ALEX Lesson Plan

     

Solving Systems of Linear Equations -- Part 2 Substitution

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  This lesson provided by:  
Author:Morgan Boyd
Organization:Retirement
  General Lesson Information  
Lesson Plan ID: 35621

Title:

Solving Systems of Linear Equations -- Part 2 Substitution

Overview/Annotation:

This lesson is the second part of solving systems of linear equations. The lesson will be taught in one class period. The concept for the lesson is to solve one equation in terms of "x" or "y" and substitute the results into the other equation. Calculating the final solution to the system will take a few more steps. This lesson will describe the remaining steps as well as examples to follow. 

This lesson results from the ALEX Resource Gap Project.

 Associated Standards and Objectives 
Content Standard(s):
Mathematics
MA2015 (2016)
Grade: 8
10 ) Analyze and solve pairs of simultaneous linear equations. [8-EE8]

a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersections of their graphs because points of intersection satisfy both equations simultaneously. [8-EE8a]

b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. [8-EE8b]

Example: 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

c. Solve real-world and mathematical problems leading to two linear equations in two variables. [8-EE8c]

Example: Given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.


NAEP Framework
NAEP Statement::
8A4a: Solve linear equations or inequalities (e.g., ax + b = c or ax + b = cx + d or ax + b > c).

NAEP Statement::
8A4c: Analyze situations or solve problems using linear equations and inequalities with rational coefficients symbolically or graphically (e.g., ax + b = c or ax + b = cx + d).



Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.8.10 - Identify the labeled point of intersection on graphs of two linear equations as a solution for both equations.


Local/National Standards:

 

Primary Learning Objective(s):

The student will be able to solve systems of linear equations using the substitution property.

Additional Learning Objective(s):

The student will be able to solve multi-step equations with one variable.

The student will be able to determine if the system of linear equations will have a solution.

 Preparation Information 

Total Duration:

31 to 60 Minutes

Materials and Resources:

Notebook

Pencil

Calculator 

Websites:

https://www.desmos.com/calculator

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-systems-topic/cc-8th-systems-with-substitution/v/the-substitution-method

Devices:

iPad, Chromebook, or MacBook for every student

Worksheets:

Bell Ringer Substitution -- for the interactive whiteboard -- attachment section

Equations by Substitution -- make copies for all students -- attachment section

Exit Slip Substitution --  for the interactive whiteboard -- attachment section

Accelerated Systems of Equations -- make copies for accelerated students -- attachment section

Technology Resources Needed:

Desktop computer with interactive whiteboard for teacher

https://www.desmos.com/calculator

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-systems-topic/cc-8th-systems-with-substitution/v/the-substitution-method

 iPad, Chromebook, or MacBook for every student -- to graph the lines to check for accuracy

 

Background/Preparation:

Teacher:

The lesson will be taught in one class period. The teacher will need to preview the video from Khan Academy. The website has many example problems, and the teacher can use as many as necessary. This lesson needs to be taught after introducing the first part of the lesson, "System of Equations -- Part 1 Graphing." 

Student:

The student will need to know how to solve multi-step equations. When an equation has two variables, the student will need to know how to solve in terms of one variable. The student will need to be familiar with the Substitution Property. The substitution property of equality states that if x = y, then x can be substituted in for y in any equation, and y can be substituted for x in any equation. The following is an example:

x = 2 and y = 4

2x + 3y -8

evaluate .... 2(2) + 3(4) - 8 = 4 + 12 - 8 = 8

Substitution means to replace the variable in one equation with what the variable is equal to from the other equation.

  Procedures/Activities: 

Before:

As students enter the room, the teacher will display the bell ringer on the interactive whiteboard. The students will write their answers on their own paper. The teacher will make an informal assessment. Students must be able to solve multi-step equations in order to solve systems of equations by substitution. The teacher will solicit students to answer the bell ringer.

During:

*The lesson will be taught in one class period.*

1. The teacher will start the video from Khan Academy: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-systems-topic/cc-8th-systems-with-substitution/v/the-substitution-method.

2. The teacher can show many types of examples. The website has lines in standard form as well as y-intercept form. The teacher will stop the video and revisit the concept of solving in terms of "y" or "x".

Example:

3x + 6y = -9

3x + 6y - 6y = -9 - 6y subtract 6y from both sides

3x = -6y - 9  put the "y" term in front

3x/3 = -6y/3 - 9/3  divide everything by 3

x = -2y - 3 solved for "x" in terms of "y"

3. The teacher will do an informal assessment to check for understanding. The teacher will start the video again.

4. As the video finishes the last example, the teacher will open the website, DESMOS.com (https://www.desmos.com/calculator). The teacher will type in the two equations and see where the two lines cross. The teacher will show the students that the solution will be the same. The teacher will tell the students that the method does not change the solution.

5. The teacher will hand out the worksheet, "Equations by Substitution" from the attachment section. The teacher will allow the students to work in groups with at least two technology devices. The students must show their work. One of the students in the group will use online graphing tool to check the answers. The teacher will monitor the groups and their discussions. The teacher may extend the time for some groups or assign a peer-tutor.

6. The teacher will check for understanding by asking the groups to work the problems on the interactive whiteboard.

*The lesson concludes day 2 and the next day will be elimination.*

After:

The teacher will display the exit slip from the attachment section on the interactive whiteboard. The students will answer on their own paper and turn in when they leave the room.



Attachments:
**Some files will display in a new window. Others will prompt you to download.
  Assessment  

Assessment Strategies

Informal:

The teacher will assess the students' understanding with the bell ringer and the video. The teacher will monitor the students in the groups to check for accurate use of terminology as well as comprehension of the mathematical concept.

Formal:

The teacher will use the exit slip for the formal assessment. The student will show all the work to explain the solution.

Acceleration:

The accelerated students will have a challenging worksheet to complete. The assignment is in the attachment section called "Challenging Equations". 

Intervention:

The teacher will place students in groups of 4. The teacher will assign a peer-tutor. The teacher will let the groups use a technological device. The student will use the online graphing website to check their answers. The teacher can extend the time or shorten the number of problems.


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.