Teaching Techniques to Tackle Some Sticky Topics in Algebra 2

1 / 16

# 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?.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Teaching Techniques to Tackle Some Sticky Topics in Algebra 2' - emily

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### 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?
• 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