lesson plan solving systems by graphing

7/31/2019 Lesson Plan Solving Systems by Graphing

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Norm Ebsary Multimedia #2 Lesson Plan: Solving Systems by Graphing

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Lesson Plan Solving Systems by Graphing

Introduction to the Lesson : Systems of linear equations will have 1solution (independent), no unique solution (dependent), and no solution(inconsistent). Students will learn to graph, a nalyze , and solve systems

of equations by using slope - intercept, standard, and p oint - slope formsof equations. Students will learn how to f ind 1 solution, no uniquesolution, or no solution by graphing system of equations. Emphasis will beon graphing systems of equations, with stude nts leveraging their graphingskills as well as using GeoGebra to capture exact solutions.

Explanation of Math Involved : The primary math involved in solvingsystems by graphing is graphing. By graphing these linear equations, thesolution needs to be com mon to both equations. By graphing these linear

equations, students in addition will have to perform substitution to verifythe solution is valid for both equations.

Use 3 - Steps as shown below -1. Graph both equations using slope - intercept format.

a. Plot y intercept (b). b. Count - out slope by rise and run, plot 2 nd point. c. Connect 2 points with straight line.

2. Determine the solution, if it exists: a. One solution - point of intersection. b. Infinite solution - coincident, equivalent equations. c. No solution - parallel lines, slopes of both lines are equal.

3. Validate solution, by performing check .a. Substitute x and y coordinates found (if exists) back into

original equations. Solve equations to ensure correctness, that equations balance properly.

Instructional Methods : Visual based using Interactive Electronic text,PowerPoint, and G eoGebra with interactive kinesthetic exercises. Sostudents will follow teacher with classroom examples - using handout ofgraph paper. After graphing examples in class, students will haveclassroom assignment using GeoGebra - exploring solutions of 2 linear equations manipulating slope (m) and y intercept (b) of each equation.


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Step by step procedure : A Daily Agenda is organized, to keep thestudents aware of the class lesson th at day . The lesson is organized asshown below in the PowerPoint, the students see this as they enter theclassroom and it is reviewed a t the start of the class by the teacher.

Figure 1: Classroom Lesson Daily Agenda The step by step procedure will follow the Daily Agenda shown above:

1. Warmup - See A ppendix A for 6 graphing problems. 2. Lesson Introduction - based on Power Point and electronic textbook,

students review linear equations with slope - intercept, standard,and point - slope forms, then are introduced to lesson concepts withsystems of equati ons and how to solve by graphing.

a. Students do 3 classwork examples using graph paper b. Students work in teams of 2 to 3 for GeoGebra activity

3. Lesson Quiz assesses students comprehension of the lesson. 4. Homework start - students have the 15 minutes or more to start

the homework and ask questions about the assignment .


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Key questions to be asked :1. Lines with the same slope have how many solutions? 2. How can a system of equa tions have 1 Solution? 3. How can a system of equations have infinite Solutions? 4. If a system of equations has no solutions, what do these equations

have in common?

Description of class activities :1. Warmup activity - 3 problems on graphing slope - intercept,

stan dard, and point - slope form of linear equations. 2. Review graphing and introduce systems of equations. 3. Classroom examples - 3 different examples where students explore

1 solution, infinite solutions, and no solutions. 4. GeoGebra interactive exercise, exploring l inear solutions by

changing slope and y intercept values using sliders. 5. Lesson Quiz - checks comprehension and provides additional

assessment. 6. Homework start, begin homework assignment and help answer final

doubts and questions.

Closure to the lesson : Students working on homework assignment, as away of assessing their understanding of the class lesson. Students endthe lesson by practicing their systems graphing through homeworkassignment.

Assignments for students : A total of 10 problems, to be solved bygraphing and classifying Independent, Dependent, or Inconsistent.


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As sessments : in 6 levels as follows -1. Classwork activity - observations on how students complete

exercise activities for length of time and correctness of content. 2. Homework - review homework for completeness and correctness of

content.

3. Warmup - Warmup is based on previous lesson, so the ease inwhich students complete the Warmup correctly is observed andnoted.

4. Lesson Quiz - at the end of lesson to check for understanding. 5. Quiz - section short assessment using system of equations by

graphing, 10 problems total. 6. Test - chapter test provides measure of how students comprehend

th e graphing of system equations and how this interacts withearlier and later sections of the chapter.

