just read the number the hand is nearest to. At 4:23 the hand is nearest to the 5 (25 minutes) but it has not reached it: it is 3 marks after the 4. And for the hour, remember: at 5:55 the hour hand is almost on the 6, but the time is 5:55, not 6:55.

8.3

Digital time: am, pm and the 24-hour clock

Year 4
Digital 12-hour time with am and pm, 24-hour time, Convert between analogue, 12-hour and 24-hour

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Digital time: am, pm and the 24-hour clockComing soon

A digital clock shows the time in numbers: the hour, a colon (:), then the minutes. A quarter past 3 is 3:15. The minutes always have two digits, so 5 minutes past 3 is 3:05.

A day has 24 hours, but a clock face only has 12. So each time on the clock happens twice every day. We use am and pm to tell them apart.

am is for the morning: from midnight (12 at night) until noon (12 midday).
pm is for the afternoon and evening: from noon until midnight.

One whole day. The 12-hour clock restarts at 12 noon. The 24-hour clock keeps counting up to 24:00.

Top: the same two times on a 12-hour display (7:45 am and 7:45 pm). Bottom: on a 24-hour display (07:45 and 19:45).

The 24-hour clock does not need am or pm. It counts the hours from 00 to 23 and always shows four digits: two for the hour and two for the minutes.

Morning (am): the hour stays the same. 8:05 am is 08:05. Add a 0 at the front if the hour is only one digit.
Afternoon and evening (pm): add 12 to the hour. 4:25 pm is 4 + 12 = 16:25.
Special times: 12:30 pm stays 12:30. Just after midnight, 12:30 am is 00:30. Midnight itself is 00:00.

12-hour (morning)	24-hour	12-hour (afternoon)	24-hour
12 am	00:00	12 pm	12:00
1 am	01:00	1 pm	13:00
2 am	02:00	2 pm	14:00
3 am	03:00	3 pm	15:00
4 am	04:00	4 pm	16:00
5 am	05:00	5 pm	17:00
6 am	06:00	6 pm	18:00
7 am	07:00	7 pm	19:00
8 am	08:00	8 pm	20:00
9 am	09:00	9 pm	21:00
10 am	10:00	10 pm	22:00
11 am	11:00	11 pm	23:00

Every hour in the 12-hour and 24-hour clocks.

To go the other way, from 24-hour to 12-hour: if the hour is 13 or more, take away 12 and write pm. 21:40 is 21 − 12 = 9, so 9:40 pm.

Key ideas

am = morning (midnight to noon). pm = afternoon and evening (noon to midnight).
A digital time is the hour, a colon, then the minutes. The minutes always have two digits (3:05).
24-hour clock: no am or pm. It goes from 00:00 to 23:59 and always has four digits.
12-hour to 24-hour: am keeps the hour; pm adds 12.
24-hour to 12-hour: if the hour is 13 or more, take away 12 and write pm.
Special times: 12:00 pm is noon (12:00). 12:00 am is midnight (00:00). 12:30 pm is 12:30 but 12:30 am is 00:30.

Worked example 8.3.1

Jack wakes up at half past seven in the morning. Write the time as a digital time with am or pm.

Key words. A digital clock shows the time in numbers: hours, a colon, then minutes (7:45). am is for times between midnight and noon (the morning). pm is for times between noon and midnight (the afternoon and evening). The 24-hour clock counts the hours from 00 to 23 and does not use am or pm.

Method. am is for times from midnight to noon. pm is for times from noon to midnight. Use the clue to choose.

Look at the clue: “in the morning”. It tells us the part of the day.
Morning: am. Afternoon or evening: pm.
Choose am or pm. am is for the morning, from midnight until noon.
in the morning → am
Write the time. Hour, colon, minutes, then am or pm.
7:30 am

Check. Say it back: 7:30 am is in the morning. ✓

Watch out. 12 noon is 12:00 pm. Midnight is 12:00 am.

Worked example 8.3.2

Amira has her tea at quarter past six in the evening. Write the time as a digital time with am or pm.

Method. am is for times from midnight to noon. pm is for times from noon to midnight. Use the clue to choose.

Look at the clue: “in the evening”. It tells us the part of the day.
Morning: am. Afternoon or evening: pm.
Choose am or pm. pm is for the afternoon and evening, from noon until midnight.
in the evening → pm
Write the time. Hour, colon, minutes, then am or pm.
6:15 pm

Check. Say it back: 6:15 pm is in the evening. ✓

Watch out. 12 noon is 12:00 pm. Midnight is 12:00 am.

Worked example 8.3.3

Write 4:25 pm as a 24-hour time.

Method. For am times the hour stays the same (12 am becomes 00). For pm times add 12 to the hour (12 pm stays 12).

Look at am or pm: 4:25 pm. This tells us which rule to use.
4:25 pm
Add 12 to the hour. For pm times the 24-hour clock carries on counting after 12.
4 + 12 = 16
Write the 24-hour time. Two digits for the hour, a colon, two digits for the minutes.
16:25

Check. Change back: 16:25 is 4:25 pm. ✓

Watch out. Do not add 12 to a morning time, and do not add 12 to 12 pm.

Worked example 8.3.4

Write 8:05 am as a 24-hour time.

Method. For am times the hour stays the same (12 am becomes 00). For pm times add 12 to the hour (12 pm stays 12).

Look at am or pm: 8:05 am. This tells us which rule to use.
8:05 am
Keep the hour. For am times the hour number stays the same on the 24-hour clock.
8 stays 8. Write it with two digits: 08
Write the 24-hour time. Two digits for the hour, a colon, two digits for the minutes.
08:05

Check. Change back: 08:05 is 8:05 am. ✓

Watch out. Do not add 12 to a morning time, and do not add 12 to 12 pm.

Worked example 8.3.5

Write 21:40 as a 12-hour time with am or pm.

Method. Before 12:00 it is am and the hour stays. From 13:00 take 12 away and use pm.

Look at the hour in 21:40. It tells us whether it is morning or afternoon.
The hour is 21.
Take 12 away from the hour. After 12:00 the 24-hour clock goes 13, 14, 15... and the 12-hour clock goes 1, 2, 3... with pm.
21 − 12 = 9 pm
Write the 12-hour time. Use the colon and the minutes, then am or pm.
9:40 pm

Check. Change back: 9:40 pm is 21:40. ✓

Watch out. Midnight is 00:00. 24:00 is the same moment at the end of the day.

Worked example 8.3.6

Write 12:15 pm (just after noon) as a 24-hour time.

Method. For am times the hour stays the same (12 am becomes 00). For pm times add 12 to the hour (12 pm stays 12).

Look at am or pm: 12:15 pm. This tells us which rule to use.
12:15 pm
Keep the hour. 12:xx pm is just after noon. The hour is still 12.
12 stays 12
Write the 24-hour time. Two digits for the hour, a colon, two digits for the minutes.
12:15

Check. Change back: 12:15 is 12:15 pm. ✓

Watch out. Do not add 12 to a morning time, and do not add 12 to 12 pm.

Worked example 8.3.7

Write 00:50 as a 12-hour time with am or pm.

Method. Before 12:00 it is am and the hour stays. From 13:00 take 12 away and use pm.

Look at the hour in 00:50. It tells us whether it is morning or afternoon.
The hour is 0.
Change the hour. 00 is just after midnight. On the 12-hour clock we say 12, and it is am.
00 → 12 am
Write the 12-hour time. Use the colon and the minutes, then am or pm.
12:50 am

Check. Change back: 12:50 am is 00:50. ✓

Watch out. Midnight is 00:00. 24:00 is the same moment at the end of the day.

Worked example 8.3.8

The clock shows the time on a Saturday afternoon. Write the time as a 24-hour time.

Method. Read the clock, add am or pm for the part of the day, then (if asked) change it to the 24-hour clock.

Look at the short hand (the hour hand). It tells us the hour. Use the last number it has passed.
The short hand is between 3 and 4. It has passed 3 but has not reached 4, so the hour is 3.
Look at the long hand (the minute hand). It tells us the minutes. Count in fives from the 12, then count single marks.
The long hand points at 4. Count in fives: 5, 10, 15, 20.
4 × 5 = 20 minutes
Read the time in numbers and add am or pm. The question says it is the afternoon or evening, so it is pm.
3:20 pm = 3:20 pm
Change to the 24-hour clock. am keeps the hour. pm adds 12 (except 12 pm).
pm: add 12 to the hour. 3 + 12 = 15.
15:20

Check. 3:20 pm is 15:20 on the 24-hour clock. ✓

Watch out. A clock face cannot tell you am or pm. You need a clue.

Worked example 8.3.9

Which clock shows 15:20? Write the letter.

ABCD

Method. Work out where both hands should be. Then check each clock.

