# ALEX Lesson Plan

## System of Equations -- Part I Graphing

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This lesson provided by:
 Author: Morgan Boyd Organization: Retirement
General Lesson Information
 Lesson Plan ID: 35613 Title: System of Equations -- Part I Graphing Overview/Annotation: Systems of Equations will be taught over a three-day period: the first day will include a lesson regarding equations that can be solved by graphing, the second day will include a lesson regarding equations that can be solved by substitution, and the third day will include a lesson regarding equations that can be solved by elimination. The students will graph two lines on the same coordinate axis and determine where the two lines cross. The teacher will be able to rock the teenage world with the website "DESMOS". Solving the equations graphically will enhance the graphing skill of the students. The lesson will explain all the ways to graph a line.This lesson results from the ALEX Resource Gap Project.
Associated Standards and Objectives
Content Standard(s):
 Mathematics MA2019 (2019) Grade: 8 12. Solve systems of two linear equations in two variables by graphing and substitution. a. Explain that the solution(s) of systems of two linear equations in two variables corresponds to points of intersection on their graphs because points of intersection satisfy both equations simultaneously. b. Interpret and justify the results of systems of two linear equations in two variables (one solution, no solution, or infinitely many solutions) when applied to real-world and mathematical problems. Unpacked Content Evidence Of Student Attainment:Students: Graph a system of two linear equations, recognizing that the ordered pair for the point of intersection is the x-value that will generate the given y-value for both equations. Recognize that graphed lines with one point of intersection (different slopes) will have one solution, parallel lines (same slope, different y-intercepts) have no solutions, and lines that are the same (same slope, same y-intercept) will have infinitely many solutions. Use substitution to solve a system, given two linear equations in slope-intercept form or one equation in standard form and one in slope-intercept form. Make sense of their solutions by making connections between algebraic and graphical solutions and the context of the system of linear equations.Teacher Vocabulary:System of linear equations Point of intersection One solution No solution Infinitely many solutions Parallel lines Slope-intercept form of a linear equation Standard form of a linear equationKnowledge:Students know: The properties of operations and equality and their appropriate application. Graphing techniques for linear equations (using points, using slope-intercept form, using technology). Substitution techniques for algebraically finding the solution to a system of linear equations.Skills:Students are able to: generate a table from an equation. Graph linear equations. Identify the ordered pair for the point of intersection. Explain the meaning of the point of intersection (or lack of intersection point) in context. Solve a system algebraically using substitution when both equations are written in slope-intercept form or one is written in standard form and the other in slope-intercept form.Understanding:Students understand that: any point on a line when substituted into the equation of the line, makes the equation true and therefore, the intersection point of two lines must make both equations true. Graphs and equations of linear relationships are different representations of the same relationships, but reveal different information useful in solving problems, and allow different solution strategies leading to the same solutions.Diverse Learning Needs: Essential Skills:Learning Objectives: M.8.12.1: Define variables. M.8.12.2: Recall how to estimate. M.8.12.3: Recall how to solve linear equations. M.8.12.4: Demonstrate how to graph solutions to linear equations. M.8.12.5: Recall how to graph ordered pairs on a Cartesian plane. M.8.12.6: Recall that linear equations can have one solution (intersecting), no solution (parallel lines), or infinitely many solutions (graph is simultaneous). M.8.12.7: Define simultaneous. M.8.12.8: Recall how to solve linear equations. M.8.12.9: Recall properties of operations for addition and multiplication. M.8.12.10: Discover that the intersection of two lines on a coordinate plane is the solution to both equations. M.8.12.11: Define point of intersection. M.8.12.12: Recall how to solve linear equations. M.8.12.13: Demonstrate how to graph on the Cartesian plane. M.8.12.14: Identify ordered pairs. M.8.12.15: Recall how to solve linear equations in two variables by using substitution. M.8.12.16: Create a word problem from given information. M.8.12.17: Recall how to solve linear equations. M.8.12.18: Explain how to write an equation to solve real-world mathematical problems. Prior Knowledge Skills:Define quadrant, coordinate plane, coordinate axes (x-axis and y-axis), horizontal, vertical, and reflection. Demonstrate an understanding of an extended coordinate plane. Draw a four-quadrant coordinate plane. Draw and extend vertical and horizontal number lines. Interpret graphing points in all four quadrants of the coordinate plane in real-world situations. Recall how to graph points in all four quadrants of the coordinate plane. Alabama Alternate Achievement Standards AAS Standard: M.AAS.8.12 Solve two-step linear equations where coefficients are less than 10 and answers are integers.

Local/National Standards:

Primary Learning Objective(s):

The student will be able to determine the solution to the system of equations by graphing.

The student will be able to explain if two lines will intersect, are parallel, or are the same line.

The student will be able to graph linear equations using slope intercept form.

The student will be able to graph a linear equation using x- and y-intercepts.

Preparation Information