Why it is harder than it looks
Time runs in sixties, not tens, so 1:15 plus 50 minutes is not 1:65. It also crosses the hour, crosses midday, and sometimes crosses midnight, and each crossing is a place where a child who is subtracting digit by digit goes wrong. Add the fact that the same moment can be written 2:45, quarter to three, or 14:45, and there is a lot to hold.
Before starting elapsed time, a child needs to tell the time to five minutes confidently and to count on in fives and tens. If either is shaky, fix that first; elapsed time will not survive on top of uncertain clock reading.
The number line method
Draw a plain line. Write the start time at the left and the end time at the right. Now hop from the start to the end in friendly jumps, writing each jump above the line, and add up the jumps at the end. The trick is to choose jumps that land on tidy times: first hop to the next o'clock, then hop whole hours, then hop the remaining minutes.
Worked example, 10:45 to 1:20. Hop 15 minutes to 11:00. Hop 2 hours to 1:00. Hop 20 minutes to 1:20. Total: 2 hours and 35 minutes. No borrowing, no base 60 arithmetic, and every step is a number a child can check on a clock.
Worked example, 9:20 to 11:05. Hop 40 minutes to 10:00, hop 1 hour to 11:00, hop 5 minutes to 11:05. Total: 1 hour and 45 minutes.
Worked example crossing midday, 11:30 to 2:15. Hop 30 minutes to 12:00, hop 2 hours to 2:00, hop 15 minutes to 2:15. Total: 2 hours and 45 minutes. The midday crossing is invisible with this method, which is the point.
A teaching order
- Whole hours only: 2:00 to 5:00. Children count hours on the clock face.
- Within one hour: 3:10 to 3:45. Count on in fives around the face.
- Crossing one hour, tidy start: 4:00 to 5:20, then 4:30 to 5:20.
- Crossing one hour, untidy both ends: 10:45 to 1:20, using the number line.
- Crossing midday and midnight, and 24-hour times such as 21:40 to 06:15.
- Backwards problems: it finished at 3:15 and lasted 50 minutes, when did it start? Hop the same way, in the other direction.
- Word problems with timetables, which is where elapsed time actually appears in life and in tests.
The three mistakes to expect
- Subtracting like ordinary numbers: 1:20 minus 10:45 done digit by digit. The number line makes this impossible, which is why it is the method to teach first.
- Treating an hour as 100 minutes: writing 1 hour 75 minutes, or converting 1.5 hours to 1 hour 50. Practise converting both ways until 1.5 hours is automatically 90 minutes.
- Losing the midday or midnight crossing: counting 11:30 to 2:15 as nine hours because they went the wrong way round the clock. Ask which is later, before counting.
Where it shows up
Elapsed time is usually a Grade 2 to Grade 5 topic (Year 3 to Year 6 in the UK and New Zealand, Year 2 to Year 5 in Australia), and it keeps appearing afterwards inside timetable questions, speed calculations and shift rosters. Practising with real timetables, a TV guide or a train schedule is worth more than another abstract worksheet once the method is secure.