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# Teaching Techniques to Tackle Some Sticky Topics in Algebra 2 - PowerPoint PPT Presentation

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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### Teaching Techniques to Tackle Some Sticky Topics in Algebra 2

Presenters

Liz McClain

Steve Rives

• Piecewise Functions

• Function Characteristics :

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

• 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).

• Functions with restricted domains

• Piecewise Function Activity

• Extension of the Piecewise Activity

• Technology

• Have students make a table and graph the function

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?”

• 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?

• Students erase a piece of their graph.

• Students write their function with this restricted domain.

• With a neighbor, students check each other’s work.

• 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)

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 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 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.

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