Year 4: Timetables and time problems

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.

1. Find the row for Park. Each row goes across the table.
   Look along the row Park.
2. Find the column for Bus 3. Each column goes down the table.
   Look down the column Bus 3.
3. Read where they meet. This box holds the time we want.
   09:12

Check. Look again: the box in row Park and column Bus 3 says 09:12. ✓

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

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.

1. Find the row for Station. Each row goes across the table.
   Look along the row Station.
2. Find the column for Bus 1. Each column goes down the table.
   Look down the column Bus 1.
3. Read where they meet. This box holds the time we want.
   08:24

Check. Look again: the box in row Station and column Bus 1 says 08:24. ✓

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

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. Look along the Market row to find 08:28. Then look at the top of that column to read which bus it is.

1. Find the Market row. Each row goes across the table.
   Market: 07:58, 08:28, 08:58, 09:43
2. Find 08:28 in the row. It is the second time.
   08:28 is in the second column.
3. Read the heading of the column. The heading at the top tells us which bus it is.
   The heading is Bus 2.

Check. Bus 2 is in the second column, and so is 08:15 at the Library. ✓

Watch out. Read the heading of the column, not the number of the time.

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.

1. Find the row for Library. Each row goes across the table.
   Look along the row Library.
2. Find the column for Bus 4. Each column goes down the table.
   Look down the column Bus 4.
3. Read where they meet. This box holds the time we want.
   09:30

Check. Look again: the box in row Library and column Bus 4 says 09:30. ✓

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

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.

1. 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.
2. Find the row for Park in the same column. This gives the time the same bus arrives.
   The bus arrives at Park at 08:10.
3. 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.
4. 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 08:10: the minutes after the o'clock: 10 minutes
5. 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 + 10 = 25
   Total: 25 minutes

Check. Count on from the start: 07:45 + 25 minutes = 08:10. ✓

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

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.

1. Find the row for Library and the column for Bus 2. This gives the time the bus leaves.
   The bus leaves Library at 08:15.
2. Find the row for Park in the same column. This gives the time the same bus arrives.
   The bus arrives at Park at 08:40.
3. 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.
4. Work out each jump. Each jump is easy to do in your head.
   08:15 to 08:40: 40 − 15 = 25 minutes
5. 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
   Total: 25 minutes

Check. Count on from the start: 08:15 + 25 minutes = 08:40. ✓

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

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.

1. Find the row for Library and the column for Bus 3. This gives the time the bus leaves.
   The bus leaves Library at 08:45.
2. Find the row for Park in the same column. This gives the time the same bus arrives.
   The bus arrives at Park at 09:12.
3. 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.
4. Work out each jump. Each jump is easy to do in your head.
   08:45 to 09:00: 15 minutes to the next o'clock
   60 − 45 = 15 minutes
   09:00 to 09:12: the minutes after the o'clock: 12 minutes
5. 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 + 12 = 27
   Total: 27 minutes

Check. Count on from the start: 08:45 + 27 minutes = 09:12. ✓

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

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.

1. Find the row for Library and the column for Bus 4. This gives the time the bus leaves.
   The bus leaves Library at 09:30.
2. Find the row for Park in the same column. This gives the time the same bus arrives.
   The bus arrives at Park at 09:55.
3. 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.
4. Work out each jump. Each jump is easy to do in your head.
   09:30 to 09:55: 55 − 30 = 25 minutes
5. 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
   Total: 25 minutes

Check. Count on from the start: 09:30 + 25 minutes = 09:55. ✓

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

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.

1. Look along the row for Library. We want the first bus that leaves at or after the time you arrive. A bus that has already gone is no use.
   07:45, 08:15, 08:45, 09:30
2. Choose the first bus that is not too early. You arrive at 08:00.
   The next bus is Bus 2 at 08:15.
3. 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.
4. Work out each jump. Each jump is easy to do in your head.
   08:00 to 08:15: the minutes after the o'clock: 15 minutes
5. 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
   Total: 15 minutes

Check. Count on from the start: 08:00 + 15 minutes = 08:15. ✓

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

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.

