 Secondary Mathematics I

Strand: ALGEBRA - Reasoning With Equations and Inequalities (A.REI)

Understand solving equations as a process of reasoning and explain the reasoning (Standard A.REI.1). Solve equations and inequalities in one variable (Standard A.REI.3). Solve systems of equations. Build on student experiences graphing and solving systems of linear equations from middle school. 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 (Standards A.REI.5-6). Represent and solve equations and inequalities graphically (Standards A.REI.10-12).

Standard A.REI.6

Solve systems of linear equations exactly and approximately (numerically, algebraically, graphically), focusing on pairs of linear equations in two variables.

• Accurately weighing pennies I
This task asks students to solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
• Accurately weighing pennies II
This task is a somewhat more complicated version of ''Accurately weighing pennies I'' as a third equation is needed in order to solve part (a) explicitly.
• ALGEBRA - Reasoning With Equations and Inequalities (A.REI) - Sec Math I Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for the Secondary Mathematics I - Reasoning with Equations and Inequalities (A.REI).
• Cash Box
The purpose of this task is to gives students an opportunity to engage in Mathematical Practice #3 Construct viable arguments and critique the reasoning of others. This task gives a teacher the opportunity to ask students not only for a specific answer of whether the dollar came from in the cash box or not, but for students to construct an argument as to how they came to their solution.
• Estimating a Solution via Graphs
The purpose of this task is to give students an opportunity use quantitative and graphical reasoning to detect an error in a solution.
• Find A System
The purpose of this task is to encourage students to think critically about both the algebraic and graphical interpretation of systems of linear equations. They are expected to take what they know about solving systems of linear equations, and then reverse the usual process.
• Introduction to the Materials (Math 1)
Introduction to the Materials in the Mathematics One of the The MVP classroom experience begins by confronting students with an engaging task and then invites them to grapple with solving it. As students ideas emerge, take form, and are shared, the teacher orchestrates the student discussions and explorations towards a focused mathematical goal. As conjectures are made and explored, they evolve into mathematical concepts that the community of learners begins to embrace as effective strategies for analyzing and solving problems.
• 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.
• Module 5: Systems of Equations & Inequalities - Student Edition (Math 1)
The Mathematics Vision Project, Secondary Math One Module 5, Systems of Equations and Inequalities, has two learning cycles, built around a common story context that is used throughout the module. The first learning cycle begins by making the representations, tables, graphs, equations, and diagrams, needed for the rest of the module available.
• Module 5: Systems of Equations & Inequalities - Teacher Notes (Math 1)
The Mathematics Vision Project, Secondary Math One Module 5 Teacher Notes, Systems of Equations and Inequalities, has two learning cycles, built around a common story context that is used throughout the module. The first learning cycle begins by making the representations, tables, graphs, equations, and diagrams, needed for the rest of the module available.
• Pairs of Whole Numbers
This task addresses solving systems of linear equations exactly, and provides a simple example of a system with three equations and three unknowns.
• Quinoa Pasta 2
This task is a variant of 8.EE Quinoa Pasta 1, where all the relevant information is given as part of the task statements and the students are asked to set up a system of equations.
• Quinoa Pasta 3
This task is an example of a mathematical modeling problem (SMP 4) and it also illustrates SMP 1 (Making sense of a problem). This task is a variant of 8.EE Quinoa Pasta 1 and A-REI.6 Quinoa Pasta 2.
• Rate Problems video
This video introduces the explains the topic.
• Solving Rational Expressions video
This video introduces and explains the topic.
• 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 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 Two Equations in Two Unknowns
The goal of this task is to help students see the validity of the elimination method for solving systems of two equations in two unknowns. http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Lindsey  Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer  Throndsen.

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