Secondary Mathematics III

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

Understand solving equations as a process of reasoning and explain the reasoning (Standard A.REI.2). Represent and solve equations and inequalities graphically (Standard A.REI.11).
• ALGEBRA - Reasoning with Equations and Inequalities (A.REI) - Sec Math III Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for the Secondary Mathematics III - Reasoning with Equations and Inequalities (A.REI).
• An Extraneous Solution
The goal of this task is to examine how extraneous solutions can arise when solving rational 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.
This video introduces and explains the topic.
• Applying Rational 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.
• Applying Rational Equations video
This video introduces and explains the topic.
This task provides a simple but interesting and realistic context in which students are led to set up a rational equation (and a rational inequality) in one variable, and then solve that equation/inequality for an unknown variable.
• Canoe Trip
The goal of this task is to set up and solve an equation involving a simple rational expression.
• GeoGebra
GeoGebra is dynamic online geometry software. Constructions can be made with points, vectors, segments, lines, polygons, conic sections, inequalities, implicit polynomials and functions. All of them can be changed dynamically afterwards.
• Integer Solutions to Inequality
This task asks students to solve equations and inequalities in one variable.
• Introduction to Polynomials - College Fund
This task could serve as an introduction to polynomials or as an application after students are familiar with this type of function.
• Introduction to the Materials (Math 3)
Introduction to the Materials in the Mathematics Three 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.
• Module 4: Rational Expressions and Functions - Student Edition (Math 3)
The Mathematics Vision Project, Secondary Math Three Module 4, Rational Expressions and Functions, students work with the fractions that are ratios of polynomials, rational expressions and functions.
• Module 4: Rational Expressions and Functions - Teacher Edition (Math 3)
The Mathematics Vision Project, Secondary Math Three Module 4, Rational Expressions and Functions, students work with the fractions that are ratios of polynomials, rational expressions and functions.
• Optimization Problems: Boomerangs
This lesson unit is intended to help educators assess how well students are able to interpret a situation and represent the constraints and variables mathematically, select appropriate mathematical methods to use, explore the effects of systematically varying the constraints, and interpret and evaluate the data generated and identify the optimum case, checking it for confirmation.
The purpose of the task is to show students a situation where squaring both sides of an equation can result in an equation with more solutions than the original one.
• Solving a Simple Cubic Equation
The purpose of this task is twofold. First, it prompts students to notice and explain a connection between the factored form of a polynomial and the location of its zeroes when graphed. Second, it highlights a complication that results from a seemingly innocent move that students might be tempted to make: "dividing both sides by x."
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.