Secondary Mathematics I
Educational Links

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.12

Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

• 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).
• Fishing Adventures 3
  This task is the last in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Students write and solve inequalities, and represent the solutions graphically.
• Graphing Systems of Inequalities
  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.
• Graphing Systems of Inequalities video
  This video introduces and explains the topic.
• 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 Inequalities
  This lesson contains an activity that allows students to use a coordinate plane to create linear inequalities.
• 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.
• Perpendicular Lines video
  This video introduces and explains perpendicular lines.
• Representing Inequalities Graphically
  This lesson unit is intended to help educators assess how well students are able to use linear inequalities to create a set of solutions.
• Solution Sets
  The purpose of this task is to give students a chance to go beyond the typical problem and make the connections between points in the coordinate plane and solutions to inequalities and equations.
• Solving and Graphing Linear Inequalities in Two Variables
  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 and Graphing Linear Inequalities in Two Variables video
  This video introduces and explains the concept.
• Solving Rational Expressions video
  This video introduces and explains the topic.
• Stairway - Student Task
  This task students to design a stairway for a custom home. They will need to gather information regarding design, safety, and the utility of staircases.
• Student Task: Cubic Graph
  In this task, students will look at the properties of a cubic equation.

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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.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.