###### Secondary Mathematics I [2011]
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Solve systems of equations.
Build on student experiences graphing and solving systems of linear equations from middle school to focus on justification of the methods used. Include cases where the two equations describe the same line (yielding infinitely many solutions) and cases where two equations describe parallel lines (yielding no solution); connect to GPE.5, which requires students to prove the slope criteria for parallel lines.
A.REI.6
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

• Can You Get to the Point, Too? - A Solidify Understanding Task
Solving systems of linear equations by elimination (A.REI.5, A.REI.6) This task solidifies the strategies for solving systems of equations. Students will begin by writing a system of equations to represent the shopping scenarios. Students will recognize that we can obtain an equivalent system of equations by replacing one or both equations in the system. Systems of Equations and Inequalities Module - Task 8
• Can You Get to the Point, Too? - Teacher Notes
Teacher Notes for the task "Can You Get to the Point, Too?" (A.REI.5, A.REI.6) Systems of Equations and Inequalities Module - Task 8
• Everything Balances Out in the End
In this unit of three lessons, from Illuminations, students use a pan balance to study equality, order of operations, numerical and variable expressions and other key algebraic concepts.
• Get to the Point! - A Solidify Understanding Task
Solving systems of linear equations in two variables (A.REI.6) This task is designed to solidify graphical, numerical and algebraic strategies for solving a system of two linear equations. Systems of Equations and Inequalities Module - Task 6
• Get to the Point! - Teacher Notes
Teacher Notes for the "Get to the Point!" task. (A.REI.6) Systems of Equations and Inequalities Module - Task 6
• Linear Functions
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Linear Functions video
This video compares proportional and non-proportional linear functions.
• Mixture Problems
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Mixture Problems video
This video introduces and explains the concept.
• Rate Problems
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Rate Problems video
This video introduces the explains the topic.
• Reasoning with Equations and Inequalities
The Utah State Office of Education (USOE) and educators around the state of Utah developed these guides for the Secondary Mathematics 1 Cluster "Understand solving equations as a process of reasoning and explain the reasoning" / Standard A.REI.1 and Cluster "Solve equations and inequalities in one variable" / Standard A.REI.3 and Cluster "Solve systems of equations" / Standards A.REI.5 and A.REI.6.
• Shopping for Cats and Dogs - A Develop Understanding Task
An introduction to solving systems of linear equations by elimination (A.REI.5, A.REI.6) Systems of Equations and Inequalities Module - Task 7
• Shopping for Cats and Dogs - Teacher Notes
Teacher Notes for "Shopping for Cats and Dogs" task. (A.REI.5, A.REI.6) Systems of Equations and Inequalities Module - Task 7
• Solving Systems of Equations by Graphing
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Solving Systems of Linear Equations by Elimination
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Solving Systems of Linear Equations by Elimination video
This video introduces and explains the concept.
• Solving Systems of Linear Equations by Graphing
This is a video introduction and explanation of the topic.
• Solving Systems of Linear Equations by Substitution
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Solving systems of Linear Equations by Substitution video
This is a video introduction and explanation of the topic.
• Taken Out of Context - A Practice Understanding Task
Working with systems of linear equations, including inconsistent and dependent systems (A.REI.6) Systems of Equations and Inequalities Module - Task 10
• Taken Out of Context - Teacher Notes
Teacher Notes for "Taken Out of Context" task. (A.REI.6) Systems of Equations and Inequalities Module - Task 10

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