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The activity begins with the presentation of the problem
to the class. This can be done as a handout
or using overhead transparencies.
In either case it is advisable to go through the problem with the class
to make sure everyone understands the situation, especially as some student
may not be familiar with cell phone billing plans.
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Have the students do questions A and B in small groups or individually.
If some students prefer numerical approaches to algebraic ones you should
suggest they do Question B first, or omit Question A until after they have
done Question C.
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Share answers as a whole class.
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Have the students do Question C. There are a number of different
approaches they might take:
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Drawing the graph on paper based on the numbers calculated in Question
B
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Drawing the graph on paper based on the equations derived in Question A
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Drawing the graph using a graphing calculator based on the equations derived
in Question A
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Drawing the graph using a spreadsheet based on the numbers calculated in
Question B
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Drawing the graph using Geometer's Sketchpad based on the numbers calculated
in Question B [How To]. Students who did
not do Question A can use Geometer's Sketchpad to find the equation of
the line [How To]. (Student Handouts
are available to support this activity.)
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Have the students do question D in small groups, and then share their answers
with the class.
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For questions E and F, have the students start a new GSP sketch and graph
the lines for the first two companies. Then have them construct two
points: one on the Y axis, and one floating freely [How
To]. Have them construct the line between their points and measure
the equation and slope of the line [How To].
The result should resemble the sample sketch.
By manipulating the two points they can place the Cell Rules line so that
it meets the requirements of the questions, and read off the equation.
(Student Handouts are available to
support this activity.)
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