Plan for providing feedback : for classwork activity and Warmup , thefeedback will be interactive as students progress through theassignment - I will be w alking around the classroom interacting withstudents and providing direct feedback on my observations. Forhomework, I also provide direct feedback while grading the assignmentsfor completeness and correctness as I take attendance and students areworkin g on their Warmup assignments. For Quiz and Tests, studentsreceive their corrected versions back in a timely manner and problemsare reviewed in class.

Answer keys to assignments and assessments : See Appendix A

Supplement activities lesson : See Appendix B


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Connections section : There is opportunity to utilize systems of equationsfor real - life applications. Several examples are provided in thehomework assignment, for example problem #30 below :

Y = .15x + 200 Radi o Barn Weekly + Commission Y = .10x + 300 Woofer, Etc. Weekly + Commission

Figure 2: Ge oGe bra System of Equation for Home work Example So the solution by graphing the system is x = 2000, or 2000 units ofsales - both salaries are equal. Here is the check:

Y = .15(2000) + 200 = 500Y = .10(2000) + 300 = 500

Both salaries are equal, at $500 for sales of 2000 units. Thisshows a real - life connection, that students are always askingWhen am I going to use this?, well here it is!


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Appendix A: Answer keys to assig nments and assessments

Figure 3 : Lesson Warm - Up


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Figure 4 : Lesson Warm - Up solution key

Gr aphing Syst ems of

Equations1. Graph and solve the system.

Classify each system by graphing. Tell how many solutionsthere are.

2. 3. 4.

4x + y = 1 x + 3 y = 10

5x + 3y = 10 x 0.6 y = 2

12 x 18y = 9 6 x + 9 y = 13

4x + 5y = 103x 8 y = 15

( 1, 3)

dependent;infinitely many

inconsistent;no solutions

independent;one solution

Figure 5 : Lesson Quiz with solution k ey


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Graphing Systems of Equations38. inconsistent

39. dependent

40. independent

41. inconsistent

42. inconsistent

43. dependent

44. a. c = 20 d + 30c = 25 d

b. The cost wouldbe the same for a

6-day stay.

44. (continued)c. The Pooch Pad

would be cheaper fora 7 -day stay.

45. x = minutes,y = flyers;

45. (continued)After 10 minutes thenumbers of flyerswill be equal.

46. Answers may vary.Sample: y = x + 3

47. Answers may vary.Sample: y = 4 x + 8

48. Answers may vary.

Sample: y = 2 x + 73

y = 6x + 80y = 4x + 100

Figure 6 : Homework solution key

Graphing Systems of Equations49. No; they would be

the same line, andthe system would bedependent andconsistent.

50. An independentsystem has onesolution. The slopesare different, but they -intercepts could bethe same. Aninconsistent systemhas no solution. Theslopes are the same,and the y -interceptsare different.

50. (continued)

A dependent systemhas an infinitenumber of solutions.The slopes andy -intercepts are thesame.

51. Answers may vary.Sample: 3 x + 4 y = 12


Sample: y = + 75x

2


Sample: 10 x + 2 y = 45x y = 2

54. They are the sameequation written indifferent forms.

55. a. p : independent,n : dependent

b. n = 1600 p + 14,800

c. n = 6000 + 32,000



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Graphing Systems of Equations55. (continued)

d. About(3.91, 8545);profits are

maximized ifabout 8545widgets are soldfor about $3.91each.

56. C

57. G

58. B

59. H

60. [2] The slope of 2 x 5 y = 23 is and the slope of

3y 7 x = 8 is . Since the slopes are not equal,

the lines are not parallel and they do notcoincide. Therefore, the lines intersect; thesystem has exactly one solution and is consistent.

[1] does not include explanation

61. [4] Answers may vary. Sample:(a) A second equation is 4 x 6 y = 10, or any

equation of the form 2 ax 3 ay = 5 a .

(b) A second equation is 2 x 3 y = 6 or anyequation of the form 2 ax 3 ay = 5 b ,where a b .

[3] minor error in either part (a) or (b)

257

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=/


Figure 9 : Quiz on Linear Systems


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Figure 10 : Chapter Test on Linear Systems


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Appendix B : Supplement activities lesson Downloaded from UnitedStreaming.com a video on Linear Equations withemphasis on graph ing. The tile of the video isAdventurous_World_of_Algebra__The__Program_3__Linear_Equations and has a run -time of approximately 45 minutes. The supporting cast is called the Standard

Deviants, that provide an effective yet humorous at times lesson on LinearAlgebra

Figure 11 : Vide from UnitedStreaming.com on Linear Algebra


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lesson plan solving systems by graphing

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