EDCI 591 Unit Plan Linear Functions

Ryan Hoffman Glen Woodworth

Jamie Walker

Lesson 1: Getting Credit

Course Algebra 1

Time Frame Three 50-Minute Class Periods

Topic Modeling Linear Relationships

Prior Knowledge • Solving multi-step equations • Plotting coordinate points on a Cartesian coordinate graph • Relationships between quantitative variables

Objectives • “Calculate the rate of change in one variable as another variable increases,” (Hirsch, 2008, T150)

• “Describe the relationships among the graph, symbolic rule, table of values, and related situations for a linear function,” (Hirsch, 2008, T150)

• “Interpret the meaning of the slope and y-intercept of the graph of a linear function in a context,” (Hirsch, 2008, T150)

Standards Addressed

Indiana Standards • A1.2.1: “Translate among various representations of linear

functions including tables, graphs, words, and equations,” (Indiana Department of Education, 2009)

• A1.2.2: “Graph linear equations and show that they have constant rates of change,” (Indiana Department of Education, 2009)

• A1.2.3: “Determine the slope, x-intercept, and y-intercept of a line given its graph, its equation, or two points on the line and determine the equation of a line given sufficient information,” (Indiana Department of Equation, 2009)

• A1.2.4: “Write, interpret, and translate among equivalent forms of equations for linear functions (slope-intercept, point-slope, and standard) recognizing that equivalent forms reveal more or less information about a given situation,” (Indiana Department of Education, 2009)

NCTM Process Standards • Communication

• Connections • Representation

Materials • Graphing paper • Graphing calculator (optional) • Ruler • Pencil • Markers • Large graphing paper for presenting

Launch

• To launch the context, a short one-minute video will be played that deals with a man telling customers how much money can be made by selling credit cards http://www.youtube.com/watch?v=Hhtfx4pW9fQ

• The teacher will explain to students that they will be recognizing linear relationships between variables

• Students will explore how to represent those relationships through graphs, tables, and function rules

• A background of selling cards from a salesman’s point of view should be discussed to give students background information

• Students unfamiliar to credit cards may have difficulty relating to the context of the problem

• To finish the launch, the teacher should guide students through “Think About This Situation,” see appendix A

Explore

• Students will work in groups of two-three and complete investigation one, problems one, two, and three on day one

• On day two, students will work on problems four, five, and six • By the end of day two, groups will have selected one of the six

problems to be presented and discussed on day three • See appendix A for the investigation • Guiding questions to ask while students are working include

the following: • Is there a rule or relationship here? • How does the rule work, and how it is helpful? • Why does the rule work the way it does? • Is there information here that lets me predict what’s going to

happen? • How is the NOW-NEXT rule generated? • Does your rule work for all cases? • Now that I have an equation, how do the numbers

(parameters) in the equation relate to the problem context? • How can I write the expression in terms of things I care

about? • How is this number in the sequence related to the one that

came before? Homework • Students will be assigned the following problems on the

following nights: • Day one: A1, A2 • Day two: C14, C15 • Day three: C20, R23

• See appendix B for the homework problems • Problems will be graded based on completion

Assessment • Formal assessment will follow at the conclusion of the unit (unit test)

Summary

• On day three, groups will present the problems worked in class with an open discussion

• As a class, the concepts of linear functions, slope, y-intercept, tables of values, graphs, etc., will be discussed

• Evaluation of the presentations should be done by the teacher to see if additional instruction is necessary

• See appendix C for a copy of an evaluation rubric

Accommodations • Accommodations will be provided as stated in students’ IEPs.

References Cash Flow From Credit Cards. (2008, August 14). Sell Credit Cards. Retrieved June 26, 2009, from http://www.youtube.com/watch?v=Hhtfx4pW9fQ Hirsch, C.R., Fey, J.T., Hart, E.W., Schoen, H.L., & Watkins, A.E. (2008). Core-Plus

Mathematics, Course 1. Columbus, OH: McGraw Hill Glencoe. Hirsch, C.R., Fey, J.T., Hart, E.W., Schoen, H.L., & Watkins, A.E. (2008). Core-Plus

Mathematics, Course 1: Teacher’s Guide Part A. Columbus, OH: McGraw Hill Glencoe.

Indiana Department of Education, Indiana’s High School Standards. Retrieved February

24, 2009, from Indiana Department of Education: http://dc.doe.in.gov/Standards/AcademicStandards/StandardSearch.aspx.

National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics. Reston, VA: Author.

