Mathnasium has an extensive curriculum. However, we also use alternative material when necessary. For example, we incorporate PARCC, SAT, and ACT preparation as these tests come close and use workbooks and worksheets in those test formats. It’s important for our students to gain familiarity with test formats and myriad possible ways in which questions may be given. Each test has a standard set of topics that may be examined, but test developers are always creating new and ingenious methods for testing their subject’s comprehension. It’s an evolutionary race between test-developers and test-takers. Hence, while our charter is teaching deep math comprehension, we also teach test taking skills.
In addition to standardized testing, we also prepare students for specialized tests. The Bergen Academies and it’s sister school, Bergen Technologies, is a magnet school in Bergen County. It has a rigorous entrance examination. The math exam measures number sense, reading comprehension, logic, and speed. The following question is a sample from an admission test that measures all those criteria.
A clock loses 1 second every minute. It shows the correct time at 10 AM on February 4th. When will it show the correct time again? (Note: A person can see whether it is AM or PM on this clock).
This question requires understanding of proportions. However, we’ll need to answer this quickly to avoid losing time. How appropriate, since it’s about a clock that loses time. Finally, we’ll also need to understand why it will show the correct time again, and when that happens. This reminds me of this excerpt from Lewis Carroll’s, “The Rectory Umbrella”,
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Which is better, a clock that is right only once a year, or a clock that is right twice every day? “The latter,” you reply, “unquestionably.” Very good, now attend. I have two clocks: one doesn’t go at all, and the other loses a minute a day: which would you prefer? “The losing one,” you answer, “without a doubt.” Now observe: the one which loses a minute a day has to lose twelve hours, or seven hundred and twenty minutes before it is right again, consequently it is only right once in two years, whereas the other is evidently right as often as the time it points to comes round, which happens twice a day.
That exchange was simplified and modernized as a joke about the limits of computer comprehension. A computer is asked, which it would prefer, a dead clock or a slow clock that loses 1 hour a day. The computer replies, the dead clock, because it is right twice every day, whereas the slow clock is right once every 12 days. I hope either exchange tickled your funny bone. Try asking Siri :-) More important, we expect it’s evident why the computer reasoned that the slow clock would be right once every 12 days.
The BA question above does note that the observer can determine whether it’s AM or PM, so, to answer that question, the slow clock would have to lose 24 hours to show the same time again.
Let’s answer the question with a minimum of arithmetic using proportional reasoning (a component of number sense).
The clock loses 1 second every 1 minute. Thus...
it loses 60 seconds every 60 minutes, in other words…
it loses 1 minute every 1 hour. Thus...
it loses 60 minutes every 60 hours, or in other words…
it loses 1 hour every 60 hours. Hence...
it loses 24 hours every 60 x 24 hours, or in other words…
it loses 24 hours every 60 days (since 24 hours make a day).
Now we’ll skip up the number line in day segments that total 60 days from February 4th. Assuming February has 28 days, there is 25 days to March 1st, 31 days to April 1st, and 4 more day to April 5th at 10 AM when the clock shows the correct time again.
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Have you ever seen time fly? Throw your broken clocks! And since we're discussing slow time, here's a timely discussion about our relative perception of time.
Contact:
Ruby Yao and Benedict Zoe, Mathnasium of Fort Lee
201-969-6284 (WOW-MATH), fortlee@mathnasium.com
246 Main St. #A
Fort Lee, NJ 07024
Happily serving communities of Cliffside Park, Edgewater, Fort Lee, Leonia, and Palisades Park.