Say the time we want: 15:20 is 12 + 3 = 3 pm, so 3:20 pm. We need the hour and the minutes in numbers.
3:20
Find where the minute hand should point. The long hand shows the minutes.
The minute hand points at the 4 (4 × 5 = 20 minutes).
Find where the hour hand should be. The short hand shows the hour.
The hour hand is between 3 and 4 (it has passed 3).
Check each clock. Read each clock. The right one has both hands in the right places.
A: shows 3:20 ✓
B: shows 4:15 × not a match
C: shows 8:15 × not a match
D: shows 3:40 × not a match
Choose the clock.
A

Check. Clock A has the minute hand at 20 minutes and the hour hand past 3. ✓

Watch out. A clock with the hands the wrong way round (short hand for minutes) shows a different time.

Watch out

12 is special. 12:30 pm is not 24:30 and 12:30 am is not 12:30 in the 24-hour clock. At 12 noon the 24-hour hour is 12. Just after midnight it is 00. Also, do not add 12 to a morning time: 4:25 am is 04:25, but 4:25 pm is 16:25.

8.4

Units of time: seconds, minutes, hours, days and weeks

Year 4
Convert between units of time, Hours to minutes, minutes to seconds, weeks to days, Mixed units of time

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Units of time: seconds, minutes, hours, days and weeksComing soon

We measure time in lots of different units. Short times are in seconds and minutes. Longer times are in hours, days, weeks, months and years. Here is how they fit together:

Going to the right (big unit to small unit) we multiply. Going back to the left (small unit to big unit) we divide.

The facts to know: 60 seconds = 1 minute | 60 minutes = 1 hour | 24 hours = 1 day | 7 days = 1 week | 12 months = 1 year.

Big unit to small unit: multiply. There are more small units than big units. 3 hours is 3 × 60 = 180 minutes. A table helps:

hours	1	2	3	4	5
minutes	60	120	180	240	300

A ratio table for hours and minutes. Each time we add 1 hour we add 60 minutes.

Small unit to big unit: divide. There are fewer big units. 240 minutes is 240 ÷ 60 = 4 hours. If something is left over, it is the remainder: 135 minutes = 2 hours and 15 minutes left over, because 2 × 60 = 120 and 135 − 120 = 15.

Mixed units. To change 3 hours 20 minutes to minutes, change the hours first (3 × 60 = 180) and then add the 20 minutes: 180 + 20 = 200 minutes.

Parts of an hour. Half an hour is 30 minutes. A quarter of an hour is 15 minutes. Three quarters of an hour is 45 minutes. So 1½ hours is 60 + 30 = 90 minutes.

Key ideas

60 seconds = 1 minute. 60 minutes = 1 hour. 24 hours = 1 day. 7 days = 1 week. 12 months = 1 year.
Big unit to small unit: multiply. Small unit to big unit: divide.
When you divide, the remainder is the small units left over: 135 minutes = 2 hours 15 minutes.
Mixed units: change the big unit first, then add the small units.
Half an hour = 30 minutes, a quarter of an hour = 15 minutes. 1½ hours = 90 minutes.
There are 60 minutes in an hour, not 100.

Worked example 8.4.1

Change 5 minutes into seconds.

Key words. To convert is to change from one unit to another. 60 seconds = 1 minute. 60 minutes = 1 hour. 24 hours = 1 day. 7 days = 1 week. 12 months = 1 year. To go from a big unit to a small unit we multiply. To go from a small unit to a big unit we divide.

Method. There are 60 seconds in 1 min. Going from minutes to seconds (big unit to small unit), we multiply by 60.

Write the fact. We need to know how many of the small unit make one of the big unit.
1 min = 60 seconds
Multiply by 60. We have 5 minutes, so we need 5 lots of 60.
5 × 60 = 5 × 6 × 10 = 30 × 10 = 300
Write the answer with its unit.
5 minutes = 300 seconds

Check. Go back: 300 ÷ 60 = 5. ✓

Watch out. A big unit changes to a bigger number of small units. 5 minutes must be more than 5 seconds.

Worked example 8.4.2

How many minutes are there in 3 hours?

Method. There are 60 minutes in 1 h. Going from hours to minutes (big unit to small unit), we multiply by 60.

Write the fact. We need to know how many of the small unit make one of the big unit.
1 h = 60 minutes
Multiply by 60. We have 3 hours, so we need 3 lots of 60.
3 × 60 = 3 × 6 × 10 = 18 × 10 = 180
Write the answer with its unit.
3 hours = 180 minutes

Check. Go back: 180 ÷ 60 = 3. ✓

Watch out. A big unit changes to a bigger number of small units. 3 hours must be more than 3 minutes.

Worked example 8.4.3

Change 6 days into hours.

Method. There are 24 hours in 1 day. Going from days to hours (big unit to small unit), we multiply by 24.

Write the fact. We need to know how many of the small unit make one of the big unit.
1 day = 24 hours
Multiply by 24. We have 6 days, so we need 6 lots of 24.
6 × 24 = 6 × 20 + 6 × 4 = 120 + 24 = 144
Write the answer with its unit.
6 days = 144 hours

Check. Go back: 144 ÷ 24 = 6. ✓

Watch out. A big unit changes to a bigger number of small units. 6 days must be more than 6 hours.

Worked example 8.4.4

How many days are there in 5 weeks?

Method. There are 7 days in 1 week. Going from weeks to days (big unit to small unit), we multiply by 7.

Write the fact. We need to know how many of the small unit make one of the big unit.
1 week = 7 days
Multiply by 7. We have 5 weeks, so we need 5 lots of 7.
5 × 7 = 35 (a times-table fact)
Write the answer with its unit.
5 weeks = 35 days

Check. Go back: 35 ÷ 7 = 5. ✓

Watch out. A big unit changes to a bigger number of small units. 5 weeks must be more than 5 days.

Worked example 8.4.5

Change 420 seconds into minutes.

Method. There are 60 seconds in 1 min. Going from seconds to minutes (small unit to big unit), we divide by 60.

Write the fact. We need to know how many of the small unit make one of the big unit.
1 min = 60 seconds
Divide by 60. Going from seconds to minutes (small unit to big unit) we divide. We find how many lots of 60 are in 420.
420 ÷ 60 = 42 ÷ 6 = 7 (divide by 10, then by 6)
Write the answer with its unit.
420 seconds = 7 minutes

Check. 7 × 60 = 420 = 420. ✓

Watch out. A small unit changes to a smaller number of big units. 420 seconds must be fewer than 420 minutes.

Worked example 8.4.6

Change 240 minutes into hours.

Method. There are 60 minutes in 1 h. Going from minutes to hours (small unit to big unit), we divide by 60.

Write the fact. We need to know how many of the small unit make one of the big unit.
1 h = 60 minutes
Divide by 60. Going from minutes to hours (small unit to big unit) we divide. We find how many lots of 60 are in 240.
240 ÷ 60 = 24 ÷ 6 = 4 (divide by 10, then by 6)
Write the answer with its unit.
240 minutes = 4 hours

Check. 4 × 60 = 240 = 240. ✓

Watch out. A small unit changes to a smaller number of big units. 240 minutes must be fewer than 240 hours.

Worked example 8.4.7

Change 135 minutes into hours and minutes.

Method. There are 60 minutes in 1 h. Going from minutes to hours (small unit to big unit), we divide by 60. The remainder is the left over minutes.

Write the fact. We need to know how many of the small unit make one of the big unit.
1 h = 60 minutes
Divide by 60. Going from minutes to hours (small unit to big unit) we divide. We find how many lots of 60 are in 135.
60 × 2 = 120
60 × 3 = 180 is too big
135 − 120 = 15 left over
135 ÷ 60 = 2 remainder 15
Write the whole hours and the left over minutes. The remainder is the minutes that do not make another whole h.
135 minutes = 2 hours 15 minutes

Check. 2 × 60 = 120 and 120 + 15 = 135. ✓

Watch out. The remainder is minutes, not a decimal. 135 minutes is not 2.15 hours.

Worked example 8.4.8

Change 23 days into weeks and days.

Method. There are 7 days in 1 week. Going from days to weeks (small unit to big unit), we divide by 7. The remainder is the left over days.

Write the fact. We need to know how many of the small unit make one of the big unit.
1 week = 7 days
Divide by 7. Going from days to weeks (small unit to big unit) we divide. We find how many lots of 7 are in 23.
7 × 3 = 21
7 × 4 = 28 is too big
23 − 21 = 2 left over
23 ÷ 7 = 3 remainder 2
Write the whole weeks and the left over days. The remainder is the days that do not make another whole week.
23 days = 3 weeks 2 days

Check. 3 × 7 = 21 and 21 + 2 = 23. ✓

Watch out. The remainder is days, not a decimal. 23 days is not 3.2 weeks.

Worked example 8.4.9

Change 3 hours 20 minutes into minutes.

Method. Change the hours into minutes first. Then add the minutes you already have.

Change 3 hours into minutes. 1 h = 60 minutes, so multiply by 60.
3 × 60 = 3 × 6 × 10 = 18 × 10 = 180
Add the 20 minutes. Now we add on the minutes that were left.
180 + 20 = 200
Write the answer with its unit.
3 hours 20 minutes = 200 minutes

Check. 200 ÷ 60 = 3 remainder 20, which is 3 hours 20 minutes. ✓

Watch out. There are 60, not 100, minutes in a h.

