1. Equation of the Line Unit Page y = m x+ b I. Objectives of the Unit Objectives of the Unit Objectives of the Unit II. Concepts Concepts III. Terms used in the Unit: Terms used in the Unit: Terms used in the Unit: IV. Skills: Skills: V. Annotated Resources: Annotated Resources: Annotated Resources: VI. Standards covered within instruction of the unit: Standards covered within instruction of the unit: Standards covered within instruction of the unit: VII. Assignments: Assignments: VIII. Final Assignment Final Assignment Final Assignment IX. Cellular phone service plans Cellular phone service plans Cellular phone service plans (used for the final assignment) Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences. In addition, algebraic skills and concepts are developed and used in a wide variety of problem-solving situations. Mr. Nguyen Fall 2005 Algebra 1

2. Objectives of the Unit: This unit will focus on the development of linear equations from plotting points to finding and using an equation than can be used to solve real world problems. Students will be able to do this by learning the slope-intercept form of an equation.

3. Concepts: Students will be able to use symbolic reasoning and calculations which are central themes in Algebra. Through this understanding, students will be able to use these skills and concepts in a variety of problem solving situation Students will be able to use symbolic reasoning and calculations which are central themes in Algebra. Through this understanding, students will be able to use these skills and concepts in a variety of problem solving situation

4. Terms used in the Unit: Slope. Standard form. Slope intercept form Slope. Standard form. Slope intercept form Point slope form. Rise/Run. y-intercept Point slope form. Rise/Run. y-intercept x-intercept. m, b. Parallel x-intercept. m, b. Parallel Perpendicular. Positive slope. Negative slope Perpendicular. Positive slope. Negative slope

5. Skills: Recognizing positive and negative slopes Recognizing positive and negative slopes Find the slope of an equation using two points. Find the slope of an equation using two points. Recognize parallel and perpendicular slopes. Recognize parallel and perpendicular slopes. Find Y= m x + b using two points. Find Y= m x + b using two points. Graph Y= m x + b. Graph Y= m x + b. Applying the equation to real-world problems Applying the equation to real-world problems

6. Annotated Resources: http://id.mind.net/~zona/mmts/functionInstitute/functionInstitute.html http://id.mind.net/~zona/mmts/functionInstitute/functionInstitute.html http://id.mind.net/~zona/mmts/functionInstitute/functionInstitute.html (Good site for all functions in algebra through Trigonometry, easy to navigate and fuels students interest, all forms of a line are shown with step-by-step guide. Extends to other areas of math and science with resources, (Good site for all functions in algebra through Trigonometry, easy to navigate and fuels students interest, all forms of a line are shown with step-by-step guide. Extends to other areas of math and science with resources, http://mathforum.org/library/drmath/view/52848.html http://mathforum.org/library/drmath/view/52848.html http://mathforum.org/library/drmath/view/52848.html (a question and answer page for math, but the link also has the basic question relating to the equation of a line and with answers.) It also relates the slope-intercept form of a line with the point slope form of a line. (a question and answer page for math, but the link also has the basic question relating to the equation of a line and with answers.) It also relates the slope-intercept form of a line with the point slope form of a line. http://ext.sac.edu/faculty_staff/kashi_majid/equation_of_line.htm http://ext.sac.edu/faculty_staff/kashi_majid/equation_of_line.htm http://ext.sac.edu/faculty_staff/kashi_majid/equation_of_line.htm (Good site to plug in the coordinates to find: equation, slope, y-intercept, parallel, perpendicular. Use as a reference point) (Good site to plug in the coordinates to find: equation, slope, y-intercept, parallel, perpendicular. Use as a reference point) http://www.math.duke.edu/education/webfeats/Slope/slope1.html http://www.math.duke.edu/education/webfeats/Slope/slope1.html http://www.math.duke.edu/education/webfeats/Slope/slope1.html (Good basic explanation of the terms and each how the slope intercept, follow through step by step, why is m used as the variable) (Good basic explanation of the terms and each how the slope intercept, follow through step by step, why is m used as the variable) http://www.eduplace.com/math/mathsteps/7/d/index.html http://www.eduplace.com/math/mathsteps/7/d/index.html http://www.eduplace.com/math/mathsteps/7/d/index.html (Alternative explanation of linear equation covering slope, graphs, relationships, etc (Alternative explanation of linear equation covering slope, graphs, relationships, etc

7. Standards Covered Within the Unit: 6.0 Students graph a linear equation and compute the x- and y- intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4). 6.0 Students graph a linear equation and compute the x- and y- intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4). 7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula. 8.0 Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point. 7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula. 8.0 Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point. 9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets 9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets

