ALEX Lesson Plan

     

Systems of Equations Part 3 -- Solving by Elimination

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  This lesson provided by:  
Author:Morgan Boyd
Organization:Retirement
  General Lesson Information  
Lesson Plan ID: 35662

Title:

Systems of Equations Part 3 -- Solving by Elimination

Overview/Annotation:

This lesson will be completed in one class period. This lesson, the third in the series, will focus on another way of solving linear systems, the elimination method. When using this method, the students will multiply one or both of equations to make one of the variables equal. Afterward, the students will add the equations to eliminate the variable.  

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 equation
Knowledge:
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 solve systems of equations using the elimination method.

Additional Learning Objective(s):

The student will write linear equations in standard form.

 Preparation Information 

Total Duration:

31 to 60 Minutes

Materials and Resources:

Technology Resources Needed:

Background/Preparation:

Teacher:

Solving systems of linear equations by graphing and solving systems of linear equations by substitution should have been taught prior to teaching this lesson. This lesson will be taught in one class period. The teacher will need to preview the PowerPoint presentations.

Student:

The student needs to know how to write linear equations in standard form, Ax + By = C. The student will need to know the definitions of the following terms: coefficients, eliminate, opposites, and solution. The terms and definitions will be included on the bell ringer.

  Procedures/Activities: 

Before:

The teacher will have the bell ringer on the interactive whiteboard as the students enter the room. The document, Bell Ringer Elimination, is located in the attachment section. The answers are on the second page. The student will write the answers in their notebooks. The teacher will call on students to answer the definitions for elimination and solution. The teacher will select students to write the lines in standard form.

 

During:

  1. The teacher will show the video for solving by elimination. (https://www.youtube.com/watch?v=8kRG7jlBMAY)
  2. The teacher can post the two PowerPoint presentations in Google Classroom. The students will be able to use the presentations with the exercises in their groups and follow along with the teacher as the lesson is presented.
  3. The teacher will open the PowerPoint presentation, “Systems Add or Minus”. 
  4. The teacher will go slowly through the examples. While explaining the examples, the teacher can do another informal assessment. The teacher does not continue the slides until all students are ready.
  5. After “Systems Add or Minus”, the teacher will open the presentation, “Systems Multiplication”. 
  6. The teacher will explain each example thoroughly. The presentation has informal assessments in the slides.
  7. The teacher will hand out the worksheet from the website, Kuta Software. (https://cdn.kutasoftware.com/Worksheets/Alg1/Systems%20of%20Equations%20Elimination.pdf)
  8. The teacher will put students in groups of four students. The students can use their devices to watch the presentations from Google Classroom to assist in answering the questions on the worksheet. The groups can have a peer-tutor to help intervention students. The worksheet will be an informal assessment tool.
  9. The teacher will do a one-on-one intervention with the groups.
  10. The teacher will ask students to work problems on the interactive whiteboard.

After:

The teacher will hand out the exit slip, “Exit Elimination”. The students will turn in the exit slip as they leave the classroom. The teacher will use the exit slip as the formal assessment. 



Attachments:
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  Assessment  

Assessment Strategies

Informal Assessments:

The teacher will check for understanding of the standard form of a line during the bell ringer.

The teacher will check for understanding during both PowerPoint presentations.

The teacher will use the worksheet from Kuta Software to assess student understanding of solving systems of equations using elimination. 

Formal Assessment:

The teacher will use the exit slip and an overall summation of the lesson in its entirety to formally assess students. 

Acceleration:

The teacher will assign the worksheet, "ACC Elimination". The worksheet has more challenging coefficients and multiplication with both linear equations. The answers are on page two.

Intervention:

The teacher will have copies of the PowerPoint slides for the students. The teacher will allow students to be in groups with a peer-tutor. The teacher will monitor and assist students one-on-one.


View the Special Education resources for instructional guidance in providing modifications and adaptations for students with significant cognitive disabilities who qualify for the Alabama Alternate Assessment.