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. Some Sticky Topics in Algebra 2. Piecewise Functions Function Characteristics : Positive and Negative or (non-negative, non-positive). What Does Research Say?.

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some sticky topics in algebra 2
Some Sticky Topics in Algebra 2
  • Piecewise Functions
  • Function Characteristics :

Positive and Negative or (non-negative, non-positive)

what does research say
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).
piecewise compound functions
Piecewise/Compound Functions
  • Functions with restricted domains
  • Piecewise Function Activity
  • Extension of the Piecewise Activity
  • Technology
part 1 functions with restricted domains
Part 1: Functions with restricted domains
  • Have students make a table and graph the function
discussion of just part of the graph
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?”

slide7
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?

discuss restricted domains
Discuss restricted domains.
  • Students erase a piece of their graph.
  • Students write their function with this restricted domain.
  • With a neighbor, students check each other’s work.
part 2 piecewise function compound function activity
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)
slide10

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.
slide11
Students transpose their graphs together, by laying their transparencies onto one another’s, and answer the following questions.
      • Together, do these graphs describe a function? (Explain)
      • How could you describe the new function rule?
discuss piece wise functions
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

part 3 piecewise function more practice
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 other’s work.
  • Students transpose their graphs together and create a piecewise function.
  • Pair of students finds another pair of students and they check each other’s work.
  • Have students share with overhead transparency and written function.
  • Summarize characteristics of Compound Functions/ Piece-wise Functions.
using technology to graph piecewise functions
Using Technology to Graph Piecewise Functions
  • Part 1:Graphing 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.

part 2 via the internet
Part 2 : Via the Internet
  • http://gcalc.net/
  • http://my.nctm.org/eresources/repository/shared/concord/resources_files/Piecewise.html
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