Angles on a clockface


I worked this problem with some 5th graders last year.  Since I was unsure about their exposure to angles, I began by asking if they knew the degree measure of a right angle, from 12 to 3 on the clock.  From there, I told them I would divide up that 90 degrees into 3 sections, drawing in the 1 and 2 on the clock.  How many degrees between the 12 and 1?

Then I followed the solution provided, and continued by asking them for the degree measure of the angle between 12 and 8, which is the degrees between the 2 hands at 8:00.  Then we stepped through how many degrees we lose by moving the minute hand from the 12 to between the 5 and 6 after 24 minutes.  Then we need to add the few degrees the hour hand moved in 24 minutes.

This approach reminded me that there are two approaches to teaching math.  One way is to repeat the same problem over and over, which little change until the algorithm in memorized.  Another more fun way is to begin with an elementary problem, and do only a small number of those before immediately continuing to progressively more difficult problems.

After I asked them how many degrees were in a right angle, the students then unprompted told me the degree measure from 12 to 6 and then 12 to 9, pretty much by rote.  But I didn’t want to hear their answers to elementary problems.  I wanted to quickly propel them to more difficult problems: the degree measure from 12 to 8 and then at 8:24.  I think they had fun solving this problem and internalized the concept better by solving 1 more difficult problem than a page full of identical easier problems.

(Source: Math Olympiad for Elementary and Middle School)

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