Worked example 8.4.10

How many minutes are there in 1½ hours?

Method. Change the whole hours to minutes, then find the fraction of a h and add.

Change the 1 whole hour into minutes. 1 h = 60 minutes.
1 × 60 = 60
Find the fraction of a h. 12 of 60 means divide 60 into 2 equal parts.
60 ÷ 2 = 30
12 of a h = 30 minutes
Add the parts together.
60 + 30 = 90 minutes

Check. Check: 90 ÷ 60 = 1.5 hours. ✓

Watch out. Half an hour is 30 minutes, so 1½ hours is 90 minutes, not 1 hour 50 minutes.

Worked example 8.4.11

Which is longer: 2 hours or 100 minutes?

Method. To compare two times, change them to the same unit. Then compare the numbers.

Change 2 hours into minutes. We can only compare when both are in the same unit.
2 × 60 = 120 minutes
Write the other time in minutes. 100 minutes is already in minutes.
100 minutes
Compare the numbers. The bigger number is the longer time.
120 is bigger than 100.
The longer time is 2 hours.

Check. 2 hours = 120 minutes and 100 minutes = 100 minutes. ✓

Watch out. Do not compare the numbers 2 and 100 without changing the units. They are different units!

Watch out

1.5 hours is not 1 hour 50 minutes. The number after the point is not minutes. 1.5 hours means 1 and a half hours, so it is 1 hour and 30 minutes (90 minutes). And an hour has 60 minutes, not 100, so 2.25 hours is not 2 hours 25 minutes. Always change to minutes using 60.

8.5

Months, years and the calendar

Year 4
Years to months, months to years, Days in each month; leap years, Reading a calendar and finding dates

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Months, years and the calendarComing soon

A year has 12 months. So to change years into months we multiply by 12 (4 years = 4 × 12 = 48 months), and to change months into years we divide by 12.

Years to months: multiply by 12. Months to years: divide by 12.

Days in each month. Some months have 31 days, some have 30, and February is different: 28 days, or 29 in a leap year. Here is a trick to remember. Make a fist. Say the months along your knuckles and the dips between them. Every knuckle is a month with 31 days. Every dip is a month with 30 days (except February). After July, go back to the first knuckle for August.

The knuckle trick. Knuckles are 31-day months. Dips are 30-day months. February is a dip with 28 days (29 in a leap year). July and August are both knuckles.

Years and leap years. A normal year has 365 days. Every 4 years there is a leap year with 366 days. In a leap year, February has 29 days, not 28. How to check if a year is a leap year: look at the last two digits. If they can be divided by 4 with nothing left over, it is a leap year (2024: 24 ÷ 4 = 6). 2030 is not: 30 ÷ 4 = 7 remainder 2.

Weeks. There are 7 days in a week. A year has 52 weeks and 1 extra day (52 × 7 = 364).

March 2026
Mon	Tue	Wed	Thu	Fri	Sat	Sun
						1
2	3	4	5	6	7	8
9	10	11	12	13	14	15
16	17	18	19	20	21	22
23	24	25	26	27	28	29
30	31

A calendar for March 2026. Each row is a week and each column is a day of the week. 5 March and 6 March are a Thursday and a Friday. 20 March is a Friday. Dates in the same column are 7 days apart.

Finding dates. To find a date some days or weeks later, add the days. If the answer is bigger than the number of days in the month, take away the days in the month. The first day after the end of the month is the 1st of the next month. For example: 20 June + 2 weeks is 20 + 14 = 34. June has 30 days, so 34 − 30 = 4: it is 4 July.

Key ideas

12 months = 1 year. Years to months: × 12. Months to years: ÷ 12.
31 days: January, March, May, July, August, October, December. 30 days: April, June, September, November.
February has 28 days, and 29 days in a leap year.
A year has 365 days. A leap year has 366 days and comes every 4 years (the last two digits divide by 4).
7 days = 1 week. Dates in the same column of a calendar are 7 days apart.
To find a later date: add the days, and if you go past the end of the month, take away the days in the month.

Worked example 8.5.1

How many days are there in July?

Key words. A calendar shows the days and dates of the months. A leap year has 366 days instead of 365, because February has 29 days. Date means the day of the month (like 14 March).

Method. Use your knuckles. Each knuckle is a month with 31 days. Each dip between knuckles is a month with 30 days (except February).

Make a fist and say the months, starting on the first knuckle. Start at the first knuckle for January.
Jan: knuckle
Feb: dip
Mar: knuckle
Apr: dip
May: knuckle
Jun: dip
Jul: knuckle
Find out if July is a knuckle or a dip. Knuckle: 31 days. Dip: 30 days. February is the odd one out.
July is a knuckle: 31 days.
Write the answer.
July has 31 days.

Check. The rhyme way: April, June, September and November have 30. February has 28 or 29. All the rest have 31. ✓

Watch out. February is the only month that does not have 30 or 31 days.

Worked example 8.5.2

How many days are there in September?

Key words. A calendar shows the days and dates of the months. A leap year has 366 days instead of 365, because February has 29 days. Date means the day of the month (like 14 March).

Method. Use your knuckles. Each knuckle is a month with 31 days. Each dip between knuckles is a month with 30 days (except February).

Make a fist and say the months, starting on the first knuckle. August is a knuckle too: after July go back to the first knuckle and start again.
Aug: knuckle
Sep: dip
Find out if September is a knuckle or a dip. Knuckle: 31 days. Dip: 30 days. February is the odd one out.
September is a dip: 30 days.
Write the answer.
September has 30 days.

Check. The rhyme way: April, June, September and November have 30. February has 28 or 29. All the rest have 31. ✓

Watch out. February is the only month that does not have 30 or 31 days.

Worked example 8.5.3

How many days are there in February 2028?

Key words. A calendar shows the days and dates of the months. A leap year has 366 days instead of 365, because February has 29 days. Date means the day of the month (like 14 March).

Method. Use your knuckles. Each knuckle is a month with 31 days. Each dip between knuckles is a month with 30 days (except February).

Make a fist and say the months, starting on the first knuckle. Start at the first knuckle for January.
Jan: knuckle
Feb: dip
Find out if February is a knuckle or a dip. Knuckle: 31 days. Dip: 30 days. February is the odd one out.
February is a dip with 28 days, but in a leap year it has 29. 2028 is a leap year, so February 2028 has 29 days.
Write the answer.
February has 29 days.

Check. The rhyme way: April, June, September and November have 30. February has 28 or 29. All the rest have 31. ✓

Watch out. February is the only month that does not have 30 or 31 days.

Worked example 8.5.4

Is 2028 a leap year?

Key words. A calendar shows the days and dates of the months. A leap year has 366 days instead of 365, because February has 29 days. Date means the day of the month (like 14 March).

Method. A leap year can be divided by 4 with nothing left over. To check, divide the last two digits by 4.

Look at the last two digits of 2028. Because 100 divides exactly by 4, only the last two digits matter.
The last two digits are 28.
Divide 28 by 4. If there is no remainder, the number is in the 4 times table.
4 × 7 = 28. 28 ÷ 4 = 7 exactly.
Decide.
2028 can be divided by 4 exactly, so it is a leap year. Yes

Check. 4 × 507 = 2,028 = 2028. ✓

Watch out. A leap year has 366 days, and February has 29 days.

Worked example 8.5.5

Is 2030 a leap year?

Key words. A calendar shows the days and dates of the months. A leap year has 366 days instead of 365, because February has 29 days. Date means the day of the month (like 14 March).

Method. A leap year can be divided by 4 with nothing left over. To check, divide the last two digits by 4.

Look at the last two digits of 2030. Because 100 divides exactly by 4, only the last two digits matter.
The last two digits are 30.
Divide 30 by 4. If there is no remainder, the number is in the 4 times table.
4 × 7 = 28. 30 − 28 = 2 left over.
Decide.
2030 cannot be divided by 4 exactly, so it is not a leap year. No

Check. 4 × 507 = 2,028, and 2030 is 2 more. ✓

Watch out. A leap year has 366 days, and February has 29 days.

Worked example 8.5.6

How many days are there in June and July together?

Key words. A calendar shows the days and dates of the months. A leap year has 366 days instead of 365, because February has 29 days. Date means the day of the month (like 14 March).

Method. Find how many days are in each month. Then add them up.

Write the number of days in each month. Use the knuckles. Knuckle = 31, dip = 30, February = 28 (29 in a leap year).
June: 30 days
July: 31 days
Add the days. The total is all the days together.
30 + 31 = 61
Write the answer.
June and July: 61 days

Check. Check by adding in a different order. ✓

Watch out. Check February: it has 28 days, or 29 in a leap year.

Worked example 8.5.7

How many months are there in 4 years?

Method. There are 12 months in 1 year. Going from years to months (big unit to small unit), we multiply by 12.

