Teaching Techniques to Tackle Some Sticky Topics in Algebra 2

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Teaching Techniques to Tackle Some Sticky Topics
in Algebra 2

• Presenters
• Liz McClain
• Steve Rives

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Some Sticky Topics in Algebra 2

• Piecewise Functions
• Function Characteristics
• Positive and Negative or (non-negative,
  non-positive)

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What Does Research Say?

• The function concept is one of the central
  concepts in all of mathematics (Knuth, 2000
  Romberg, Carpernter, Fennema, 1993 Yerushalmy
  Schwartz, 1993).
• Understanding multiple representations of
  functions and the ability to move between them is
  critical to mathematical development (Knuth,
  2000 Rider, 2007).

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Piecewise/Compound Functions

• Functions with restricted domains
• Piecewise Function Activity
• Extension of the Piecewise Activity
• Technology

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Part 1 Functions with restricted domains

• Have students make a table and graph the function

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Discussion of just part of the graph.

• On overhead, erase part of my graph.
• Discuss with students
• How could we define the domain?
• How do you think we could write the rule
  to this function?

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• Repeat.
• Take the complete graph and erase a different
  part of the graph.
• Discuss
• How could we define the domain?
• How do you think we could write the rule to
  this function?

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Discuss restricted domains.

• Students erase a piece of their graph.
• Students write their function with this
  restricted domain.
• With a neighbor, students check each others work.

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Part 2 Piecewise Function / Compound Function
Activity

• Materials Students will need transparency paper
  and marker
• Set Up
• Divide the classroom.
• Half of the students graph the linear function
• (A),
• Half of the students graph the quadratic function
  (B)

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• Students make a table and graph the function on
  their paper.
• Students copy their graph onto a transparency.
• Students pair up with students from the other
  group.

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• Students transpose their graphs together, by
  laying their transparencies onto one anothers,
  and answer the following questions.
• Together, do these graphs describe a function?
  (Explain)
• How could you describe the new function rule?

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Discuss Piece-wise Functions

• A few groups share their results with the class.
  
• Students evaluate the piecewise function.
• Real world situations that require piecewise
  functions.
• Students ideas?
• cell phone plans, IRS tax rates,
  purchasing in bulk

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Part 3 Piecewise Function More Practice

• If time allows and if needed, you can continue
  this activity.
• Students pick a function from a collection of
  functions you have defined.
• Students make a table and graph the function on
  their paper.
• Students copy their graphs onto transparencies.
• Students find a partner and check each others
  work.
• Students transpose their graphs together and
  create a piecewise function.
• Pair of students finds another pair of students
  and they check each others work.
• Have students share with overhead transparency
  and written function.
• Summarize characteristics of Compound Functions/
  Piece-wise Functions.

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Using Technology to Graph Piecewise Functions

• Part 1Graphing Calculator
• Graph
• Procedure
• Press Mode . Select Func and the default
  settings.
• Press Y . Turn off all functions and stat
  plots. Enter Y function.
• Use the TEST menu operations to define the
  piecewise function. Choose a graph style.

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• Try graphing this piecewise function

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Part 2 Via the Internet

• http//gcalc.net/
• http//my.nctm.org/eresources/repository/shared/co
  ncord/resources_files/Piecewise.html