Time (III): Elapsed time

1Summary 重點摘要

From 2:15 to 3:00 is 45 minutes.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Part 1: Elapsed time is durationElapsed time is how long something takes; it is not a moment but a length of time, measured in minutes or hours. Why tell moment and duration apart? A moment is a single point, while elapsed time is the distance between two points, and they answer different questions. Example: start homework at 2:15 and finish at 3:00; the time in between is the elapsed time. Take care that 'what time' asks for a moment while 'how long' asks for a duration; misreading the question gives an answer nobody wanted.
2. Part 2: Count in 5-minute hopsCount elapsed time in 5-minute hops, moving across the clock face like skip counting, the most direct method. From 2:15, hop 2:15, 2:20, 2:25, and so on until 3:00, five minutes each hop, nine hops in all, so from 2:15 to 3:00 takes 45 minutes. Why 5 minutes each hop? Every big step on the clock face is exactly 5 minutes. Take care that the last time you land on is the end moment, not the duration; the number of hops is the duration, and 9 hops make 45 minutes.
3. Part 3: Count in two chunks for safetyCounting in two chunks is safer: count to an easy moment first, then count to the end, and add the two chunks together. From 2:15 to 3:00: first count to 2:30, which takes 15 minutes, then from 2:30 to 3:00, which takes 30 minutes, and 15 + 30 = 45 minutes. Why chunk it? Each small chunk is easy to count and hard to tangle. Take care not to lose one chunk in the adding; the sum of both chunks is the whole duration, and dropping one chunk halves the answer.
4. Part 4: Crossing an o'clock is easyIf the time crosses an o'clock, count to the hour first, then count on, because the hour is the best place to split. Example: 1:50 to 2:20: the stretch from 1:50 to 2:00 is 10 minutes, and from 2:00 to 2:20 is 20 minutes, 30 minutes in all. Why split at the hour? The hour is neat and even, and both chunks become easy to work out. The usual error is subtracting 50 from 20 straight away and getting a negative number; the duration must be split at the hour, never subtracted straight across it.
5. Part 5: More than one hourFor more than one hour, add the chunks together, keeping hours and minutes separate. From 9:40 to 11:10: 9:40 to 10:00 is 20 minutes, 10:00 to 11:00 is 60 minutes, and 11:00 to 11:10 is 10 minutes, so 90 minutes in all, which is 1 hour 30 minutes. Take care that 60 minutes make 1 hour, so the final 90 minutes must be turned into 1 hour 30 minutes for the answer; writing 90 minutes is not wrong in value, but hours and minutes are clearer and match the question better.
6. Part 6: Three kinds of questionWord problems ask in three ways; first decide which kind is asked, then choose adding or counting back. First, elapsed time: how long from 2:15 to 3:00? Answer 45 minutes. Second, end time: start at 4:00 and work 25 minutes, ending at 4:25. Third, start time: finish at 6:00 after working 40 minutes, so start at 5:20. Take care that with the start and the duration known, adding gives the end; with the end and the duration known, counting back gives the start. Reverse the direction and the answer goes wrong.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Elapsed time = end time − start time
• Minute hand: 5 minutes per number; hour hand: 1 hour per number
• Split at the hour mark and count in chunks
• 60 minutes = 1 hour; 90 minutes = 1 hour 30 minutes
• Start time: count back; end time: count forward