This lesson consists of an activity that guides students to discovering the graph scale-change theorem.  Students are given a graphic organizer which consists of four sections.  In the first section, students are to draw graphs of given functions.  In the second section, students have to complete a table of corresponding x and y values.  In order to enhance this lesson, the teacher will use technology.  There is a graphing calculator available on the computer which can be projected onto the pull down screen so that students can easily follow along and check their work.

Lesson 3-5: The Graph Scale-Change Theorem

New Jersey Core Curriculum Content Standards

4.3B  Functions and Relationships

1.  Understand relations and functions and select, convert flexibly among,

      and use various representations for them, including equations, tables 

      and graphs.

2.      Understand and perform transformations on functions

            Focus:  Communication, Technology

Learning Objectives

·         After looking at functions with vertical, horizontal, and both vertical and horizontal scale changes, students will discover the Graph Scale-Change Theorem. 

·         Students will correctly describe the effects of scale changes on functions and their graphs.

Materials

·         Colored Pencils

·         Graphing Calculators

·         Handout Section 3-5: The Graph Scale-Change Theorem

·         Handout Section 3-5: The Graph Scale-Change Theorem (2)

Preparation

                        The teacher must prepare the worksheets Section 3-5: The Graph Scale-

Change Theorem and Section 3-5: The Graph Scale-Change Theorem (2).   Also, the “Warm-Up” assignment as well as important information for the lesson needs to be typed up so that it may be displayed on the projector.  The students should have completed their homework assignment (Lesson Master 3-4).

Procedure

Before (5-8 minutes)

·        Greet the students

            -    Give a general overview of today’s class

            -    Instruct student to complete the “Warm-Up” activity

            -    While students are working, check the homework 

·        The teacher should display the “Warm-Up” assignment on the projector

            -    The Warm-Up assignment

                        1)  Multiplying by 3 gives the same answers as dividing by ____.

                        2)  Multiplying by ½ gives the same answers as dividing by ____.

                        3)   Make a general statement which summarizes questions 1 and 2

                              above.

·         Ask for volunteers to give answers to the “Warm-Up” questions

Activity (25-30 minutes)

·         Ask for volunteers to help pass out materials

            -    Three colored pencils for each student

            -    Handout: Section 3-5: The Graph Scale-Change Theorem

            -    Make sure each student has a graphing calculator

·         Handout: Section 3-5: The Graph Scale-Change Theorem

            -    Guide students to help them complete the handout

            -    The teacher should use the calculator on the computer (SmartView) when

                  graphing and looking at tables

            -     The teacher should also reference the PowerPoint slides that go along with

                   the lesson

            -     The teacher should walk around the classroom throughout the lesson to

                   ensure students are on task and understanding the material

·         Handout: Section 3-5: The Graph Scale-Change Theorem (2)

-    Give each student a copy of the worksheet

-    Instruct students to work with a partner to answer the questions

-    Students should be given approximately 8 minutes to complete the handout

-    The teacher should walk around the room answering any questions

-    If students finish early, they should work on their Weekly Review 

      assignment

-    Ask for volunteers to share their answers and to explain them (orally or on

      the board)

Summary and Reinforcement (5 minutes)

·         Ask students:

-    What did you learn today?

-    What does it mean when a graph has a vertical scale change or vertical

      stretch?

-    What does it mean when a graph has a horizontal scale change or

     horizontal stretch?

-    What happens to the graph when I replace y by ?

-    What happens to the graph when I replace x by  ?

-    What is the difference between a translation and a scale change?

·         Homework:

-          If the class did not get to the worksheet, they should complete it for homework

-          If the class did complete the worksheet, then their homework is assignment F on their assignment sheet. 

Assessment

The teacher will be able to see how much students understand and have learned by their responses to the summary questions at the end of class.  Students will be given a homework assignment to reinforce concepts learned in class and will be reviewed the following day. 

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