Appendices Appendix A

Appendix B

Appendix C

Presentation Evaluation Rubric

As indicated in the problem, students must include the following on their poster board: • Labeled graph • Table of values (with labels) • Written explanations are included on presentation paper • NOW-NEXT rules are given

Lesson 2: Symbolize It

Course Algebra 1

Time Frame Three 50-Minute Class Periods

Topic Modeling Linear Relationships

Prior Knowledge • Solving multi-step equations • Plotting coordinate points on a Cartesian coordinate graph • Relationships between quantitative variables • Calculate the rate of change in one variable as another

variable increases • Describe the relationships among the graph, symbolic rule,

table of values, and related situations for a linear function • Interpret the meaning of the slope and y-intercept of the graph

of a linear function in a context

Objectives • Using information in a table, a graph, and given conditions to write a symbolic rule for a linear function

• Understanding the relationship between slope-intercept form and standard form

Standards Addressed

Indiana Standards • A1.2.1: “Translate among various representations of linear

functions including tables, graphs, words, and equations,” (Indiana Department of Education, 2009)

• A1.2.2: “Graph linear equations and show that they have constant rates of change,” (Indiana Department of Education, 2009)

• A1.2.3: “Determine the slope, x-intercept, and y-intercept of a line given its graph, its equation, or two points on the line and determine the equation of a line given sufficient information,” (Indiana Department of Equation, 2009)

• A1.2.4: “Write, interpret, and translate among equivalent forms of equations for linear functions (slope-intercept, point-slope, and standard) recognizing that equivalent forms reveal more or less information about a given situation,” (Indiana Department of Education, 2009)

NCTM Process Standards • Communication • Connections • Representation

Materials • Graphing paper • Graphing calculator • Ruler • Pencil • Markers • Large graphing paper for presenting

Launch

• The teacher will explain to students how they can use information in a table, a graph, and given conditions to write a symbolic rule for a linear function

• The teacher will guide students through “Check Your Understanding” parts a-f as an introduction to investigation two

• See appendix A for investigation two • The terms of “coefficient of x” and “constant term” will be

introduced to students

Explore

• Students will work in groups of two-three and complete investigation two, problems one through four on day one

• On day two, students will work on problems five and six • By the end of day two, groups will have selected one of the six

problems to be presented and discussed on day three • See appendix A for the investigation • Guiding questions to ask while students are working include

the following: • Is there a rule or relationship here? • How does the rule work, and how it is helpful? • What is the difference between slope-intercept form and

standard form? • How is the NOW-NEXT rule generated? • Does your rule work for all cases? • Now that I have an equation, how do the numbers

(parameters) in the equation relate to the problem context? • How can I write the expression in terms of things I care

about?

Homework • Students will be assigned the following problems on the following nights: • Day one: A7, A8, A9 • Day two: C16, C21, C22 • Day three: R24, R25, E30

• See appendix B for the problems • Problems will be graded based on completion

Assessment • Formal assessment will follow at the conclusion of the unit

Summary

• On day three, groups will present their problems completed in class with an open discussion

• As a class, the concepts of linear functions, slope, y-intercept, tables of values, graphs, etc., will be discussed

• Evaluation of the presentations should be done by the teacher to see if additional instruction is necessary

• On day four, a review will take place in order to have a formal assessment on day five

• See appendix C for a copy of an evaluation rubric

Accommodations • Accommodations will be provided as stated in students’ IEPs.

References Hirsch, C.R., Fey, J.T., Hart, E.W., Schoen, H.L., & Watkins, A.E. (2008). Core-Plus

Mathematics, Course 1. Columbus, OH: McGraw Hill Glencoe. Hirsch, C.R., Fey, J.T., Hart, E.W., Schoen, H.L., & Watkins, A.E. (2008). Core-Plus

Mathematics, Course 1: Teacher’s Guide Part A. Columbus, OH: McGraw Hill Glencoe.

Indiana Department of Education, Indiana’s High School Standards. Retrieved February

24, 2009, from Indiana Department of Education: http://dc.doe.in.gov/Standards/AcademicStandards/StandardSearch.aspx.

National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics. Reston, VA: Author.

Appendices Appendix A

Appendix B

Appendix C

Presentation Evaluation Rubric

As indicated in the problem, students must include the following on their poster board: • Labeled graph • Table of values (with labels) • Written explanations are included on presentation paper • NOW-NEXT rules are given

Algebra 1 Unit 3 – Linear Functions Test

Name: _________________________

Directions: Using a six-sided die, generate a function in slope-intercept form by rolling the die. The number you receive on the first roll will be your coefficient of x. The second number you generate will be your constant. (You can make either number positive or negative).

1. Record your equation here:

a. Construct a table of points for this equation.

X Y -2 -1 0 1 2

b. Graph the line you generated. c. What is the slope of your equation? How did you know?

d. What is the y-intercept of your equation? How did you know?

e. Do problem three on page 169.

f. Do problem four on page 169.

g. Do problem five on page 170.