Module 2: Systems of Equations
Overview
This Module helps students to explore the process of solving systems of equations. Students will use mathematical representations to support the claim that atoms, and therefore mass, are conserved during a chemical reaction to make connections to solving systems of equations. Students will complete various activities from watching Youtube videos to completing Google Docs and FlipGrids explaining their rationale. Students will also read articles to analyze applications of solving systems of equations.
Systems of Equations
Module 2:
Systems of Equations
Teacher Version
- Each Lesson is made to be used within a 50 minute period.
- Each Module is made to be completed within a 5-day week.
- Each Module is based on some of the material from the Open Stax Elementary Algebra 2e: https://d3bxy9euw4e147.cloudfront.net/oscms-prodcms/media/documents/ElementaryAlgebra2e-WEB_1.pdf
- Some of the questions are based on this textbook: http://www.wallace.ccfaculty.org/book/Beginning_and_Intermediate_Algebra.pdf
- Google Classroom that supports these lessons can be accessed with code: lpazqtb
Standards:
Science:
HS-PSI-7- 7. Use mathematical representations to support the claim that atoms, and therefore mass, are conserved during a chemical reaction.
Technology:
EMPOWERED LEARNER 1C- Students use technology to seek feedback that informs and improves their practice and to demonstrate their learning in a variety of ways.
Mathematics:
CCSS.MATH.CONTENT.8.EE.C.7- Solve linear equations in one variable.
CCSS.MATH.CONTENT.8.EE.C.8- Analyze and solve pairs of simultaneous linear equations.
CCSS.MATH.CONTENT.HSA.REI.B.3- Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
CCSS.MATH.CONTENT.HSA.REI.C.5- Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
CCSS.MATH.CONTENT.HSA.REI.C.6- Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
CCSS.MATH.CONTENT.HSA.REI.C.8-(+) Represent a system of linear equations as a single matrix equation in a vector variable.
CCSS.MATH.CONTENT.HSA.REI.D.10- Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
CCSS.MATH.PRACTICE.MP2-Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP4-Model with mathematics.
CCSS.MATH.PRACTICE.MP6-Attend to precision.
Daily Outline:
Day 1:CREATING SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES
- (20 minutes) Students will read through an article about applying linear systems in reality.
- (30 minutes) Students will complete a worksheet that guides them through creating systems of equations. This is provided by a Google Doc.
Day 2: SOLVING SYSTEMS GRAPHICALLY
- (15 minutes) Students will watch a Youtube video introducing systems of equations being solved graphically. They should follow along and take notes.
- (35 minutes) Students will complete the alpine slide activity which guides them through creating a system of equations and solving it.
Day 3: SOLVING SYSTEMS BY COMBINATION
- (30 minutes) Students will follow along with the Emaze presentation based on the combination method. This includes watching a video at the end of the presentation that shows another example of this method.
- (20 minutes) Students will fill out their exit slip for the day in this Google Forms. It asks questions about applying the method to their life.
Day 4: SOLVING SYSTEMS BY SUBSTITUTION
- (10 minutes) Students will complete the warmup for solving systems by substitution. It includes prior knowledge from past lessons.
- (20 minutes) Students will follow along with a Youtube video about solving systems using substitution. Students will take notes.
- (20 minutes) Students will complete the substitution activity provided in the Google Doc below.
Day 5: LAB DAY
- (5 minutes) Students will watch a video I have created to show them how to set up a matrix from a system of equations.
- (10 minutes) Students will watch the Youtube video about balancing chemical equations using linear algebra.
- (35 minutes) Students will complete the Google Doc that will assess their application skills using linear algebra and matrices to solve systems of equations.