# Mathematical clock

You can ask students to find the number of degrees in angle A of triangle ABC if angle B equals 72 degrees and angle C is 34 degrees, and that is a reasonable and acceptable math problem.

But if you ask a student to find the number of degrees between the hands of a clock at 4:08, then this is more interesting math problem.

What if you pose the problem in this way: "Find the number of degrees between the hands of a clock at 4:08. Explain how to do this problem as if you were explaining it to someone who did not know how to do the problem, and came to you for help. Include diagrams and a complete explanation. Then find the number of degrees between the hands of a clock at 4:32, and explain how to do this also. Are there any differences in the method used for 4:08 and 4:32?"

Now you have a challenging question, an interesting answer, and "writing in mathematics"!

This was actually the first writing assignment I had every assigned, and I really didn't know what to expect, both in terms of the student's reaction to the idea of writing in a math class, and is terms of what they might actually write.

The students had done four simple "clock problems" from the text book, problems such as "Find the measure of the angle between the hands of a clock at 3 PM". If you consider that question, you will realize that the answer is simple, because the minute hand is "straight up; (vertical) and the hour hand is directly on the numeral 3, aso they hands simply form a right angle. What complicates the problem for times such as 4:08 and 4:32 is that the minute hand moves as the hour hand moves, and the angle between them changes every minute. A superficial glance at a clock might cause one to think that the calculations for other times might be also simple, but they are not, and it is a rather sophisticated math problem, one that the students found challenging. They not only rose to the challenge, but wrote excellent explanations, and presented their work in creative and imaginative ways! As a teacher, I believe that it is extremely important to challenge students in this way, and to give them opportunities to rise to the challenge!

Source: mathforum.org
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