Reflection: Connection to Prior Knowledge The Cell Phone Problem, Day 3 - Section 4: Student Solutions


When I planned this lesson, I didn't think it would be very hard for my students to find the intersection of the two curves.  Boy, was I wrong!

When asked which phone was cheapest, they answered, "Well, this one is until somewhere between 28 and 32 months."  I'd press them to pin down the number of months more precisely, and they'd look at me as if they didn't understand.  In their eyes, the graphs crossed somewhere between 28 and 32 months, and to say anything else would just be guesswork.

After a moment, one student asked, "Do you want us to plug more numbers into the equations to find the one where they're equal?"

"No," I said, "that would take you a very long time unless these happen to cross at a 'nice' point."

"Well," she replied, "I don't see any other way to do it."

"Have you ever found the point where two graphs cross before?"

(After some thought) "Yes, when we solved systems of linear equations.  But those were straight lines."

"That's true, but that was a similar problem.  Could you solve this one in a similar way?"

At this point, the more students began to chime in with some of the different ways they had solved systems of equations in the past.  Since in this case both equations were already given in a "y = ..." form, they settled on the substitution method before long.

They quickly wrote down their new equation ... and stopped.  They were faced with a proportion in which x appeared in all four terms.  I walked away as they began arguing about how to solve it...


  It's Harder Than You'd Think
  Connection to Prior Knowledge: It's Harder Than You'd Think
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The Cell Phone Problem, Day 3

Unit 7: Rational Functions
Lesson 3 of 17

Objective: SWBAT model average monthly costs using rational functions and make comparisons between several different functions. SWBAT identify the intersection points of graphs of simple rational functions.

Big Idea: Graphs and equations make the choice clearer, but even a mathematical model has its limitations. Can the cost of the phone really be infinite?

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Math, modeling, Algebra, Function Operations and Inverses, Algebra 2, master teacher project, rational function
  45 minutes
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