Write the fact. We need to know how many of the small unit make one of the big unit.
1 year = 12 months
Multiply by 12. We have 4 years, so we need 4 lots of 12.
4 × 12 = 48 (a times-table fact)
Write the answer with its unit.
4 years = 48 months

Check. Go back: 48 ÷ 12 = 4. ✓

Watch out. A big unit changes to a bigger number of small units. 4 years must be more than 4 months.

Worked example 8.5.8

Change 30 months into years and months.

Method. There are 12 months in 1 year. Going from months to years (small unit to big unit), we divide by 12. The remainder is the left over months.

Write the fact. We need to know how many of the small unit make one of the big unit.
1 year = 12 months
Divide by 12. Going from months to years (small unit to big unit) we divide. We find how many lots of 12 are in 30.
12 × 2 = 24
12 × 3 = 36 is too big
30 − 24 = 6 left over
30 ÷ 12 = 2 remainder 6
Write the whole years and the left over months. The remainder is the months that do not make another whole year.
30 months = 2 years 6 months

Check. 2 × 12 = 24 and 24 + 6 = 30. ✓

Watch out. The remainder is months, not a decimal. 30 months is not 2.6 years.

Worked example 8.5.9

Look at the calendar for March 2026. What day of the week is 17 March?

March 2026
Mon	Tue	Wed	Thu	Fri	Sat	Sun
						1
2	3	4	5	6	7	8
9	10	11	12	13	14	15
16	17	18	19	20	21	22
23	24	25	26	27	28	29
30	31

Key words. A calendar shows the days and dates of the months. A leap year has 366 days instead of 365, because February has 29 days. Date means the day of the month (like 14 March).

Method. Find the date in the calendar. Then look at the top of its column to read the day of the week.

Find 17 in the calendar. The dates are in rows. Each row is one week.
17 March
Look straight up the column. The day names are at the top of each column.
The column is headed Tue.
Write the answer.
17 March is a Tuesday.

Check. Dates in the same column are 7 days apart: 17 + 7 = 24, which is also a Tuesday. ✓

Watch out. Read straight up the column. A date in the row above or below is a different day.

Worked example 8.5.10

Noah’s birthday party is 2 weeks after 20 June. What is the date of the party?

Key words. A calendar shows the days and dates of the months. A leap year has 366 days instead of 365, because February has 29 days. Date means the day of the month (like 14 March).

Method. Add the days to the date. If the answer is bigger than the number of days in the month, take that number away and move to the next month.

Change 2 weeks into days. 1 week = 7 days.
2 × 7 = 14 days
Add the days to the date. Count on from the date.
20 + 14 = 34
34 is more than the days in June, so move to the next month. June has 30 days. Take them away to see how far into the next month we are.
34 − 30 = 4
Write the date.
4 July

Check. Count back 14 days from 4 July to get to 20 June. ✓

Watch out. June has 30 days, so after the 30th comes the 1st of the next month.

Worked example 8.5.11

A library book is borrowed on 25 March. It has to go back 10 days later. What date is that?

Key words. A calendar shows the days and dates of the months. A leap year has 366 days instead of 365, because February has 29 days. Date means the day of the month (like 14 March).

Method. Add the days to the date. If the answer is bigger than the number of days in the month, take that number away and move to the next month.

Add the days to the date. Count on from the date.
25 + 10 = 35
35 is more than the days in March, so move to the next month. March has 31 days. Take them away to see how far into the next month we are.
35 − 31 = 4
Write the date.
4 April

Check. Count back 10 days from 4 April to get to 25 March. ✓

Watch out. March has 31 days, so after the 31th comes the 1st of the next month.

Watch out

February is the odd one out, and the 31 days are not all together. Many children think that months alternate 31, 30, 31, 30 all year. But July and August both have 31 days. And do not say a leap year has 30 days in February. It has 29. A leap year has 366 days in the whole year.

Exercise 8E Months, years and the calendar

Non-calculator

FHow many days are there in each month?

(a)March

(b)April

(c)November

(d)August

Done

FChange each time into the unit shown.

(a)3 years into months

(b)5 years into months

(d)30 months into years and months

Done

FIs each year a leap year? Write yes or no.

(a)2024

(b)2031

(d)2050

Done

FWrite the names of the months that have exactly 30 days.

Done

FUse the calendar for June 2026.

June 2026
Mon	Tue	Wed	Thu	Fri	Sat	Sun
1	2	3	4	5	6	7
8	9	10	11	12	13	14
15	16	17	18	19	20	21
22	23	24	25	26	27	28
29	30

(a)What day of the week is 10 June?

(b)What day of the week is 26 June?

(c)How many Sundays are there in June?

(d)How many days are there from 5 June to 19 June?

Done

FHow many days are there in these months together?

(a)January and February 2026

(b)July and August

(c)September, October and November

Done

PSWork out each date.

(a)3 weeks after 14 September

(b)10 days after 27 January

Done

PSHow many days are there from 1 January to 31 March (including both days)?

(a)in 2027

(b)in 2028 (a leap year)

Done

PSAisha is 3 years and 4 months old. How many months old is she?

Done

PSLeo was born on 29 February 2020.

(a)Which is the next year, after 2020, when there is a 29 February?

(b)How old will Leo be on 29 February in that year?

Done

RTom says, “In a leap year, February has 30 days.” What mistake has he made?

Done

RWrite always, sometimes or never for each sentence.

(a)A month has 30 days.

(b)A leap year has 366 days.

(c)The year after a leap year is also a leap year.

Done

RChallenge. Find two months that are next to each other and both have 31 days. Can you find another pair?

Done

8.6

How long does it take? Durations, start times and end times

Year 4
Calculate durations of time, Find start times and end times, Across noon and midnight

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: How long does it take? Durations, start times and end timesComing soon

The duration of something is how long it takes. To find a duration, we do not take one time away from the other like in a normal subtraction, because there are 60 minutes in an hour. We count on instead, on a number line.

Three easy jumps. Start at the start time.

Jump to the next o’clock.
Jump along in whole hours until you reach the hour of the end time.
Jump the last minutes to the end time.

From 3:40 to 6:15: 20 minutes to the next o’clock, then 2 hours, then 15 minutes. Total: 2 hours and 20 + 15 = 35 minutes, which is 2 hours 35 minutes.

Add the jumps. Add the hours, then add the minutes. If the minutes come to 60 or more, change 60 minutes into 1 hour.

Finding an end time. If a film starts at 2:25 pm and lasts 1 hour 50 minutes, add the whole hours first (2:25 + 1 hour = 3:25), then count on the minutes through the next o’clock: 3:25 + 35 minutes = 4:00, then 4:00 + 15 minutes = 4:15 pm.

Finding a start time. Count back from the end time. Take away the whole hours first, then the minutes, going back to the o’clock on the way.

Across noon or midnight. The same method works. Count on to 12:00 (noon or midnight), then carry on. The 24-hour clock makes this easier: 22:30 to 06:15 is 22:30 → 24:00 (1 hour 30 minutes) and 00:00 → 06:15 (6 hours 15 minutes).

10:30 pm to 6:15 am. Count on to midnight, then on to 6:15 am. 1 h 30 min + 6 h 15 min = 7 h 45 min.

Key ideas

Duration = how long something takes. To find it, count on: to the next o’clock, then whole hours, then the last minutes.
There are 60 minutes in an hour. 3:50 to 4:20 is 30 minutes (10 + 20), not 70.
End time = start time + duration. Add the whole hours first, then the minutes.
Start time = end time − duration. Count back the whole hours first, then the minutes.
Across noon or midnight, count on to 12:00 and then carry on. Pay attention to am and pm.
Check by counting: start + duration should give the end time.

Worked example 8.6.1

A swimming lesson starts at 3:10 pm and finishes at 3:45 pm. How long is the lesson?

Key words. The duration is how long something takes (how much time goes by). To count on is to jump forward from one time to another. The start time is when something begins. The end time is when it finishes.

Method. Count on from the start to the end on a number line: first to the next o'clock, then in whole hours, then the last minutes. Then add the jumps.

Draw a number line and count on from the start time to the end time. Counting on in easy jumps (first to the next o'clock, then whole hours, then the last minutes) is easier than taking one time away from the other.
Work out each jump. Each jump is easy to do in your head.
3:10 pm to 3:45 pm: 45 − 10 = 35 minutes
Add the jumps. Add the hours together, then add the minutes together. If the minutes reach 60 or more, change 60 minutes into 1 hour.
Minutes: 35
Total: 35 minutes

Check. Count on from the start: 3:10 pm + 35 minutes = 3:45 pm. ✓

Watch out. There are 60 minutes in an hour, not 100. 3:50 to 4:20 is 30 minutes, not 70.

Worked example 8.6.2

Mei starts reading at 4:40 pm and stops at 5:25 pm. How long does she read for?

Method. Count on from the start to the end on a number line: first to the next o'clock, then in whole hours, then the last minutes. Then add the jumps.

