Solving Systems of Linear Equations by Graphing

# Solving Systems of Linear Equations by Graphing

## Solving Systems of Linear Equations by Graphing

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
##### Presentation Transcript

1. 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).

2. 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).

3. 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.

4. 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?

5. 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”

6. 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”

7. 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”