Curriculum and Instruction – Mathematics

Quarter 2 Bridge Math

Introduction

In 2014, the Shelby County Schools Board of Education adopted a set of ambitious, yet attainable goals for school and student performance. The District is committed to these goals, as further described in our strategic plan, Destination2025. By 2025,

80% of our students will graduate from high school college or career ready 90% of students will graduate on time 100% of our students who graduate college or career ready will enroll in a post-secondary opportunity

In order to achieve these ambitious goals, we must collectively work to provide our students with high quality, college and career ready aligned instruction. The Tennessee State Standards provide a common set of expectations for what students will know and be able to do at the end of a grade. College and career readiness is rooted in the knowledge and skills students need to succeed in post-secondary study or careers. The TN State Standards represent three fundamental shifts in mathematics instruction: focus, coherence and rigor.

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Focus

The Standards call for a greater focus in mathematics. Rather than racing to cover topics in a mile-wide, inch-deep curriculum, the Standards require us to significantly narrow and deepen the way time and energy is spent in the math classroom. We focus deeply on the major concepts of each subject so that students can gain strong foundations: solid conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the math classroom. For Bridge Math, account for 65-75% of time spent on the major conccepts of algebra 1, geometry and algebra 2.The supporting and additional content from algebra 1, geometry and algebra 2 are incorporated into the subject to provide more understanding about the major concepts of those courses.

Coherence

Thinking across grades/courses:learning of mathematics is carefully connected across grades and subjects so that students can build new understanding on to foundations built in previous years. Each standard is not a new event, but an extension of previous learning. Linking to major topics:Instead of allowing additional or supporting topics to detract from the focus of the grade, these concepts serve the grade/subject level focus.

Rigor

Conceptual understanding: The Standards call for conceptual understanding of key concepts, such as place value and ratios. Students must be able to access concepts from a number of perspectives so that they are able to see math as more than a set of mnemonics or discrete procedures. Procedural skill and fluency: The Standards call for speed and accuracy in calculation. Students are given opportunities to practice core functions such as solving one-and two-step equations so that they have access to more complex concepts and procedures.Application: The Standards call for students to use math flexibly for applications in problem-solving contexts. In content areas outside of math, particularly science, students are given the opportunity to use math to make meaning of and access content.

Curriculum and Instruction – Mathematics

Quarter 2 Bridge Math

The Standards for Mathematical Practice describe varieties of expertise, habits of minds and productive dispositions that mathematics educators at all levels should seek to develop in their students. These practices rest on important National Council of Teachers of Mathematics (NCTM) “processes and proficiencies” with longstanding

importance in mathematics education. Throughout the year, students should continue to develop proficiency with the eight Standards for Mathematical Practice.

This curriculum map is designed to help teachers make effective decisions about what mathematical content to teach so that, ultimately our students, can reach Destination 2025. To reach our collective student achievement goals, we know that teachers must change their practice so that it is in alignment with the three mathematics instructional shifts.

Throughout this curriculum map, you will see resources as well as links to tasks that will support you in ensuring that students are able to reach the demands of the standards in your classroom. In addition to the resources embedded in the map, there are some high-leverage resources around the content standards and mathematical practice standards that teachers should consistently access:

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The TN Mathematics StandardsThe Tennessee Mathematics Standards:https://www.tn.gov/education/article/mathematics-standards

Teachers can access the Tennessee State standards, which are featured throughout this curriculum map and represent college and career ready learning at reach respective grade level.

Standards for Mathematical PracticeMathematical Practice Standardshttps://drive.google.com/file/d/0B926oAMrdzI4RUpMd1pGdEJTYkE/view

Teachers can access the Mathematical Practice Standards, which are featured throughout this curriculum map. This link contains more a more detailed explanation of each practice along with implications for instructions.

Purpose of the Mathematics Curriculum Maps

This curriculum framework or map is meant to help teachers and their support providers (e.g., coaches, leaders) on their path to effective, college and career ready (CCR) aligned instruction and our pursuit of Destination 2025. It is a resource for organizing instruction around the TN State Standards, which define what to teach and what students need to learn at each grade level. The framework is designed to reinforce the grade/course-specific standards and content—the major work of the grade (scope)—and provides a suggested sequencing and pacing and time frames, aligned resources—including sample questions, tasks and other planning tools. Our hope is that by curating and organizing a variety of standards-aligned resources, teachers will be able to spend less time wondering what to teach and searching for quality materials (though they may both select from and/or supplement those included here) and have more time to plan, teach, assess, and reflect with colleagues to continuously improve practice and best meet the needs of their students.