1. 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
2. Choose the first bus that is not too early. You arrive at 08:50.
   The next bus is Bus 3 at 08:58.
3. 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.
4. Work out each jump. Each jump is easy to do in your head.
   08:50 to 08:58: 58 − 50 = 8 minutes
5. 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: 8
   Total: 8 minutes

Check. Count on from the start: 08:50 + 8 minutes = 08:58. ✓

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

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.

1. Look along the row for Park. We want the first bus that leaves at or after the time you arrive. A bus that has already gone is no use.
   08:10, 08:40, 09:12, 09:55
2. Choose the first bus that is not too early. You arrive at 09:00.
   The next bus is Bus 3 at 09:12.
3. 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.
4. Work out each jump. Each jump is easy to do in your head.
   09:00 to 09:12: the minutes after the o'clock: 12 minutes
5. 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: 12
   Total: 12 minutes

Check. Count on from the start: 09:00 + 12 minutes = 09:12. ✓

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

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.

1. Read the times for Train 1. We need when it leaves Westbridge and when it arrives at Northam.
   Leaves: 9:10 am. Arrives: 10:25 am.
2. 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.
3. Work out each jump. Each jump is easy to do in your head.
   9:10 am to 10:00 am: 50 minutes to the next o'clock
   60 − 10 = 50 minutes
   10:00 am to 10:25 am: the minutes after the o'clock: 25 minutes
4. 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: 50 + 25 = 75
   75 minutes = 1 hour 15 minutes
   Total: 1 hour 15 minutes

Check. Count on from the start: 9:10 am + 1 hour 15 minutes = 10:25 am. ✓

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

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.

1. Read the times for Train 2. We need when it leaves Westbridge and when it arrives at Northam.
   Leaves: 10:05 am. Arrives: 11:20 am.
2. 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.
3. Work out each jump. Each jump is easy to do in your head.
   10:05 am to 11:00 am: 55 minutes to the next o'clock
   60 − 5 = 55 minutes
   11:00 am to 11:20 am: the minutes after the o'clock: 20 minutes
4. 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: 55 + 20 = 75
   75 minutes = 1 hour 15 minutes
   Total: 1 hour 15 minutes

Check. Count on from the start: 10:05 am + 1 hour 15 minutes = 11:20 am. ✓

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

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.

1. Read the times for Train 3. We need when it leaves Westbridge and when it arrives at Northam.
   Leaves: 11:40 am. Arrives: 1:05 pm.
2. 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.
3. 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
4. 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.

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.

1. Find Cartoon Club in the guide. Its length is the time from its start to the start of the next programme.
   Cartoon Club starts at 4:00 pm. The next programme starts at 4:30 pm.
2. 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.
3. Work out each jump. Each jump is easy to do in your head.
   4:00 pm to 4:30 pm: the minutes after the o'clock: 30 minutes
4. 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
   Total: 30 minutes

Check. Count on from the start: 4:00 pm + 30 minutes = 4:30 pm. ✓

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

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.

1. Find News Round in the guide. Its length is the time from its start to the start of the next programme.
   News Round starts at 5:15 pm. The next programme starts at 5:45 pm.
2. 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.
3. Work out each jump. Each jump is easy to do in your head.
   5:15 pm to 5:45 pm: 45 − 15 = 30 minutes
4. 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
   Total: 30 minutes

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

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

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.

1. Find Bake It! in the guide. Its length is the time from its start to the start of the next programme.
   Bake It! starts at 5:45 pm. The next programme starts at 6:30 pm.
2. 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.
3. Work out each jump. Each jump is easy to do in your head.
   5:45 pm to 6:00 pm: 15 minutes to the next o'clock
   60 − 45 = 15 minutes
   6:00 pm to 6:30 pm: the minutes after the o'clock: 30 minutes
4. 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 + 30 = 45
   Total: 45 minutes

Check. Count on from the start: 5:45 pm + 45 minutes = 6:30 pm. ✓

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

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.

1. Find Quiz Night in the guide. Its length is the time from its start to the start of the next programme.
   Quiz Night starts at 6:30 pm. The next programme starts at 7:15 pm.
2. 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.
3. Work out each jump. Each jump is easy to do in your head.
   6:30 pm to 7:00 pm: 30 minutes to the next o'clock
   60 − 30 = 30 minutes
   7:00 pm to 7:15 pm: the minutes after the o'clock: 15 minutes
4. 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: 6:30 pm + 45 minutes = 7:15 pm. ✓

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

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.

