## Wednesday, February 17, 2010

### Teaching Elapsed Time

Teaching time is always a little problematic with a class, as some students will have this well and truly conquered by year 10 and others will struggle.

Elapsed time is a difficult topic for many as it drags in a lot of sub topics. With each step it is important to draw student's attention to possible mistakes and also to any parallels with an analogue clock.

A common method is to find the number of hours elapsed and then add the remaining minutes on either side (eg. for 2.14 to 4.15: 2.14 -> 3.00 -> 4.00 -> 4.15 would be 46min + 1 hour + 15 mins = 2 hours 1 minute)

The usual approach is to
a) draw a number line
Issues: Students don't relate a number line with time, and commonly place decimal marks (eg. 10 between each hour) rather than 12 (for 5 minute intervals).
b) place the start and finish time on the number line.
Issues: Students don't realise that the start time and end time have to be placed in that order. Eg. if the start time is 8am and the end time is 7am they want to put 7am first on the number line.
c) mark on the hour after the start time and the hour before the start time
Issues: Students have difficulty adding the two times inside the interval. If 7.30am is the start time, they might add 7.00am instead of 8am or for a 4.30 finish time they might add 5.00pm or 3pm.
d) mark on midday and midnight if they lie between the start and finish time
Issues: This is problematic especially with times over 12 hours where both midday and midnight are involved. Students are often not sure whether 12pm or 12am is midday or midnight. They also get confused moving from 12am to 1 am (counter-intuitive).
e) calculate the time between each number on the timeline
Issues: This is the bugbear of the exercise. Students are not sure of the answer counting up to the nearest hour and counting back to the previous hour. Eg Finding the time between 1.17am and 2am or 4.00pm and 4.55pm. Many issues here are related to issues in part c)
f) add the elapsed times
Issues: Students write times such as 7hrs 85 minutes not realising 85mins is greater than an hour.

An alternate approach is to go up in hours and add the remainder (eg. 2.14-> 3.14 -> 4.14 -> 4.15 = 2 hours 1 minute). This may help struggling students and reduce the amount of calculation required.