The map is meant to support effective planning and instruction to rigorous standards; it is not meant to replace teacher planning or prescribe pacing or instructional practice. In fact, our goal is not to merely “cover the curriculum,” but rather to “uncover” it by developing students’ deep understanding of the content and mastery of the standards. Teachers who are knowledgeable about and intentionally align the learning target (standards and objectives), topic, task, and needs (and assessment) of the learners are best-positioned to make decisions about how to support student learning toward such mastery. Teachers are therefore expected--with the support of their colleagues, coaches, leaders, and other support providers--to exercise their professional judgement aligned to our shared vision of effective instruction, the Teacher Effectiveness Measure (TEM) and related best practices. However, while the framework allows for flexibility and encourages each teacher/teacher team to make it their own, our expectations for student learning are non-negotiable. We must ensure all of our children have access to rigor—high-quality teaching and learning to grade-level specific standards, including purposeful support of literacy and language learning across the content areas.

Additional Instructional Support

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Shelby County Schools adopted our current math textbooks for grades 9-12 in 2010-2011. The textbook adoption process at that time followed the requirements set forth by the Tennessee Department of Education and took into consideration all texts approved by the TDOE as appropriate. We now have new standards; therefore, the textbook(s) have been vetted using the Instructional Materials Evaluation Tool (IMET). This tool was developed in partnership with Achieve, the Council of Chief State Officers (CCSSO) and the Council of Great City Schools. The review revealed some gaps in the content, scope, sequencing, and rigor (including the balance of conceptual knowledge development and application of these concepts), of our current materials. The additional materials purposefully address the identified gaps in alignment to meet the expectations of the CCR standards and related instructional shifts while still incorporating the current materials to which schools have access. Materials selected for inclusion in the Curriculum Maps, both those from the textbooks and external/supplemental resources (e.g., EngageNY), have been evaluated by district staff to ensure that they meet the IMET criteria.

How to Use the Mathematics Curriculum Maps

OverviewAn overview is provided for each quarter. The information given is intended to aid teachers, coaches and administrators develop an understanding of the content the students will learn in the quarter, how the content addresses prior knowledge and future learning, and may provide some non-summative assessment items.

Tennessee State StandardsThe TN State Standards are located in the left column. Each content standard is identified as the following: Major Work, Supporting Content or Additional Content.; a key can be found at the bottom of the map. The major work of the grade should comprise 65-85% of your instructional time. Supporting Content are standards that supports student’s learning of the major work. Therefore, you will see supporting and additional standards taught in conjunction with major work. It is the teacher’s responsibility to examine the standards and skills needed in order to ensure student mastery of the indicated standard.

ContentTeachers are expected to carefully craft weekly and daily learning objectives/ based on their knowledge of TEM Teach 1. In addition, teachers should include related best practices based upon the TN State Standards, related shifts, and knowledge of students from a variety of sources (e.g., student work samples, MAP, etc.). Support for the development of these lesson objectives can be found under the column titled ‘Content’. The enduring understandings will help clarify the “big picture” of the standard. The essential questions break that picture down into smaller questions and the objectives provide specific outcomes for that standard(s). Best practices tell us that clearly communicating and making objectives measureable leads to greater student mastery.

Instructional Support and Resources

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District and web-based resources have been provided in the Instructional Resources column. Throughout the map you will find instructional/performance tasks, i-Ready lessons and additional resources that align with the standards in that module. The additional resources provided are supplementary and should be used as needed for content support and differentiation.

Topics Addressed in Quarter Polynomials Relations and Functions Graphing in the Coordinate Plane Solving Equations and Inequalities

Overview The content at the beginning of this quarter introduces students to polynomial expressions and how to add, subtract, and multiply polynomials. They understand factoring as the reverse process of multiplication and this understanding is extended and connected to factoring polynomial expressions and solving basic polynomial equations. Throughout middle school, students compared linear functions, practiced the process of solving linear equations and inequalities and systems of linear equations. Now instead of just solving, they formalize descriptions of what they learned before (variable, solution sets, etc.) and learn the formal definition of a function and are able to explain, justify, and evaluate their reasoning as they strategize methods for solving linear and non-linear equations in abstract and contextual situations. Students take their experience solving systems of linear equations further as they learn a formal definition for the graph of an equation and use it to explain the reasoning of solving systems graphically, and graphically represent the solution to systems of linear inequalities and interpret solutions within the context of problems.

Fluency The high school standards do not set explicit expectations for fluency, but fluency is important in high school mathematics. Fluency in algebra can help students get past the need to manage computational and algebraic manipulation details so that they can observe structure and patterns in problems. Such fluency can also allow for smooth progress toward readiness for further study/careers in science, technology, engineering, and mathematics (STEM) fields. These fluencies are highlighted to stress the need to provide sufficient supports and opportunities for practice to help students gain fluency. Fluency is not meant to come at the expense of conceptual understanding. Rather, it should be an outcome resulting from a progression of learning and thoughtful practice. It is important to provide the conceptual building blocks that develop understanding along with skill toward developing fluency.