Draw a number line and count on from the start time to the end time. Counting on in easy jumps (first to the next o'clock, then whole hours, then the last minutes) is easier than taking one time away from the other.
Work out each jump. Each jump is easy to do in your head.
4:40 pm to 5:00 pm: 20 minutes to the next o'clock
60 − 40 = 20 minutes
5:00 pm to 5:25 pm: the minutes after the o'clock: 25 minutes
Add the jumps. Add the hours together, then add the minutes together. If the minutes reach 60 or more, change 60 minutes into 1 hour.
Minutes: 20 + 25 = 45
Total: 45 minutes

Check. Count on from the start: 4:40 pm + 45 minutes = 5:25 pm. ✓

Watch out. There are 60 minutes in an hour, not 100. 3:50 to 4:20 is 30 minutes, not 70.

Worked example 8.6.3

A coach leaves at 9:20 am and arrives at 12:05 pm. How long is the journey?

Method. Count on from the start to the end on a number line: first to the next o'clock, then in whole hours, then the last minutes. Then add the jumps.

Draw a number line and count on from the start time to the end time. Counting on in easy jumps (first to the next o'clock, then whole hours, then the last minutes) is easier than taking one time away from the other.
Work out each jump. Each jump is easy to do in your head.
9:20 am to 10:00 am: 40 minutes to the next o'clock
60 − 20 = 40 minutes
10:00 am to 12:00 pm: whole hours: 2 hours
12:00 pm to 12:05 pm: the minutes after the o'clock: 5 minutes
Add the jumps. Add the hours together, then add the minutes together. If the minutes reach 60 or more, change 60 minutes into 1 hour.
Hours: 2 hours
Minutes: 40 + 5 = 45
Total: 2 hours 45 minutes

Check. Count on from the start: 9:20 am + 2 hours 45 minutes = 12:05 pm. ✓

Watch out. There are 60 minutes in an hour, not 100. 3:50 to 4:20 is 30 minutes, not 70.

Worked example 8.6.4

The clocks show when a football match starts and finishes. How long is the match?

startend

Method. Count on from the start to the end on a number line: first to the next o'clock, then in whole hours, then the last minutes. Then add the jumps.

Read the first clock. This is the start time.
The first clock shows 2:20 (twenty past two).
Read the second clock. This is the end time.
The second clock shows 4:05 (five past four).
Draw a number line and count on from the start time to the end time. Counting on in easy jumps (first to the next o'clock, then whole hours, then the last minutes) is easier than taking one time away from the other.
Work out each jump. Each jump is easy to do in your head.
2:20 to 3:00: 40 minutes to the next o'clock
60 − 20 = 40 minutes
3:00 to 4:00: whole hours: 1 hour
4:00 to 4:05: the minutes after the o'clock: 5 minutes
Add the jumps. Add the hours together, then add the minutes together. If the minutes reach 60 or more, change 60 minutes into 1 hour.
Hours: 1 hour
Minutes: 40 + 5 = 45
Total: 1 hour 45 minutes

Check. Count on from the start: 2:20 + 1 hour 45 minutes = 4:05. ✓

Watch out. There are 60 minutes in an hour, not 100. 3:50 to 4:20 is 30 minutes, not 70.

Worked example 8.6.5

A train leaves at 14:35 and arrives at 17:10. How long is the journey?

Method. Count on from the start to the end on a number line: first to the next o'clock, then in whole hours, then the last minutes. Then add the jumps.

Draw a number line and count on from the start time to the end time. Counting on in easy jumps (first to the next o'clock, then whole hours, then the last minutes) is easier than taking one time away from the other.
Work out each jump. Each jump is easy to do in your head.
14:35 to 15:00: 25 minutes to the next o'clock
60 − 35 = 25 minutes
15:00 to 17:00: whole hours: 2 hours
17:00 to 17:10: the minutes after the o'clock: 10 minutes
Add the jumps. Add the hours together, then add the minutes together. If the minutes reach 60 or more, change 60 minutes into 1 hour.
Hours: 2 hours
Minutes: 25 + 10 = 35
Total: 2 hours 35 minutes

Check. Count on from the start: 14:35 + 2 hours 35 minutes = 17:10. ✓

Watch out. There are 60 minutes in an hour, not 100. 3:50 to 4:20 is 30 minutes, not 70.

Worked example 8.6.6

Priya goes to sleep at 10:30 pm and wakes up at 6:15 am. How long does she sleep for?

Method. Count on from the start to the end on a number line: first to the next o'clock, then in whole hours, then the last minutes. Then add the jumps.

Draw a number line and count on from the start time to the end time. Counting on in easy jumps (first to the next o'clock, then whole hours, then the last minutes) is easier than taking one time away from the other.
Work out each jump. Each jump is easy to do in your head.
10:30 pm to 11:00 pm: 30 minutes to the next o'clock
60 − 30 = 30 minutes
11:00 pm to 6:00 am: whole hours: 7 hours
6:00 am to 6:15 am: the minutes after the o'clock: 15 minutes
Add the jumps. Add the hours together, then add the minutes together. If the minutes reach 60 or more, change 60 minutes into 1 hour.
Hours: 7 hours
Minutes: 30 + 15 = 45
Total: 7 hours 45 minutes

Check. Count on from the start: 10:30 pm + 7 hours 45 minutes = 6:15 am. ✓

Watch out. There are 60 minutes in an hour, not 100. 3:50 to 4:20 is 30 minutes, not 70.

Worked example 8.6.7

A film starts at 2:25 pm. It lasts 1 hour 50 minutes. What time does it finish?

Method. Add the whole hours first. Then add the minutes, jumping to the next o'clock if you pass it.

Start at the start time and count on the whole hours first. Adding whole hours is easy: the minutes stay the same.
2:25 pm + 1 hour = 3:25 pm
Count on the 50 minutes. Going to the next o'clock first makes the sum easy. The minutes left are added after.
Jump to the next o'clock: 60 − 25 = 35 minutes, so 3:25 pm + 35 min = 4:00 pm.
Jump the rest: 50 − 35 = 15 minutes, so 4:00 pm + 15 min = 4:15 pm
Look at the number line. It shows all the jumps from the start to the end.
Write the end time.
4:15 pm

Check. Count back from the end: 4:15 pm − 1 hour 50 minutes = 2:25 pm. ✓

Watch out. The minutes go up to 60, then the hour changes. 2:45 + 30 minutes is 3:15, not 2:75.

Worked example 8.6.8

A bus journey starts at 15:40 and takes 2 hours 35 minutes. What time does it end? Write the time as a 24-hour time.

Method. Add the whole hours first. Then add the minutes, jumping to the next o'clock if you pass it.

Start at the start time and count on the whole hours first. Adding whole hours is easy: the minutes stay the same.
15:40 + 2 hours = 17:40
Count on the 35 minutes. Going to the next o'clock first makes the sum easy. The minutes left are added after.
Jump to the next o'clock: 60 − 40 = 20 minutes, so 17:40 + 20 min = 18:00.
Jump the rest: 35 − 20 = 15 minutes, so 18:00 + 15 min = 18:15
Look at the number line. It shows all the jumps from the start to the end.
Write the end time.
18:15

Check. Count back from the end: 18:15 − 2 hours 35 minutes = 15:40. ✓

Watch out. The minutes go up to 60, then the hour changes. 2:45 + 30 minutes is 3:15, not 2:75.

Worked example 8.6.9

A concert finishes at 5:10 pm. It lasted 2 hours 35 minutes. What time did it start?

Method. Count back from the end time: first the whole hours, then the minutes, going through the o'clock if you need to.

Start at the end time and count back the whole hours first. Taking away whole hours is easy: the minutes stay the same.
5:10 pm − 2 hours = 3:10 pm
Count back the 35 minutes. Going back to the o'clock first makes the sum easy. Then we take away the minutes that are left.
Go back to the o'clock first: 3:10 pm − 10 min = 3:00 pm.
Go back the rest: 35 − 10 = 25 minutes, so 3:00 pm − 25 min = 2:35 pm
Look at the number line. The arrows show the jumps back from the end time.
Write the start time.
2:35 pm

Check. Count on from the start: 2:35 pm + 2 hours 35 minutes = 5:10 pm. ✓

Watch out. When you count back through an o'clock the hour goes down by one. 3:10 minus 20 minutes is 2:50.

Worked example 8.6.10

Omar’s cycling trip ended at 09:05. It took 1 hour 30 minutes. What time did it start? Write the time as a 24-hour time.

Method. Count back from the end time: first the whole hours, then the minutes, going through the o'clock if you need to.

Start at the end time and count back the whole hours first. Taking away whole hours is easy: the minutes stay the same.
09:05 − 1 hour = 08:05
Count back the 30 minutes. Going back to the o'clock first makes the sum easy. Then we take away the minutes that are left.
Go back to the o'clock first: 08:05 − 5 min = 08:00.
Go back the rest: 30 − 5 = 25 minutes, so 08:00 − 25 min = 07:35
Look at the number line. The arrows show the jumps back from the end time.
Write the start time.
07:35

Check. Count on from the start: 07:35 + 1 hour 30 minutes = 09:05. ✓

Watch out. When you count back through an o'clock the hour goes down by one. 3:10 minus 20 minutes is 2:50.

