For problems where the start time and the amount of time that has passed are known the following steps are used.
Because we use the language START, CHANGE, END when we are working on addition and subtraction at the beginning of the year, it transfers right over to elapsed time. Subtraction is done when the end time is given, but either the start time or the time that has passed are not.
This is also an example of when students are unable to complete each side independently. Students immediately identify that they cannot do 20-40, and that they need to regroup to continue. Once they have a new starting time, they can subtract each side and have the missing time.
This is when things get a little tricky. Upon first looking at this you would think I'd lost my mind. But here's an example story problem.
Sarah's family was driving across the country on a road trip. They reached Florida at 2:20 a.m., and immediately went to bed. They drove for 12 hours and 40 minutes. What time must they have started their drive?
Because the start is unknown, it's a subtraction problem. First, students identify that since they traveled after midnight, they have to convert into daytime. They add 12 hours to the start time.
Once that's completed, they have a new start time. Now, they are unable to do the minutes, so they again regroup. Now, again, this seems like a lot of steps and quite complicated. Because it's 12 hours I also talk to my students how that 12 just basically cancels itself out. But if 11 hours were used in this example, the steps would be used. Once students have mastered the steps from above, it really is simple for them to add the one additional step.
We also transferred the same steps to adding and subtracting lengths and then converting them.
While this takes me back to my days in Geometry doing proofs over and over again, that little line in the middle really helps my kids not just carry and borrow between.
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