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References: https://www.engageny.org/ http://www.corestandards.org/ http://www.nctm.org/ http://achievethecore.org/

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESUnit 4 - Chapter 11: Polynomials (McGraw-Hill Bridge Math)

Chapter 8: Polynomials & Factoring (Prentice Hall Algebra I)(Allow approximately 2 weeks for instruction, review, and assessment)

Conceptual Category: Ways of Looking: Revisiting ConceptsDomain: Symbolic Mathematics (W-SM)

W-SM7 Perform polynomial arithmetic, including adding, subtracting, multiplying, dividing, factoring, and simplifying results.

Enduring Understanding(s): The properties of integers apply to

polynomials.

Essential Question(s): Why is it important to know the operations of

integers to understand the properties of polynomials?

Objective(s): Students will write polynomials in standard

form. Students will add & subtract polynomials. Students will multiply polynomials by

monomials. Students will factor polynomials into a

monomial factor and a polynomials factor.

McGraw-Hill Bridge Math11-1 Add and Subtract Polynomials11-2 Multiply by a Monomial11-3 Divide and Find Factors

Prentice Hall Algebra 18-1 Adding and Subtracting Polynomials8-2 Multiplying and FactoringConcept Byte: Using Models to Multiply

Task(s):Illustrative: Powers of 11Polynomial Web Quest TasksPolynomial Farm Task

Additional Resources:Khan Academy Videos: Intro to Polynomials Khan Academy Videos: Adding & Subtracting Polynomials

Vocabulary:Polynomial, monomial, coefficient, constant, binomial, trinomial, like terms, simplify, standard form, extracting factors, greatest common factor (GCF)

Writing in Math:Tell whether you prefer to group terms or use columns to add or subtract polynomials. Explain why you prefer that method.

Explain how subtraction of polynomials is related to addition of polynomials.

How is algebraic multiplication of a monomial and a polynomial similar to arithmetic multiplication of a single-digit number and a multi-digit number?

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

Khan Academy Videos: Intro to factorization Khan Academy Videos: Factoring monomialsKhan Academy Videos: Common monomial factorsKhan Academy Videos: Factoring polynomials by taking common factorsBetter Lesson: Adding and Subtracting Polynomials Lesson 5 - Adding and Subtracting PolynomialsLesson 6 - Multiplying Polynomials by MonomialsMath Planet Lesson: Monomials and Polynomials

Conceptual Category: Ways of Looking: Revisiting Concepts

Domain: Symbolic Mathematics (W-SM)W-SM7 Perform polynomial arithmetic, including adding, subtracting, multiplying, dividing, factoring, and simplifying results.

Enduring Understanding(s):The properties of integers apply to polynomials.

Essential Question(s): How are the properties of real numbers

related to polynomials?

Objective(s): Students will multiply a binomial by a

binomial. Students will write polynomials in standard

form. Students will expand a product of two

binomials.

McGraw-Hill Bridge Math11-4 Multiply Two Binomials

Prentice Hall Algebra 18-3 Multiplying Binomials

Task(s):Multiplying Binomials TaskMultiplying Polynomials Formative Assessment Task

Additional Resources:EngageNY Lesson: Multiplying PolynomialsKhan Academy: Multiplying Binomials by BinomialsRegents Prep: Multiplying BinomialsVirtual Nerd VideoLearnzillion: Dividing Polynomials Using Long Division

Vocabulary: binomial, distributive property, product, terms, expanding, sum and difference of two squares,

Writing in Math:Have students create multiple representations of binomial multiplication.Have students write a response to the following: Can the product of two binomials ever have more than three terms? Explain your thinking.

Chapter 2 Essential Algebra (McGraw-Hill Bridge Math)Chapter 1 - Foundations of Algebra, Chapter 2 Solving Equations & Chapter 4 An Introduction to Functions (PH Algebra I)

(Allow approximately 1.5 weeks for instruction, review, and assessment)Conceptual Category: Making Connections Enduring Understanding(s): McGraw-Hill Bridge Math Vocabulary: coordinate plane, quadrant, ordered

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

Domain: Symbolic & Numeric Mathematics (M-SN)

M-SN3. Recognize functions as mappings of an independent variable into a dependent variable.

Understand that a function is a rule that assigns to each input exactly one output.

Graphs can be used to visually represent the relationship between two variable quantities as they both change.

The variables used to represent domain values, range values, and the function as a whole, are arbitrary. Changing variable names does not change the function.

