## Thursday, January 9, 2014

### Elapsed Time Problems Using an Empty Number Line

Some time ago I gave students the question:
A movie starts at 3:40 p.m. and lasts 2 and 3/4 hours. What time will it finish?
The students (who had a very algorithmic approach to addition and subtraction) produced solutions such as:
This particular student figuring that 5:85 is not a familiar time, decided that maybe he should have subtracted instead but then ends up with an equally bewildering 0:95!

In a previous post, I showed how the empty number line is a great tool to improve students' abilities in addition and subtraction. Today it was great to see some Grade 5 students use the empty number line to solve an elapsed time problem. The question we gave was as follows:
Mr. Huxter has a problem; he has forgotten his Grade 5 math and started cooking his turkey too late. His family couldn't eat until 8:30 p.m.! The turkey took 3 and 3/4 hours to cook. If his family wanted to eat at 6:00 p.m., what time should he have started to cook the turkey?
These students were able to decompose numbers in a variety of ways so were able to get the solution in a variety of ways:

One student used a mental number line to solve this and wrote his strategy thus:
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We followed up the question by asking "What time did Mr. Huxter put his original turkey in?" It was again interesting to see a variety of successful approaches:

This example below, the student starts by taking 30 minutes off to get to a friendly 8:00:
This question involved finding the start time using the end time and the elapsed time. It will be interesting to see how they solve problems when they are given the start and end times and have to find the elapsed time, or when they are given the start and elapsed time and have to find the end time. I suspect that as long as they continue to use the empty number line, they will no find these problems any more difficult.
In fact, past experience tells me that the more they use the number line, the more they will be able to visualise this and thus solve these mentally.