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Teaching Techniques to Tackle Some Sticky Topics in Algebra 2

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Some Sticky Topics in Algebra 2

- Piecewise Functions
- Function Characteristics :

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

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

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

Part 1: Functions with restricted domains

- Have students make a table and graph the function

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?”

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.

- 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

- 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)

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.

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

- 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

- 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

- 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

- http://gcalc.net/
- http://my.nctm.org/eresources/repository/shared/concord/resources_files/Piecewise.html

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