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 2

  • Piecewise Functions

  • Function Characteristics :

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


What does research say
What Does Research Say? 2

  • 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 2

  • 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 2

  • Have students make a table and graph the function


Discussion of just part of the graph
Discussion of just “part” 2of 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?”


Teaching techniques to tackle some sticky topics in algebra 2

  • Repeat. 2

  • 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. 2

  • 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 2

  • 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)


Teaching techniques to tackle some sticky topics in algebra 2


Teaching techniques to tackle some sticky topics in algebra 2


Discuss piece wise functions
Discuss Piece-wise Functions transparencies onto one another’s, and answer the following questions.

  • 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 transparencies onto one another’s, and answer the following questions.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 transparencies onto one another’s, and answer the following questions.

  • 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.


Teaching techniques to tackle some sticky topics in algebra 2


Part 2 via the internet
Part 2 : Via the Internet transparencies onto one another’s, and answer the following questions.

  • http://gcalc.net/

  • http://my.nctm.org/eresources/repository/shared/concord/resources_files/Piecewise.html