Watch out

An hour is 60 minutes, not 100. From 3:50 to 5:20 is not “2 hours 30” and the minutes cannot go above 59. 3:50 to 4:00 is 10 minutes, 4:00 to 5:00 is 1 hour, 5:00 to 5:20 is 20 minutes: 1 hour 30 minutes. Also, when you count back through an o’clock, the hour goes down.

8.7

Timetables and time problems

Year 4
Read timetables, Journey times and waiting times, Solve time word problems

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Timetables and time problemsComing soon

A timetable is a table that tells us when things happen: buses, trains, TV programmes, lessons. Each row goes across and each column goes down. To find a time, find the right row and the right column, and read where they meet.

Bus timetable (24-hour times)
Stop	Bus 1	Bus 2	Bus 3	Bus 4
Library	07:45	08:15	08:45	09:30
Market	07:58	08:28	08:58	09:43
Park	08:10	08:40	09:12	09:55
Station	08:24	08:54	09:30	10:09

Each column is one bus journey. Bus 1 leaves the Library at 07:45 and gets to the Station at 08:24.

Journey time. To find how long a journey takes, find the time you leave and the time you arrive. Then count on from the first time to the second time (see section 8.6). Bus 1 from the Library to the Station: 07:45 → 08:00 is 15 minutes and 08:00 → 08:24 is 24 minutes, so 15 + 24 = 39 minutes.

Waiting time. If you arrive at a stop at a certain time, you wait for the next bus. It is the first bus that leaves at or after the time you arrive. The waiting time is the time from when you arrive to when it leaves.

Train timetable
Train	Westbridge	Midford	Northam
Train 1	9:10 am	9:42 am	10:25 am
Train 2	10:05 am	10:37 am	11:20 am
Train 3	11:40 am	12:14 pm	1:05 pm

TV guide
Time	Programme
4:00 pm	Cartoon Club
4:30 pm	Wildlife Watch
5:15 pm	News Round
5:45 pm	Bake It!
6:30 pm	Quiz Night
7:15 pm	Family Film

A train timetable (read across a row for one train) and a TV guide. A programme ends when the next one starts.

TV and school timetables. In a TV guide, each programme starts when the one before it ends. So the length of a programme is the time from its start to the start of the next programme. A school timetable gives the start and end of each lesson, break and lunch.

School day
Activity	Starts	Ends
Registration	8:50 am	9:00 am
Lesson 1	9:00 am	9:50 am
Lesson 2	9:50 am	10:40 am
Break	10:40 am	10:55 am
Lesson 3	10:55 am	11:45 am
Lesson 4	11:45 am	12:35 pm
Lunch	12:35 pm	1:30 pm
Afternoon lessons	1:30 pm	3:15 pm

A school day. Lunch starts at 12:35 pm and ends at 1:30 pm.

Key ideas

Row = across. Column = down. Find the row and the column and read where they meet.
Journey time = arrival time − leaving time. Count on through the next o’clock.
Waiting time: find the next bus after you arrive (not one that has already gone), then count on to its leaving time.
In a TV guide the length of a programme is the start of the next programme minus its own start.
Times in a timetable can be 12-hour (am and pm) or 24-hour. Check which one it is.

Worked example 8.7.1

Use the bus timetable. What time does Bus 2 leave the Park?

Bus timetable (24-hour times)
Stop	Bus 1	Bus 2	Bus 3	Bus 4
Library	07:45	08:15	08:45	09:30
Market	07:58	08:28	08:58	09:43
Park	08:10	08:40	09:12	09:55
Station	08:24	08:54	09:30	10:09

Key words. A timetable is a table that shows times. Each row goes across and each column goes down. The journey time is how long the trip takes. The waiting time is how long you wait.

Method. Find the right row and the right column. The answer is where they meet.

Find the row for Park. Each row goes across the table.
Look along the row Park.
Find the column for Bus 2. Each column goes down the table.
Look down the column Bus 2.
Read where they meet. This box holds the time we want.
08:40

Check. Look again: the box in row Park and column Bus 2 says 08:40. ✓

Watch out. Use a finger on the row and another on the column, so you do not slip to the next one.

Worked example 8.7.2

Use the bus timetable. How long does Bus 1 take to go from the Library to the Station?

Bus timetable (24-hour times)
Stop	Bus 1	Bus 2	Bus 3	Bus 4
Library	07:45	08:15	08:45	09:30
Market	07:58	08:28	08:58	09:43
Park	08:10	08:40	09:12	09:55
Station	08:24	08:54	09:30	10:09

Method. Count on from the start to the end on a number line: first to the next o'clock, then in whole hours, then the last minutes. Then add the jumps.

Find the row for Library and the column for Bus 1. This gives the time the bus leaves.
The bus leaves Library at 07:45.
Find the row for Station in the same column. This gives the time the same bus arrives.
The bus arrives at Station at 08:24.
Draw a number line and count on from the start time to the end time. Counting on in easy jumps (first to the next o'clock, then whole hours, then the last minutes) is easier than taking one time away from the other.
Work out each jump. Each jump is easy to do in your head.
07:45 to 08:00: 15 minutes to the next o'clock
60 − 45 = 15 minutes
08:00 to 08:24: the minutes after the o'clock: 24 minutes
Add the jumps. Add the hours together, then add the minutes together. If the minutes reach 60 or more, change 60 minutes into 1 hour.
Minutes: 15 + 24 = 39
Total: 39 minutes

Check. Count on from the start: 07:45 + 39 minutes = 08:24. ✓

Watch out. There are 60 minutes in an hour, not 100. 3:50 to 4:20 is 30 minutes, not 70.

Worked example 8.7.3

Amira gets to the Market bus stop at 08:35. She catches the next bus. How long does she wait?

Bus timetable (24-hour times)
Stop	Bus 1	Bus 2	Bus 3	Bus 4
Library	07:45	08:15	08:45	09:30
Market	07:58	08:28	08:58	09:43
Park	08:10	08:40	09:12	09:55
Station	08:24	08:54	09:30	10:09

Method. Count on from the start to the end on a number line: first to the next o'clock, then in whole hours, then the last minutes. Then add the jumps.

Look along the row for Market. We want the first bus that leaves at or after the time you arrive. A bus that has already gone is no use.
07:58, 08:28, 08:58, 09:43
Choose the first bus that is not too early. You arrive at 08:35.
The next bus is Bus 3 at 08:58.
Draw a number line and count on from the start time to the end time. Counting on in easy jumps (first to the next o'clock, then whole hours, then the last minutes) is easier than taking one time away from the other.
Work out each jump. Each jump is easy to do in your head.
08:35 to 08:58: 58 − 35 = 23 minutes
Add the jumps. Add the hours together, then add the minutes together. If the minutes reach 60 or more, change 60 minutes into 1 hour.
Minutes: 23
Total: 23 minutes

Check. Count on from the start: 08:35 + 23 minutes = 08:58. ✓

Watch out. A bus that left before you arrived does not count, even if it is the closest time.

Worked example 8.7.4

Use the train timetable. How long does Train 3 take to go from Westbridge to Northam?

Train timetable
Train	Westbridge	Midford	Northam
Train 1	9:10 am	9:42 am	10:25 am
Train 2	10:05 am	10:37 am	11:20 am
Train 3	11:40 am	12:14 pm	1:05 pm

Method. Count on from the start to the end on a number line: first to the next o'clock, then in whole hours, then the last minutes. Then add the jumps.

Find the row for Westbridge and the row for Northam in the Train 3 line. The train leaves Westbridge and arrives at Northam.
Leaves Westbridge: 11:40 am. Arrives at Northam: 1:05 pm.
Draw a number line and count on from the start time to the end time. Counting on in easy jumps (first to the next o'clock, then whole hours, then the last minutes) is easier than taking one time away from the other.
Work out each jump. Each jump is easy to do in your head.
11:40 am to 12:00 pm: 20 minutes to the next o'clock
60 − 40 = 20 minutes
12:00 pm to 1:00 pm: whole hours: 1 hour
1:00 pm to 1:05 pm: the minutes after the o'clock: 5 minutes
Add the jumps. Add the hours together, then add the minutes together. If the minutes reach 60 or more, change 60 minutes into 1 hour.
Hours: 1 hour
Minutes: 20 + 5 = 25
Total: 1 hour 25 minutes

Check. Count on from the start: 11:40 am + 1 hour 25 minutes = 1:05 pm. ✓

Watch out. There are 60 minutes in an hour, not 100. 3:50 to 4:20 is 30 minutes, not 70.

Worked example 8.7.5

How long is Wildlife Watch?

TV guide
Time	Programme
4:00 pm	Cartoon Club
4:30 pm	Wildlife Watch
5:15 pm	News Round
5:45 pm	Bake It!
6:30 pm	Quiz Night
7:15 pm	Family Film

Method. Count on from the start to the end on a number line: first to the next o'clock, then in whole hours, then the last minutes. Then add the jumps.

