Download Unit 3: Systems of Linear Equations Algebra II Essential Questions

Unit 3: Systems of Linear Equations
Algebra II
3 Weeks
Essential Questions
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How does representing functions graphically help you solve a system of equations?
How does writing equivalent equations help you solve a system of equations?
Enduring Understandings
1. To solve a system of equations, find a set of values that replace the variables in the
equations and make each equation true.
2. You can solve a system of equations by writing equivalent systems until the value on one
variable is clear. Then substitute to find the values of the other variables.
3. You can solve a system of inequalities in more than one way. Graphing the solution is
usually the most appropriate method. The solution is the set of all points that are solutions
of each inequality in the system.
Content
Students will know…
Topics (Pearson):
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(3-1) Solving Systems Using Tables/ Graphs
(3-2) Solving Systems Algebraically
(3-3) Solving Systems of Inequalities
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The graphical representation of one
solution, no solution and infinitely
many solutions.
Substitution Method
Elimination Method
Graphing Inequalities
Unit 3: Systems of Linear Equations
Algebra II
3 Weeks
21st Learning Expectations
Students will be able to…
 Employ mathematical problem solving skills effectively.
 Make decisions and solve problems in independent and collaborative settings.
21st Century Learning Skills
Students will be able to…
 ML #1 – Make sense of problems and persevere in solving them.
 ML #2 – Reason abstractly and quantitatively.
 ML #3 – Construct viable arguments and critique the reasoning of others.
 ML #4 – Model with mathematics.
 ML #5 – Use appropriate tools strategically.
 ML #6 – Attend to precision.
 ML #7 – Look for and make use of structure.
Connecticut State Standards
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A-CED 3. Represent constraints by equations or inequalities, and by systems of equations
and/ or inequalities, and interpret solutions as viable or nonviable options in a modeling
context.
A-REI 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.
A-REI 6. Solve systems of linear equations exactly and approximately, focusing on pairs
of linear equations in two variables.
A-REI 11. Explain why the x-coordinate of the points where the graphs of y=f(x) and y
=g(x) intersect are the solutions of the equation f(x)=g(x); find the solutions
approximately, or find successive approximations.
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Unit 3: Systems of Linear Equations
Algebra II
3 Weeks
Objectives
Students will be able to…
 Use a table to solve a system of linear equations.
 Graph a system of linear equations to identify a solution as one solution, no solution, or
infinitely many solutions.
 Apply the substitution method to solve a system of linear equations.
 Apply the elimination method to solve a system of linear equations.
 Choose the best method to create and solve a system of linear equations.
 Graph a system of inequalities and identify the solution set.
Assessments
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Quiz EU1 – Using a Table and Graph
Quiz EU2 – Substitution and Elimination Method
Quiz EU3 – Systems of Inequalities
Unit Test – Linear Systems
Resources
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Charles, R., Hall, B., Kennedy, D., Bass, L., Johnson, A., Murphy, S., et al. (2012).
Algebra 2: Common Core. Boston: Pearson.
Graphing Calculator
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