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## Solving Systems of Linear Equations by Graphing

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**Solving Systems of Linear Equations by Graphing**STORYBOARDS**Purpose Statement**• Solving systems of linear equations is an important algebraic skill for all students. It attends to the development of abstract reasoning skills, which are “necessary to excel in math and science”, as well as many other crucial algebraic concepts (GreatSchools Inc., 2010, para. 7).**Background Information**• This lesson is intended for eighth or ninth grade students as part of an algebra curriculum. • This lesson is designed as a hybrid. Parts of the lesson assume the traditional face-to-face classroom setting. Other parts assume the use of a computer lab where students will complete activities on internet-accessible computers. • This lesson is designed for three days of instruction and one day of summative assessment. • Students should have the following pre-requisite skills: • Write an equation in slope-intercept form to model a situation • Graph a linear equation in slope-intercept form • Create presentations using the following technologies: ShowMe, Educreations, VoiceThread, PowerPoint, Prezi, Animoto • Aligns to Common Core State Standards: • 8.EE.8a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. • 8.EE.c. Solve real-world and mathematical problems leading to two linear equations in two variables. (Common Core State Standards Initiative, 2012).**Learning Objectives**• Using graph paper and technology, students will be able to graph two linear equations on the same coordinate plane and find their point of intersection. • Students will understand that the point of intersection represents the solution to the system of linear equations. • Students will understand that a system of linear equations may have no solutions or infinite solutions. • Students will be able to solve real-world and mathematical problems by solving a system of linear equations by graphing. • Students will be able to create and solve a real-world problem by creating and solving a system of linear equations by graphing.**Learning Activity #1**Onscreen Content Description of Activity Time Frame: 10-15 minutes Location: Classroom Levels of Bloom’s (Revised): Remembering, Understanding, Applying Technology: A projector may be used to project the problem on the SMARTBoard. Introduction/Recall of Prior Knowledge: • MusicManiaand HitMusic both stream and sell music. MusicMania charges a monthly fee of $15 and an additional charge of $0.40 per song downloaded. HitMusic charges a monthly fee of $25 and an additional charge of $0.20 per song downloaded. For what number of songs will the monthly charge be the same for both?**Learning Activity #2**Onscreen Content Description of Activity Time Frame: 10-15 minutes Location: Classroom Levels of Bloom’s (Revised): Remembering, Understanding, Applying, Analyzing, Evaluating Materials: Pencil, graph paper, ruler Technology: No technology is used purposefully so that future class discussions can occur on the effectiveness of using technology to graph linear equations. Practice using pencil/paper: • Using a pencil, graph paper, and a ruler, solve the following systems of linear equations by graphing both equations on the same coordinate plane and finding their point of intersection. Check your solution in both equations! • “Example 1” • “Example 2”**Learning Activity #3**Onscreen Content Description of Activity Time Frame: 20-25 minutes Location: Computer Lab Levels of Bloom’s (Revised): Remembering, Understanding, Applying, Analyzing, Evaluating Technology: Students should use the online graphing calculator from this link: http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html Practice using technology: • Enter the link below into your Web browser: • http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html • Using the online graphing calculator, graph the following systems of equations and find the point of intersection. • “Example 1” • “Example 2” • “Example 3”**Learning Activity #4**Onscreen Content Description of Activity Time Frame: 20 minutes Location: Computer Lab Levels of Bloom’s (Revised): Remembering, Understanding, Applying, Analyzing, Evaluating, Creating Technology: Students should use the online graphing calculatorfrom this link: http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html Real-Life Application: • Solve the following real-life problems by writing and solving a system of linear equations. Graph the equations using the online graphing calculator. • “Problem 1” • “Problem 2” • “Problem 3” • “Problem 4”**Learning Activity #5**Onscreen Content Description of Activity Time Frame: 15 minutes total (video is 5 minutes long) Location: Computer Lab Levels of Bloom’s (Revised): Remembering, Understanding, Applying, Analyzing, Evaluating Technology: Students will be watching a video lesson on their computers. This will allow students to pause and rewind the video lesson as needed. Technology: Students will be responding to questions using a GoogleDoc in collaboration with a peer. Students will then share their GoogleDoc with the instructor to allow for assessment and feedback. No Solutions: • Enter the link below into your Web browser: • http://learnzillion.com/lessons/1018-determine-if-a-system-of-two-linear-equations-in-two-variables-has-no-solutions-by-graphing • Watch the video and then answer the following questions with a partner on your shared GoogleDoc: • What does it mean when a system of equations has no solution? • If a system of linear equations has no solution, what do you know about the graphs of those equations? • If a system of linear equations has no solution, what do the equations have in common?