Teacher2Teacher 
Q&A #212 
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From: Marielouise To: Teacher2Teacher Public Discussion Date: 2000052411:11:22 Subject: Re: Elapsed time I teach upper level students in high school and college, who still have trouble with this idea. Sometimes I think what we should do is what is done in Europe and keep with military time of 24 hours a day. I will give you some ideas about this situation but ask that you stay in the queue and hopefully, elementary teachers will be able to answer this question. One of the ideas about time is locked into modular arithmetic. When you look at a number 6 mod 9, this number means that 6 is equivalent to all the number greater than it which have a remainder of 6 when the number is divided by 9. For example, 15 = 9 times 1 plus remainder of 6. or, 87 = 9 times 9 plus remainder of 6. Therefore 6, 15, and 87 can all be put in the same pot! They all have remainder of 6. The clock operates mod 12. First, agree that the time starts each day at midnight. Time starts TODAY. Therefore, 2 p.m. is really 14 = 12 times 1 + 2. In three days, 2 p.m. will be 12 times 7 + 2 = 86. The seven represents the 1 cycle for the 12 hours a.m. and the 2 times 3 cycles for the three days. The elapsed time will be 86  14 = 72 hours. We know that with 24 hours in a day, 72 hours represents the three days. Suppose, you wish to find the elapsed time between 8 a.m. today and 3 p.m. tomorrow. Since 8 = 12 times 0 + 8 represents the 8 a.m. and 12 times 3 + 3 = 39 for the 3 p.m. tomorrow, the elapsed time is 39  8 = 31 hours. This is one way to approach the problem.
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