1. Find Break in the timetable. We need when it starts and when it ends.
   It starts at 10:40 am and ends at 10:55 am.
2. 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.
3. Work out each jump. Each jump is easy to do in your head.
   10:40 am to 10:55 am: 55 − 40 = 15 minutes
4. 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
   Total: 15 minutes

Check. Count on from the start: 10:40 am + 15 minutes = 10:55 am. ✓

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

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.

1. Find Lesson 3 in the timetable. We need when it starts and when it ends.
   It starts at 10:55 am and ends at 11:45 am.
2. 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.
3. Work out each jump. Each jump is easy to do in your head.
   10:55 am to 11:00 am: 5 minutes to the next o'clock
   60 − 55 = 5 minutes
   11:00 am to 11:45 am: the minutes after the o'clock: 45 minutes
4. 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: 5 + 45 = 50
   Total: 50 minutes

Check. Count on from the start: 10:55 am + 50 minutes = 11:45 am. ✓

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

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.

1. Find when Lesson 1 starts and when Lesson 2 ends. The two lessons run one after the other.
   Lesson 1 starts at 9:00 am. Lesson 2 ends at 10:40 am.
2. 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.
3. Work out each jump. Each jump is easy to do in your head.
   9:00 am to 10:00 am: whole hours: 1 hour
   10:00 am to 10:40 am: the minutes after the o'clock: 40 minutes
4. 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
   Total: 1 hour 40 minutes

Check. Count on from the start: 9:00 am + 1 hour 40 minutes = 10:40 am. ✓

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

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

1. Start at the start time and count on the whole hours first. Adding whole hours is easy: the minutes stay the same.
   1:45 pm + 1 hour = 2:45 pm
2. 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 − 45 = 15 minutes, so 2:45 pm + 15 min = 3:00 pm.
   Jump the rest: 50 − 15 = 35 minutes, so 3:00 pm + 35 min = 3:35 pm
3. Look at the number line. It shows all the jumps from the start to the end.
4. Write the end time.
   3:35 pm

Check. Count back from the end: 3:35 pm − 1 hour 50 minutes = 1:45 pm. ✓

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

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

1. Start at the start time and count on the whole hours first. Adding whole hours is easy: the minutes stay the same.
   2:10 pm + 1 hour = 3:10 pm
2. Count on the 35 minutes. The minutes fit inside the hour, so we can add them in one jump.
   3:10 pm + 35 minutes = 3:45 pm
3. Look at the number line. It shows all the jumps from the start to the end.
4. Write the end time.
   3:45 pm

Check. Count back from the end: 3:45 pm − 1 hour 35 minutes = 2:10 pm. ✓

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

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. Compare the two finishing times. The earlier time is the film that finishes first.

1. Write both finishing times. We found them in parts (a) and (b).
   Film A: 3:35 pm. Film B: 3:45 pm.
2. Compare. 3:35 pm is earlier than 3:45 pm.
   Film A finishes first.

Check. 3:35 pm + 10 minutes = 3:45 pm. ✓

Watch out. A film that starts later can still finish earlier if it is shorter. Always work out the end times.

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

1. Start at the end time and count back the whole hours first. There are no whole hours to take away.
   08:15
2. Count back the 15 minutes. The minutes fit inside the hour, so we can take them away in one jump.
   08:15 − 15 minutes = 08:00
3. Look at the number line. The arrows show the jumps back from the end time.
4. Write the start time.
   08:00

Check. Count on from the start: 08:00 + 15 minutes = 08:15. ✓

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

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

1. Start at the start time and count on the whole hours first. There are no whole hours to add.
   08:54
2. Count on the 12 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 − 54 = 6 minutes, so 08:54 + 6 min = 09:00.
   Jump the rest: 12 − 6 = 6 minutes, so 09:00 + 6 min = 09:06
3. Look at the number line. It shows all the jumps from the start to the end.
4. Write the end time.
   09:06

Check. Count back from the end: 09:06 − 12 minutes = 08:54. ✓

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