Math – Applications for Living XV

Our Math – Applications for Living class is moving on to other material, much to the relief of the group.  We had more difficulty than usual this semester with our work with units and percents (the stuff on the first test). One problem in particular seemed to be more challenging:

A computer modem uses about 7 watts even when the computer is not on; the modem is left on constantly (“24/7”).  A home in Lansing pays about $0.1137 per kilowatt-hour.  For one year, how much does it cost to keep the modem ‘on’?

I know that one challenge was that the book gave the official definition of a watt (1 joule per second), which led a few students to think that they needed to calculate how many seconds in a year.  Given this, there might be a temptation to not provide that information.  However, ignorance is not good when it is by design; the course includes a variety of information that applies to life and to science, and is one of the strengths.  It does not help that the book does a similar problem by converting watts to joules (no change) then calculating the energy use for the time period in joules (for seconds in the period), and then changes the result back to watts per hour.

The correct calculation is not that complicated:

7 watts * 24 hr/1 day  * 365 days / 1 year =  61320 watt-hours per year.       This is 61.320 kw-h

61.320 kw-h * $0.1137 / kw-h = $6.97 (rounded)

A few students had the right idea, but failed to change to kilowatt-hours — they ended up with a cost about $7000 for this modem.  The “answer desperation” of students led them to record this answer, even though they could see that it is not reasonable.

This problem was similar to one we did as an example in class … the cost of leaving phone chargers plugged in constantly.  Phone chargers are a lower power drain than modems, but there are so many more of them that their energy use is an issue.  Other ‘vampire loads’ contribute to our huge appetite for electricity (most electronics have a constant power usage, even when ‘off’).

Hidden in this modem problem is a strange thing: students knew that ‘km’ is ‘kilometers’, but are stumped by ‘kw’.  This problem, I think, is caused by the mechanical way that metric conversions are presented (‘just move that decimal point as you move from the old to the new prefix’).  We connected that strategy to the standard method (dimension analysis in this class).

 Join Dev Math Revival on Facebook:

2 Comments

• 

  By Peter Brown, September 15, 2012 @ 5:54 am

  Jack ,love this problem. You mentioned the course Math-Applications for living. Do you have a book associated with it? Brenda and I have searched the known world for a new 090 preAlgebra book- to no avail. Of course there is still this calculator/no calculator issue- although I am waiting for a response to my suggestion that if I can do it in my head faster than someone can hit the ‘on’ button on a calculator than there is some ‘pattern’ underneath worth exploring. Otherwise calculators are used all the time. What do you think of that general approach?

• 

  By Jack Rotman, September 17, 2012 @ 12:59 pm

  Peter:
  This course is partially algebra-based, and would be difficult to adapt for a pre-algebra level. Our current text is “using and understanding mathematics” by Bennett and Briggs (Pearson); good book, though very verbal.
  My approach to technology is generally ‘use it when appropriate, take advantage of it when possible’. For example, we solve exponential equations numerically in our math applications course and we use calculators heavily for the finance portion of the course.
  Hope this helps some — Jack

Other Links to this Post

RSS feed for comments on this post. TrackBack URI

Leave a comment

You must be logged in to post a comment.