**Learning Activity #6**Onscreen Content Description of Activity Time Frame: 15 minutes total (video is 5 minutes long) Location: Computer Lab Levels of Bloom’s (Revised): Remembering, Understanding, Applying, Analyzing, Evaluating Technology: Students will be watching a video lesson on their computers. This will allow students to pause and rewind the video lesson as needed. Technology: Students will be responding to questions using a GoogleDoc in collaboration with a peer. Students will then share their GoogleDoc with the instructor to allow for assessment and feedback. Infinite Solutions: • Enter the link below into your Web browser: • http://learnzillion.com/lessons/1019-determine-if-a-system-of-two-linear-equations-in-two-variables-has-infinitely-many-solutions-by-graphing • Watch the video and then answer the following questions with a partner on your shared GoogleDoc: • What does it mean when a system of equations has infinite solutions? • If a system of linear equations has infinite solutions, what do you know about the graphs of those equations? • If a system of linear equations has infinite solutions, what do the equations have in common?**Learning Activity #7**Onscreen Content Description of Activity Time Frame: 30-45 minutes Location: Computer Lab Levels of Bloom’s (Revised): Remembering, Understanding, Applying, Analyzing, Evaluating, Creating Technology: Students will have various technologies to choose from in this activity. Technology: Students should link/upload their presentation to the class website (Edmodo, Schoology, Moodle, Google site, etc.) Creating a Linear System: • Now, it’s your turn! • With a partner, create a real-life problem that could be solved by writing and solving a system of linear equations. • Then, using one of the technologies listed below, create a lesson/presentation that shows how you would solve this real-life problem using a system of linear equations. • ShowMe • Educreations • Prezi • VoiceThread • Animoto • PowerPoint**Assessment Evidence**• Socrative should be used throughout the lesson as a formative assessment tool. • This website/app allows teachers to create quizzes for students or administer a quick formative assessment if students are presented with a multiple choice, true/false, or open-ended question. • GoogleDocsshould be used during Learning Activity #5 and Learning Activity #6 as a formative assessment tool. • GoogleDocs allows the students to share a document with the instructor so the instructor can assess students’ understanding and provide feedback. • A class website, such as Edmodo, Schoology, Moodle, or a Google site, should be used during Learning Acitivty #7. • This would allow all class members to share their creations with other classmates as well as the instructor. The instructor would then be able to easily assess the students’ understanding and provide feedback. • QuizStarshould be used at the conclusion of the lesson as a summative assessment tool. • QuizStar allows the instructor to create a “quiz” and automatically grade any multiple choice or true/false questions. This web-based program also allows the instructor to integrate various multimedia into the questions.**List of Resources**• Online graphing calculator: • http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html • LearnZillion: http://learnzillion.com • ShowMe: http://www.showme.com • Educreations: http://www.educreations.com • Prezi: http://prezi.com • PowerPoint: http://office.microsoft.com/en-us/powerpoint • Animoto: http://animoto.com • VoiceThread: http://voicethread.com • Edmodo: https://www.edmodo.com • Schoology: https://www.schoology.com/home.php • Moodle: https://moodle.org • Google site: https://sites.google.com**References**• Common Core State Standards Initiative. (2012). Retrieved from www.corestandards.org/Math/Content/8/EE • GreatSchools Staff. (2010). Why is algebra so important? In Academic Skills. Greatschools Inc. Retrieved from http://www.greatschools.org/students/academic-skills/354-why-algebra.gs?page=all • LearnZillion. (2013). Determine if a system of two linear equations in two variables has no solutions by graphing. [Online Video]. Retrieved from http://learnzillion.com/lessons/1018-determine-if-a-system-of-two-linear-equations-in-two-variables-has-no-solutions-by-graphing • LearnZillion. (2013). Determine if a system of two linear equations in two variables has infinitely many solutions by graphing. [Online Video]. Retrieved from http://learnzillion.com/lessons/1018-determine-if-a-system-of-two-linear-equations-in-two-variables-has-no-solutions-by-graphing