8. Assignments Assignments A) Changes in ( X,Y ) and their correlation A) Changes in ( X,Y ) and their correlation Topics: plotting points on T-charts, noticing changes in, ( x,y ) Topics: plotting points on T-charts, noticing changes in, ( x,y ) B) Changing standard equation into the slope intercept form and back. B) Changing standard equation into the slope intercept form and back. Topics: solving for y, understanding x as a function of y, noticing change Topics: solving for y, understanding x as a function of y, noticing change C) Finding the slope and y-intercept using two coordinates on a plane. C) Finding the slope and y-intercept using two coordinates on a plane. Topics: finding the slope using rise over run and the equation Topics: finding the slope using rise over run and the equation (y2-y1) / (x2-x1), Using the slope = m to B find, understanding positive (y2-y1) / (x2-x1), Using the slope = m to B find, understanding positive and negative slope. D) Understanding parallel and perpendicular slopes: D) Understanding parallel and perpendicular slopes: Topics: same slope and negative inverse slope. Topics: same slope and negative inverse slope. E) Graphing systems of linear equations. E) Graphing systems of linear equations. Topics: solving for x and where the points meet, understanding low and high slope. Topics: solving for x and where the points meet, understanding low and high slope. F) Applications and word problems of y = mx + b. F) Applications and word problems of y = mx + b. Topics: Salary and wage, percentages, t-shirt printing. Topics: Salary and wage, percentages, t-shirt printing. G) Final assessment: G) Final assessment: Topic: Comparing cellular phone plans

9. Cellular Phone Companies ( click on the company to vist their site and service plans) Cingular Cingular Cingular Nextel Nextel Nextel T- Mobile T- Mobile T- Mobile T- Mobile Verizon Verizon Verizon What to learn more about cell phones? http://cellphones.about.com

10. Final Assignment Analyzing Cellular Phone Plans to Meet Your Needs Final Assignment Analyzing Cellular Phone Plans to Meet Your Needs Strategy:Mastery and Graphic Organizer Strategy:Mastery and Graphic Organizer TPEs AddressedTPE - 2 Monitoring student learning during instruction TPEs AddressedTPE - 2 Monitoring student learning during instruction TPE - 3 Interpretations and Use of Assessment TPE - 5 Student engagements Level of Taxonomy:Synthesis and Evaluation Level of Taxonomy:Synthesis and Evaluation Multiple Intelligences:Logical Mathematical, Visual spatial, and Intrapersonal Multiple Intelligences:Logical Mathematical, Visual spatial, and Intrapersonal Grade Level:9 - 12 Grade Level:9 - 12 Subject:Algebra I Subject:Algebra I Overview of the Lesson:Students will look at cellular phone plans from four major completing companies. (rates, options, etc.) Overview of the Lesson:Students will look at cellular phone plans from four major completing companies. (rates, options, etc.) They will then use and apply the equation of a line (y = mx + b) to determine the best possible plan to fit their given needs Students will then graph all the company’s plans together on a poster board and compare them. Students will work in groups of 3 – 4 students. Each group will be given one of the following condition: (find the best cell phone plans for: an individual, family plan, and a corporate group plan.) Students will work in groups of 3 – 4 students. Each group will be given one of the following condition: (find the best cell phone plans for: an individual, family plan, and a corporate group plan.) Lesson Process:Personnel – Teacher only Lesson Process:Personnel – Teacher only Materials - Copies of: T-mobile, Cingular, Verilzon, & Nextel phone plans. Poster board paper, color pencils, graphing paper. Preparation – Warm-up and review of the slope, y-intercept, and graphing equations of systems of line. Classroom Expectations: All students are expected to engage in the lesson. Classroom Expectations: All students are expected to engage in the lesson. Objective:Behavioral Objective: Understand the application of the equation of a line. Objective:Behavioral Objective: Understand the application of the equation of a line. Anticipatory Set:Motivation: Students will discuss cellular plans and find out for themselves which fit their needs. They will also be able to reflect on their own current plans if they have a cellular phone plan.? Anticipatory Set:Motivation: Students will discuss cellular plans and find out for themselves which fit their needs. They will also be able to reflect on their own current plans if they have a cellular phone plan.? Input (Lesson Sequence):See above. (Overview of lesson) Input (Lesson Sequence):See above. (Overview of lesson) Guided group practice: Students will compute the equations and graphic them visually on the poster boards Evaluation and Closure:Have each group review the graphs of others and compare the company’s plan to see if it fit their needs. Evaluation and Closure:Have each group review the graphs of others and compare the company’s plan to see if it fit their needs. Supplementary Activities:Have students search for other ways to use y = mx +b in real –world situations such as working on a base salary plus commission. Supplementary Activities:Have students search for other ways to use y = mx +b in real –world situations such as working on a base salary plus commission. Special Learners:Would be group with those that are strong in the math skills, they work work on the drawing of the graphs and visual presentation Special Learners:Would be group with those that are strong in the math skills, they work work on the drawing of the graphs and visual presentation California California Framework Standard: California Mathematics Academic Content Standards: 6.0 Students graph a linear equation and compute the x- and y- intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4). 6.0 Students graph a linear equation and compute the x- and y- intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4). 7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula. 8.0 Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point. 7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula. 8.0 Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point. 9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets 9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets

11. Mr. Nguyen Leuzinger High School Room: G2 [310] 263 -2202 x7551 Email: roomg2@yahoo.com roomg2@yahoo.com Office hours: M-F: 3 - 4:00 pm