 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).
• 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.
• Absolute Value
This array of resources teaching absolute value includes warm-up problems, a video introducing the topic, worked examples, practice problems, and a review.
• 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).
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.
• 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.
• 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).
• Complex Square Roots
This Illustrative Mathematics task is intended as an introduction to the algebra of the complex numbers, and also builds student's comfort and intuition with these numbers.
• 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.
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 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.
• 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.
• How does the solution change?
The equations in this task are intentionally very simple; the point of the task is not to test technique in solving equations, but to encourage students to reason about them.
• Ideal Gas Law
The goal of this task is to interpret the graph of a rational function and use the graph to approximate when the function takes a given value.
• 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.
• IXL Game: Solve Two-Step Linear Equations
This game is designed to help the student understand how to solve two-step linear equations. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use.
• Linear Equations in One Variable
This tutorial is designed to help students understand how to solve linear equations by using the addition, subtraction, multiplication and division properties of equalities.
• 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.
• Linear Inequalities
This lesson contains an activity that allows students to use a coordinate plane to create linear inequalities.
• Module 1: Sequences - Student Edition (Math 1)
The Mathematics Vision Project, Secondary Math One Module 1, Sequences is written as two intertwined learning cycles that begin by alternating from arithmetic sequence to geometric sequences, so students can compare and contrast features as they represent both types of sequences with tables, graphs, story contexts, diagrams, and equations.
• Module 1: Sequences - Teacher Notes (Math 1)
The Mathematics Vision Project, Secondary Math One Module 1 Teacher Notes, Sequences is written as two intertwined learning cycles that begin by alternating from arithmetic sequence to geometric sequences, so students can compare and contrast features as they represent both types of sequences with tables, graphs, story contexts, diagrams, and equations.
• Module 3: Features of Functions - Student Edition (Math 1)
The Mathematics Vision Project, Secondary Math One Module 3, Features of Functions, is the culminating functions module in Secondary Math I. In this module, students broaden their thinking about functions to relationships that are not either linear or exponential.
• Module 3: Features of Functions - Teacher Notes (Math 1)
The Mathematics Vision Project, Secondary Math One Module 3 Teacher Notes, Features of Functions, is the culminating functions module in Secondary Math I. In this module, students broaden their thinking about functions to relationships that are not either linear or exponential.
• Module 4: Equations & Inequalities - Student Edition (Math 1)
The Mathematics Vision Project, Secondary Math One Module 4, Equations and Inequalities, students use units in combinations to define new variables for use in modeling with equations and inequalities, and interpret expressions that are the result of combining units.
• Module 4: Equations & Inequalities - Teacher Notes (Math 1)
The Mathematics Vision Project, Secondary Math One Module 4 Teacher Notes, Equations and Inequalities, students use units in combinations to define new variables for use in modeling with equations and inequalities, and interpret expressions that are the result of combining units.
• 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.
• 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.
• 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.
• 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.
• Population and Food Supply
In this task students construct and compare linear and exponential functions and find where the two functions intersect.
• Products and Reciprocals
The purpose of this task is to test student skill at converting verbal statements into two algebraic equations and then solving those equations
• 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.
• 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
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 linear inequalities
This problem is intended to detect the ability of the student to identify errors in mathematical reasoning, and to help students see the process of solving a equation or inequality is a special kind of proof.
• 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.
• Same solutions?
The purpose of this task is to provide an opportunity for students to look for structure when comparing equations and to reason about their equivalence.
• Secondary I Textbook
Secondary I Textbook is composed of modules that are aligned with the Utah Core State Standards for Mathematics. Each lesson begins with a worthwhile task that has been designed to develop mathematical understanding, solidify that understanding, or allow for practice of the new concepts, while focusing on the mathematical goals of the chosen learning cycle.
• 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.
• Solve Quadratic Expressions by Factoring video
This video introduces and explains the concept.
• Solving Absolute Value 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.
• Solving Absolute Value Equations video
This video explains how to solve absolute value expressions.
• 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 Equations video
Answers the questions "what are equations?" and "how do we solve them?"
• Solving Linear Equations in Two Variables
This lesson unit is intended to help educators assess how well students are able to formulate and solve problems using algebra.
• Solving Linear Inequalities
Students are helped to understand how to solve inequalities in this tutorial. Simple and more advanced problems are provided for practice.
• Solving Quadratic Equations by Completing the Square
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 Quadratic Equations by Factoring
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.
• Solving Quadratic Functions by Completing the Square video
This video introduces and explains 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.
• 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.
• 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
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.
• 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.
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.
In this task, students will look at the properties of a cubic equation.
• Systems of Non-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.
• Systems of Non-Linear Equations video
This video introduces and explains the topic.
• Two Squares are Equal
This classroom task is meant to elicit a variety of different methods of solving a quadratic equation.
• Writing and Using 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.
• Writing and Using Inequalities video
This video introduces and explains the topic.
• Writing, Solving and Graphing Inequalities in One Variable
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.
• Writing, Solving and Graphing Inequalities in One Variable video
This a video introduction and explanation of the topic.
• Zero Product Property 1
This task is the first in a series that leads students to understand and apply the zero product property to solving quadratic equations. The emphasis is on using the structure of a factorable expression in order to justify the steps in a solution (rather than memorizing steps without understanding).
• Zero Product Property 2
This task is part of a series of tasks that lead students to understand and apply the zero product property to solving quadratic equations. The emphasis is on using the structure of a factorable expression to help find its solutions (rather than memorizing steps without understanding).
• Zero Product Property 3
This task is part of a series of tasks that lead students to understand and apply the zero product property to solving quadratic equations. The emphasis is on using the structure of a factorable expression to help find its solutions (rather than memorizing steps without understanding).
• Zero Product Property 4
This task is the fourth in a series of tasks that leads students to understand The Zero Product Property (ZPP) and apply it to solving quadratic equations. The emphasis is on using the structure of a factorable expression to justify the solution method (rather than memorizing steps without understanding) 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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