Find the programme in the guide. We need the start of Wildlife Watch and the start of the next programme.
Wildlife Watch starts at 4:30 pm. The next programme, News Round, starts at 5:15 pm.
Draw a number line and count on from the start time to the end time. Counting on in easy jumps (first to the next o'clock, then whole hours, then the last minutes) is easier than taking one time away from the other.
Work out each jump. Each jump is easy to do in your head.
4:30 pm to 5:00 pm: 30 minutes to the next o'clock
60 − 30 = 30 minutes
5:00 pm to 5:15 pm: the minutes after the o'clock: 15 minutes
Add the jumps. Add the hours together, then add the minutes together. If the minutes reach 60 or more, change 60 minutes into 1 hour.
Minutes: 30 + 15 = 45
Total: 45 minutes

Check. Count on from the start: 4:30 pm + 45 minutes = 5:15 pm. ✓

Watch out. There are 60 minutes in an hour, not 100. 3:50 to 4:20 is 30 minutes, not 70.

Worked example 8.7.6

How long is lunch?

School day
Activity	Starts	Ends
Registration	8:50 am	9:00 am
Lesson 1	9:00 am	9:50 am
Lesson 2	9:50 am	10:40 am
Break	10:40 am	10:55 am
Lesson 3	10:55 am	11:45 am
Lesson 4	11:45 am	12:35 pm
Lunch	12:35 pm	1:30 pm
Afternoon lessons	1:30 pm	3:15 pm

Method. Count on from the start to the end on a number line: first to the next o'clock, then in whole hours, then the last minutes. Then add the jumps.

Find lunch in the school timetable. We need when lunch starts and when it ends.
Lunch starts at 12:35 pm and ends at 1:30 pm.
Draw a number line and count on from the start time to the end time. Counting on in easy jumps (first to the next o'clock, then whole hours, then the last minutes) is easier than taking one time away from the other.
Work out each jump. Each jump is easy to do in your head.
12:35 pm to 1:00 pm: 25 minutes to the next o'clock
60 − 35 = 25 minutes
1:00 pm to 1:30 pm: the minutes after the o'clock: 30 minutes
Add the jumps. Add the hours together, then add the minutes together. If the minutes reach 60 or more, change 60 minutes into 1 hour.
Minutes: 25 + 30 = 55
Total: 55 minutes

Check. Count on from the start: 12:35 pm + 55 minutes = 1:30 pm. ✓

Watch out. There are 60 minutes in an hour, not 100. 3:50 to 4:20 is 30 minutes, not 70.

Worked example 8.7.7

Zainab must be at the Station by 09:00. What is the latest bus she can catch from the Library?

Bus timetable (24-hour times)
Stop	Bus 1	Bus 2	Bus 3	Bus 4
Library	07:45	08:15	08:45	09:30
Market	07:58	08:28	08:58	09:43
Park	08:10	08:40	09:12	09:55
Station	08:24	08:54	09:30	10:09

Key words. A timetable is a table that shows times. Each row goes across and each column goes down. The journey time is how long the trip takes. The waiting time is how long you wait.

Method. Find which buses arrive at the Station before 09:00. Then pick the one that leaves the Library the latest.

Look along the Station row. We want the arrival times that are before 09:00.
Bus 1: 08:24 (before 09:00). Bus 2: 08:54 (before 09:00). Bus 3: 09:30 (too late). Bus 4: 10:09 (too late).
Pick the latest bus that is still on time. Later means Zainab can stay at home longer.
Bus 2 arrives at 08:54.
Find when Bus 2 leaves the Library. Look in the Library row, Bus 2 column.
Bus 2 leaves the Library at 08:15.

Check. Bus 2 arrives at 08:54, which is 6 minutes before 09:00. ✓

Watch out. A bus that arrives at exactly or after 09:00 is too late.

Watch out

Read the right bus, and the next one. If you arrive at 08:35 and a bus left at 08:28, you cannot catch it: you must wait for the next one at 08:58. And check if the times are 12-hour or 24-hour before you work out how long something takes.

Exercise 8G Timetables

Non-calculator

FUse the bus timetable.

Bus timetable (24-hour times)
Stop	Bus 1	Bus 2	Bus 3	Bus 4
Library	07:45	08:15	08:45	09:30
Market	07:58	08:28	08:58	09:43
Park	08:10	08:40	09:12	09:55
Station	08:24	08:54	09:30	10:09

(a)What time does Bus 3 leave the Park?

(b)What time does Bus 1 arrive at the Station?

(c)Which bus leaves the Market at 08:28?

(d)What time does Bus 4 leave the Library?

Done

FUse the bus timetable. How long does each bus take to go from the Library to the Park?

Bus timetable (24-hour times)
Stop	Bus 1	Bus 2	Bus 3	Bus 4
Library	07:45	08:15	08:45	09:30
Market	07:58	08:28	08:58	09:43
Park	08:10	08:40	09:12	09:55
Station	08:24	08:54	09:30	10:09

(a)Bus 1

(b)Bus 2

(c)Bus 3

(d)Bus 4

Done

FUse the bus timetable. Each person arrives at a bus stop and catches the next bus. How long does each person wait?

Bus timetable (24-hour times)
Stop	Bus 1	Bus 2	Bus 3	Bus 4
Library	07:45	08:15	08:45	09:30
Market	07:58	08:28	08:58	09:43
Park	08:10	08:40	09:12	09:55
Station	08:24	08:54	09:30	10:09

(a)Jack arrives at the Library stop at 08:00.

(b)Mei arrives at the Market stop at 08:50.

(c)Omar arrives at the Park stop at 09:00.

Done

FUse the train timetable. How long does each train take to go from Westbridge to Northam?

Train timetable
Train	Westbridge	Midford	Northam
Train 1	9:10 am	9:42 am	10:25 am
Train 2	10:05 am	10:37 am	11:20 am
Train 3	11:40 am	12:14 pm	1:05 pm

(a)Train 1

(b)Train 2

(c)Train 3

Done

FUse the TV guide. How long is each programme?

TV guide
Time	Programme
4:00 pm	Cartoon Club
4:30 pm	Wildlife Watch
5:15 pm	News Round
5:45 pm	Bake It!
6:30 pm	Quiz Night
7:15 pm	Family Film

(a)Cartoon Club

(b)News Round

(c)Bake It!

(d)Quiz Night

Done

PSUse the TV guide. Ella starts watching at 4:15 pm and watches until Bake It! ends. How long does she watch for?

TV guide
Time	Programme
4:00 pm	Cartoon Club
4:30 pm	Wildlife Watch
5:15 pm	News Round
5:45 pm	Bake It!
6:30 pm	Quiz Night
7:15 pm	Family Film

Done

FUse the school timetable.

School day
Activity	Starts	Ends
Registration	8:50 am	9:00 am
Lesson 1	9:00 am	9:50 am
Lesson 2	9:50 am	10:40 am
Break	10:40 am	10:55 am
Lesson 3	10:55 am	11:45 am
Lesson 4	11:45 am	12:35 pm
Lunch	12:35 pm	1:30 pm
Afternoon lessons	1:30 pm	3:15 pm

(a)How long is the break?

(b)How long is Lesson 3?

(c)How long is it from the start of Lesson 1 to the end of Lesson 2?

Done

PSUse the school timetable. How long is the school day, from registration to the end of the afternoon?

School day
Activity	Starts	Ends
Registration	8:50 am	9:00 am
Lesson 1	9:00 am	9:50 am
Lesson 2	9:50 am	10:40 am
Break	10:40 am	10:55 am
Lesson 3	10:55 am	11:45 am
Lesson 4	11:45 am	12:35 pm
Lunch	12:35 pm	1:30 pm
Afternoon lessons	1:30 pm	3:15 pm

Done

PSUse the bus timetable. Leo catches Bus 2 from the Library to the Park. He then walks to school for 10 minutes. School starts at 09:00. Is he on time? Explain.

Bus timetable (24-hour times)
Stop	Bus 1	Bus 2	Bus 3	Bus 4
Library	07:45	08:15	08:45	09:30
Market	07:58	08:28	08:58	09:43
Park	08:10	08:40	09:12	09:55
Station	08:24	08:54	09:30	10:09

Done

PSUse the bus timetable. Aisha needs to be at the Station by 09:20. Which bus should she catch from the Library, and how many minutes early will she arrive?

Bus timetable (24-hour times)
Stop	Bus 1	Bus 2	Bus 3	Bus 4
Library	07:45	08:15	08:45	09:30
Market	07:58	08:28	08:58	09:43
Park	08:10	08:40	09:12	09:55
Station	08:24	08:54	09:30	10:09

Done

PSFilm A starts at 1:45 pm and lasts 1 hour 50 minutes. Film B starts at 2:10 pm and lasts 1 hour 35 minutes.

(a)What time does Film A finish?

(b)What time does Film B finish?

