Tuesday, November 9, 2010

Looking at Word Problems

From Math 9 textbook:

"Alicia buys a $300 jacket on lay away.  She made a down payment of $30 and is paying $15 per week.  The total paid, P dollars, after n weeks can be represented by the equation P = 15n + 30.   a) create a table of values to show the total paid in each of the first 5 weeks  b) graph the data.  Should you join the points on the graph?  explain. c) how do the patterns in the graph relate to the patterns in the table?".

Is it practical?    $300 seems like an awful lot for a teenager to pay for jacket,  which made me wonder what "lay away" means?    I am not familiar with this term.   From the second sentence it is possible to guess what lay away means and it is actually possible to complete this problem without knowing what it means.     Some questions that come to mind are: why does Alicia want to buy this jacket, and why is she willing to pay for it over the next n years?    After I checked the dictionary, I learn that lay away means you don't actually get the jacket until you have finished paying it off.    That could be a long time!    What is so special about this jacket?    Just curious.

Creating a table and graphing the points is a good idea.  

when n = 1,   P = 45
when n = 2,   P = 60
when n = 3,   P = 75
when n = 4,   P = 90
when n = 5,   P = 105

Should we join the points on the graph?   This is a good question.  It makes the student think more about the application and quantity that we are plotting.   I'm not sure what is the purpose of asking part c).   The pattern is an even increment, a linear equation.  What is meant by "patterns in the graph"?   Perhaps the author want us to notice the linear relationship?

Extension:   I think an interesting question would be,  "how long will it take for Alicia to pay off the jacket?".    Perhaps,  we can also add the question, "do you think it is worth waiting so long for a jacket that you really like?"  

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