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.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).

• A Linear and Quadratic System
The purpose of this task is to give students the opportunity to make connections between equations and the geometry of their graphs. They must read information from the graph (such as the vertical intercept of the quadratic graph or the slope of the linear one), use that information to construct and solve an equation, then interpret their solution in terms of the graph.
• 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).
• Collinear points
This task leads students through a series of problems which illustrate a crucial interplay between algebra (e.g., being solutions to equations) and geometry (e.g., being points on a curve).
• Graphing Equations in Slope Intercept Form
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 Equations in Slope Intercept Form Video
This is a video introduction to the topic.
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.
This video introduces and explains the topic.
• Intercepts of Linear Equations
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.
• Intercepts of Linear Equations video
This video introduces 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 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.
• Non-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.
• Non-linear Functions video
This video introduces non-linear functions.
• Parallel Lines
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.
• Parallel Lines video
This video explains the concept.
• Perpendicular Lines
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.
• Perpendicular Lines video
This video introduces and explains perpendicular lines.
• Point Slope Form and Standard Form of Linear Equations
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.
• Point Slope Form and Standard Form of Linear Equations video
This a video explanation of the topic.
• Proportional 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.
• Proportional Functions video
This video introduces proportional functions.
• 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.