A film starts at 19:40 and ends at 22:15. How long is the film?

Some people try to just subtract the digits and get muddled when the minutes seem to go backwards. Before we work it out together, have a think: why can't we simply subtract 19:40 from 22:15 the way we subtract ordinary numbers? It is completely fine not to know yet, we will figure this out together in a moment.

19:40 to 22:15

Watch the two clocks and the hops drawn beneath them. We count up in three hops: 20 minutes to reach 20:00, then 2 whole hours to 22:00, then 15 minutes on to 22:15. Add the hops: 20 min + 2 h + 15 min = 2 h 35 min.

08:55 to 13:10

This time the hops are: 5 minutes to 09:00, then 4 whole hours to 13:00, then 10 minutes on to 13:10. What total do the hops give us?

22:30 to 06:15 next morning

This finish time is the next morning, so the hops land on midnight first. Watch how they stop at 00:00, then carry on into the new day. The duration keeps adding forward right across midnight.

09:00 Monday to 14:00 Wednesday

This journey is longer than a single day, so the clock face cannot hold it all. We count it on paper instead. Monday to Tuesday is one whole day, which is 24 hours. Tuesday to Wednesday is another whole day, another 24 hours. That is 24 + 24 = 48 hours so far, landing us at 09:00 on Wednesday. From 09:00 to 14:00 on Wednesday is 5 more hours. So the whole span is 48 + 5 = 53 hours.

14:20 to 17:05, setting the arrival

Now watch the other way round. A train leaves at 14:20 and the journey takes 2 h 45 min. We count that duration up onto the clock to find the arrival: 40 min to 15:00, then 2 hours to 17:00, then 5 minutes on to 17:05. So the train arrives at 17:05. Same hops, but this time we add the duration to a start time to land on the finish.

Today we work through a fresh journey together: a train leaves at 14:20 and the journey takes 2 h 45 min. Before we touch the clock, let's predict each hop aloud: first the jump to the next whole hour, then the whole hours, then the last minutes. Then a pupil sets the arrival on the clock and we press Check to see if the hands are right and the hops match what we predicted.

Today we work through these journeys: each one gives a start time and how long the journey takes, and you set the arrival clock by counting the duration up onto the hands, just like the train example we set together. The elapsed readout will confirm the duration once you've set the hands.

What we learned today

• To find elapsed time, count up in hops: to the next whole hour, then the whole hours, then the last minutes.
• You can also count a duration up from a start time to set the arrival on the clock.
• When a finish time is the next day, count up to midnight (00:00) first, then carry on into the new day.
• For spans longer than a day, count each whole day as 24 hours and add the extra hours on paper, like 09:00 Monday to 14:00 Wednesday = 53 hours.

Coming up

Next we read real timetables and schedules, and we start to think about time zones, what time it is in New York or Sydney when it is afternoon here in Ireland.