(c)Which film finishes first?

Done

RNoah says, “Amira arrives at the Market stop at 08:35, so she can catch the 08:28 bus.” What mistake has Noah made? Which bus can she catch?

Bus timetable (24-hour times)
Stop	Bus 1	Bus 2	Bus 3	Bus 4
Library	07:45	08:15	08:45	09:30
Market	07:58	08:28	08:58	09:43
Park	08:10	08:40	09:12	09:55
Station	08:24	08:54	09:30	10:09

Done

RPriya says, “The 08:15 bus is quicker than the 08:45 bus from the Library to the Station.” Do you agree? Show how you know.

Bus timetable (24-hour times)
Stop	Bus 1	Bus 2	Bus 3	Bus 4
Library	07:45	08:15	08:45	09:30
Market	07:58	08:28	08:58	09:43
Park	08:10	08:40	09:12	09:55
Station	08:24	08:54	09:30	10:09

Done

RChallenge. Ella walks for 15 minutes to the Library bus stop and catches Bus 2 just in time. The bus takes her to the Station. Then she walks for 12 minutes to school.

Bus timetable (24-hour times)
Stop	Bus 1	Bus 2	Bus 3	Bus 4
Library	07:45	08:15	08:45	09:30
Market	07:58	08:28	08:58	09:43
Park	08:10	08:40	09:12	09:55
Station	08:24	08:54	09:30	10:09

(a)What time does she leave home?

(b)What time does she arrive at school?

Done

Chapter summary

Skill	Method
Analogue clock	Short, thick hand = hours. Long, thin hand = minutes. Each number is 5 minutes. Each small mark is 1 minute.
Past and to	Right-hand side of the clock: minutes past. Left-hand side: take the minutes from 60 and say to the next hour. 7:47 = 13 minutes to 8.
Special times	o’clock (12), quarter past (3), half past (6), quarter to (9).
The hour hand	Use the number it has passed. At 5:55 it is nearly at the 6, but the hour is 5.
Roman numerals	I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII = 1 to 12. Some clocks use IIII for 4.
12-hour and am/pm	am: midnight to noon. pm: noon to midnight. 12:00 pm is noon. 12:00 am is midnight.
24-hour clock	am keeps the hour (8:05 am = 08:05). pm: add 12 (4:25 pm = 16:25). 12:30 pm = 12:30. 12:30 am = 00:30.
Changing units	60 s = 1 min. 60 min = 1 h. 24 h = 1 day. 7 days = 1 week. 12 months = 1 year. Big to small: multiply. Small to big: divide.
Mixed units	2 h 15 min = 2 × 60 + 15 = 135 min. 135 min = 2 h 15 min (135 ÷ 60 = 2 remainder 15).
Fractions of an hour	Half an hour = 30 min. A quarter = 15 min. 1½ hours = 90 min (not 1 h 50 min).
Days in a month	Knuckles 31, dips 30. February 28 (29 in a leap year). A leap year has 366 days.
Counting on	To find a duration, jump to the next o’clock, then whole hours, then the last minutes. Then add the jumps.
End and start times	End time: add the hours, then the minutes through the next o’clock. Start time: count back.
Timetables	Find the right row and column. Journey time: count on from leaving to arriving. Waiting time: find the next one that has not gone.

Can you…?

I can read an analogue clock to the nearest minute, using past and to.
I can read clocks with Roman numerals and with only a few numbers.
I can put the hour hand in the right place, and read a time when the hour hand is between numbers.
I can write times as digital times with am and pm.
I can change between the 12-hour and the 24-hour clock.
I can change between seconds, minutes, hours, days, weeks, months and years.
I know how many days are in each month and what a leap year is.
I can work out how long something takes by counting on.
I can find a start time or an end time.
I can read a timetable and find journey times and waiting times.
I know that there are 60 minutes in an hour, not 100.

Key terms

Analogue clock: A clock with a round face and hands.
Digital clock: A clock that shows the time in numbers, like 4:35.
Hour hand: The short, thick hand. It shows the hour.
Minute hand: The long, thin hand. It shows the minutes.
Past: After the hour. 20 minutes past 3 is 3:20.
To: Before the next hour. 20 minutes to 4 is 3:40.
Quarter past / quarter to: 15 minutes after the hour / 15 minutes before the next hour.
am: The time from midnight to noon (the morning).
pm: The time from noon to midnight (afternoon and evening).
Noon: 12 o’clock in the middle of the day (12:00 pm).
Midnight: 12 o’clock at night (12:00 am, or 00:00 on the 24-hour clock).
24-hour clock: A clock that counts the hours from 00 to 23 and has no am or pm.
Roman numerals: Numbers written with letters: I, V, X ... Some clocks use them.
Second: A very short unit of time. 60 seconds = 1 minute.
Minute: A unit of time. 60 minutes = 1 hour.
Hour: A unit of time. 24 hours = 1 day.
Leap year: A year with 366 days. February has 29 days. It comes every 4 years.
Calendar: A table that shows the days and dates of the months.
Duration: How long something takes.
Timetable: A table that shows the times of buses, trains, TV programmes or lessons.
Journey time: How long a trip takes, from leaving to arriving.
Convert: To change from one unit to another.

Exercise 8Z Check-up (non-calculator)

Non-calculator

What time does the clock show? Write the time in words.

Done

This clock has Roman numerals. Write the time as a digital time.

Done

Write 5:40 pm as a 24-hour time.

Done

Write 21:15 as a 12-hour time with am or pm.

Done

How many minutes are there in 7 hours?

Done

Change 180 seconds into minutes.

Done

How many days are there in November?

Done

A lesson starts at 4:35 pm and ends at 5:20 pm. How long is the lesson?

Done

A show starts at 10:40 am and lasts 1 hour 35 minutes. What time does it finish?

Done

Use the bus timetable. Jack gets to the Park stop at 08:20. He catches the next bus. How long does he wait?

Bus timetable (24-hour times)
Stop	Bus 1	Bus 2	Bus 3	Bus 4
Library	07:45	08:15	08:45	09:30
Market	07:58	08:28	08:58	09:43
Park	08:10	08:40	09:12	09:55
Station	08:24	08:54	09:30	10:09

Done

Total 18 marks. Allow about 18 minutes.

Exercise 8X SATs-style questions

Non-calculator

FWhat time does the clock show? Write the time as a digital time.[1 mark]

Done

FWhich clock shows 3:40? Write the letter.[1 mark]

ABCD

Done

FA film starts at 6:45 pm. Write this time as a 24-hour time.[1 mark]

Done

FHow many minutes are there in 4 hours?[1 mark]

Done

RWhich two of these are the same as 2 hours 30 minutes? Tick two boxes.
[ ] A 150 minutes [ ] B 230 minutes [ ] C 2.5 hours [ ] D 2 hours 50 minutes[2 marks]

Done

RIs 2036 a leap year? Explain how you know.[2 marks]

Done

PSA TV programme starts at 4:50 pm and ends at 5:35 pm. How long is the programme? Show your working.[2 marks]

Done

PSLeo’s night ferry leaves at 10:35 pm. The journey takes 8 hours 50 minutes. What time does the ferry arrive? Remember to write am or pm. Show your working.[3 marks]

Done

PSUse the bus timetable. Jack arrives at the Market stop at 08:20. He catches the next bus. (a) How long does he wait? (b) What time does the bus get to the Station?[3 marks]

Bus timetable (24-hour times)
Stop	Bus 1	Bus 2	Bus 3	Bus 4
Library	07:45	08:15	08:45	09:30
Market	07:58	08:28	08:58	09:43
Park	08:10	08:40	09:12	09:55
Station	08:24	08:54	09:30	10:09

Done

RAmira says, “2¼ hours is 2 hours 25 minutes.” Is she correct? Show how you know.[2 marks]

Done

← Chapter 7: Length, mass, capacity, perimeter and area Chapter 9: Shapes, angles and symmetry →

Year 4 Telling the Time and the 24-Hour Clock: worked examples and questions with answers

By the end of this chapter you will be able to

You should already know

Where this leads

Exercise P Do you remember?

Telling the time: o'clock, half past, quarter past and quarter to

Key ideas

Watch out

Exercise 8A Telling the time on an analogue clock

Reading to the nearest minute, and clocks with Roman numerals

Key ideas

Watch out

Exercise 8B Reading to the nearest minute

Digital time: am, pm and the 24-hour clock

Key ideas

Watch out

Exercise 8C Digital time, am, pm and the 24-hour clock

Units of time: seconds, minutes, hours, days and weeks

Key ideas

Watch out

Exercise 8D Changing units of time

Months, years and the calendar

Key ideas

Watch out

Exercise 8E Months, years and the calendar

How long does it take? Durations, start times and end times

Key ideas

Watch out

Exercise 8F Durations, start times and end times

Timetables and time problems

Key ideas

Watch out

Exercise 8G Timetables

Chapter summary

Can you…?

Key terms

Exercise 8Z Check-up (non-calculator)

Exercise 8X SATs-style questions