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Teaching Techniques to Tackle Some Sticky Topics in Algebra 2

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

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  1. Teaching Techniques to Tackle Some Sticky Topics in Algebra 2 Presenters Liz McClain Steve Rives

  2. Some Sticky Topics in Algebra 2 • Piecewise Functions • Function Characteristics : Positive and Negative or (non-negative, non-positive)

  3. 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).

  4. Piecewise/Compound Functions • Functions with restricted domains • Piecewise Function Activity • Extension of the Piecewise Activity • Technology

  5. Part 1: Functions with restricted domains • Have students make a table and graph the function

  6. 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?”

  7. 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?

  8. 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.

  9. 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)

  10. 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.

  11. 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?

  12. 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

  13. 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.

  14. 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.

  15. Try graphing this piecewise function:

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

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