As each calendar year comes to an end and a new year approaches, we often see two special symbols in the media getting ready for the big partying that goes on December 31-January 1. One is the little Baby New Year, all decked out in his diaper and top hat. The other is old Father Time, a decrepit, white-haired and bearded old gentleman walking around with the aid of a cane. Now, the old man was once a baby on the previous January 1, right? So he must have aged tremendously during the intervening 12 months, in fact, lived his whole life in the span of one year.
Incredible, when you think about it, isn’t it?
But did you ever notice that we never see this “year character” grow up through childhood, adolescence, adulthood, senior citizen years, etc.? This inspired me to think of a problem for students to work on as they return to school after the Christmas break.
The ProblemLet us create a Year Person (Yppy, for short) who is born at the stroke of midnight of Dec 31/Jan 1. He lives out his entire existence in the course of one year, passing away to the great beyond at the stroke of midnight of the following December 31. We can arbitrarily set his “age” at death at most any reasonable number. For purposes of simplifying the matter here, we can allow an “age” of 100 years; the old man does seem to be about that age in most caricatures. Now we can pose a series of interesting questions.
- At what date (month/day) would Yppy enter kindergarten?
- At what date would Yppy be riding a real two-wheel bicycle (without training wheels)?
- At what date would Yppy become a teenager?
- At what date would Yppy be permitted to have a driver’s license?
- At what date would Yppy be eligible to vote in a national election?
- At what date would Yppy get married if we assume an “age” of 25 years? (You choose another number if you like.)
- Referring to the old cliche “don’t trust anyone over 30″, at what date should we not trust Yppy?
- Referring to another old cliche “life begins at 40″, when should “life begin” for our Yppy?
- Centrum Silver vitamin pills are advertised for persons “over 50″. When could Yppy start taking these vitamins?
- At what date would Yppy retire from his job at the clock factory, if 65 is an appropriate retirement “age” for this company?
- At what date would Yppy become a grandfather, assuming he had children who then had offspring who age at Yppy’s rate of living? (I leave it to you set a year-equivalent age for this one.)
- At what date would Yppy become an octogenarian?
- The year 1996 was a presidential election year of course. And Yppy (the ‘96 version, that is) became eligible at “18 years”, but that was early on in the calendar year; the election wasn’t until November. So what was Yppy’s “age” when he went to the polls to cast his ballot?
A Closing Note
The value of such a problem as this, in addition to its unique comic aspect, lies in the promotion of proportional thinking, a concept in which many students are notably weak. Here we are seeking that certain point (i.e., date) in the 365-day “lifetime” for Yppy that is proportional to some given age in the 0-100 year range for an equivalent regular human. At least initially, a student might set up the following proportion [y = “year” number; d = days elapsed]:
y d ------ = ----- 100 365
The year number arises from the specific question being asked; the “days elapsed” figure is the result of the solution process. Of course, that number must later be converted into a “date” of the mo./day format.
Another value for its use in the classroom is that some of the questions above have answers that vary, according to how an individual chooses to ascribe a certain “year” number to Yppy. This promotes creative thinking and discussion among students.
This problem has been used successfully with middle school students, giving them a sufficient challenge to their problem solving abilities and a change-of-pace activity. Readers are invited to add their own variations to the questions suggested above.
This article was published. “Yppy’s Year of Life: A Problem for the New Year”. Ohio Journal of School Mathematics. Spring 1998; #38 pp. 2-3.