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Solving Systems of Linear Equations by Graphing

Solving Systems of Linear Equations by Graphing. STORYBOARDS. Purpose Statement.

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Solving Systems of Linear Equations by Graphing

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  1. Solving Systems of Linear Equations by Graphing STORYBOARDS

  2. 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). • 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).

  3. 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 two or three days of instruction and one day of summative assessment. • Students should have the following pre-requisite skills: • Write an equation to model a situation in slope-intercept form • Graph a linear equation in slope-intercept form

  4. Learning Objectives • Using a pencil and graph paper, students will be able to graph two linear equations on the same coordinate plane and find their point of intersection. • Using 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.

  5. Learning Activity #1 Onscreen Content Supporting Information Time Frame: 10-15 minutes Location: Classroom This is an introduction to the lesson to capture the attention of the students. The instructor should guide the students in writing a linear equation for MusicMania and for HitMusic. The instructor should then guide the students in graphing both linear equations on the same coordinate plane. A class discussion should then occur about what the lines on the graph represent and what their point of intersection represents. 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?

  6. Learning Activity #2 Onscreen Content Supporting Information Time Frame: 10-15 minutes Location: Classroom Levels of Bloom’s (Revised): Remembering, Understanding, Applying, Analyzing, Evaluating Both examples should provide the equations in slope-intercept form. 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”

  7. Learning Activity #3 Onscreen Content Supporting Information Time Frame: 20-25 minutes Location: Computer Lab Levels of Bloom’s (Revised): Understanding, Applying, Analyzing Technology: Students should use the online graphing calculator from this link: http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html Some initial instruction on how to enter the equations and find the intersection point may be required. The use of this technology will allow students to focus on finding the solution to the system of equations instead of the precision and time that is needed when graphing linear equations using pencil and paper. This technology also allows students to find the solution with an accurate decimal approximation when the solution has non-integer values as opposed to the estimating that occurs with paper and pencil. 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 their point of intersection. • “Example 1” • “Example 2” • “Example 3”

  8. Learning Activity #4 Onscreen Content Supporting Information Time Frame: 20 minutes Location: Computer Lab Levels of Bloom’s (Revised): Remembering, Understanding, Applying, Analyzing Technology: Students should use the online graphing calculator to graph each system of equations. Problem 3 should require students to write two linear equations with the same slope. Therefore, the lines will be parallel and there will be no solution. Problem 4 should require students to write the same linear equation. Therefore, the they will be the same line and have infinite solutions. 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”

  9. Learning Activity #5 Onscreen Content Supporting Information Time Frame: 15 minutes total (video is 5 minutes long) Location: Computer Lab Levels of Bloom’s (Revised): Remembering, Understanding, Applying, Analyzing 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?

  10. Learning Activity #6 Onscreen Content Supporting Information Time Frame: 15 minutes total (video is 5 minutes long) Location: Computer Lab Levels of Bloom’s (Revised): Remembering, Understanding, Applying, Analyzing 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?

  11. Evaluation/Assessment • 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. • GoogleDocs is 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. • QuizStar should 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.

  12. 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

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