Essential Question(s): What are the characteristics of a function

and how can you use those characteristics to represent the function in multiple ways?

Objective(s): Students will determine whether a

relation is a function. Students will identify the domain and

range of a relation. Students will represent mathematical

relationships using graphs.

2-2 The Coordinate Plane, Relations, and Functions

Prentice Hall Algebra 1Review: Graphing in the Coordinate Plane p. 604-1 Using Graphs to Relate Two Quantities4-6 Formalizing Relations and FunctionsTask(s):Illustrative Math: Points on a GraphCpalms: Writing Functions

Additional Resource(s):EngageNY: Representing, Naming, and Evaluating FunctionsFunctions and Their Graphs (section 3.1)Learnzillion: Domain and Range of a FunctionScmoop: FunctionsBetter Lesson: Introducing FunctionsKhan Academy: Relations and Functions IntroductionKhan Academy: Relations and Functions

pair, x-coordinate, y-coordinate, function, independent variable, dependent variable, mapping, relation, domain, range

Writing in Math: Have students list what they know about linear

functions. With a partner, have the students list what they

want to find out about linear functions. Each pair must list at least one thing they want to find out about linear functions.

Conceptual Category: Ways of Looking: Revisiting Concepts

Domain: Graphic Mathematics (W-GM)

W-GM1. Understand that a linear function models a situation in which a quantity changes at a constant rate, m, relative to another.

Conceptual Category: Applications: Ways of Looking at the World

Domain: Applications with Functions (A-AF)A-AF1. Solve problems involving applications of

Enduring Understanding(s): Functions describe situations where

one quantity determines another The relationship between quantities

can be represented in different ways, including tables, equations and graphs.

Sometimes the value of one quantity can be determined if the value of another is known.

Essential Question(s): Why is the concept of a function important

and how do you use function notation to show a variety of situations modeled by functions?

McGraw-Hill Bridge Math2-3 Linear Functions

Prentice Hall Algebra 11-8 An Introduction to EquationsConcept Byte: Using Tables to Solve Equations p.594-2 Patterns and Linear Functions

Task(s):Illustrative Math: Modeling With a Linear FunctionIllustrative Math: Linear Functions

Additional Resource(s):Great Minds Module (pgs. 92-115, 267)

Vocabulary: zero pairs, linear function, open sentence

Writing in Math: What are the differences between an expression

and an equation? Does a mathematical expression have a

solution? Explain.

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESlinear equations. What does it mean for a quantity to change

at a constant rate? In what ways can we manipulate an

algebraic equation to find the value of an unknown quantity?

Objective(s): Students will write an equation

symbolically to express a contextual problem.

Students will graph linear functions. Students will solve linear equations by

making a table.

Modeling With a Linear FunctionBetter Lesson: Rate of ChangeMath Shell: Matching Situations, Graphs and Linear Equations

Conceptual Category: Making ConnectionsDomain: Symbolic & Verbal Mathematics (M-SV)

M-SV4. Solve literal equations for any variable; interpret the results based on units.

Enduring Understanding(s): An equation represents two quantities that

are equal and can be used as a tool to find an unknown value

Literal equations can be used to model real-world situations.

The properties of equality can be used repeatedly to isolate any particular variable.

Essential Question(s): How can a formula be rearranged to

highlight a quantity of interest using the same reasoning as in solving equations?

How do we rewrite a literal equation and why is it sometimes necessary to do so?

Objective(s): Students will rewrite and use literal

equations and formulas. Students will use multiplication

properties of equality to solve equations.

McGraw-Hill Bridge Math2-5 Solve Multi-Step Equations

Prentice Hall Algebra 12-2 Solving Two-Step Equations2-3 Solving Multi-Step EquationsConcept Byte: Modeling Equations With Variables on Both Sides2-4 Solving Equations With Variables on Both Sides

Task(s):Multi-Step EquationsUtah Education Network: Solving Equations, LiterallyCpalms: Solving a Linear Literal Equation

Additional Resources:Learnzillion Video Lesson: Solve a multi-step equationLearnzillion Video Lesson: Solve an equation with variables on both sidesLearnzillion Video Lesson: Solving word problemsBetter Lesson: Literal Equations (Solving Literal Equations, Literal Equations Scavenger Hunt, and Algebraic Properties of Literal Equations

Vocabulary: literal equation

Writing in Math:Explain the steps used to solve multi-step equations.Why is it sometimes necessary to rewrite literal equations before solving them?

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

Chapter 2 Essential Algebra (CONTINUED) & Chapter 6 Linear Systems of EquationsChapter 3 Solving Inequalities, Chapter 5 Linear Functions, and Chapter 6 Systems of Equations (PH Algebra I)

(Allow approximately 1.5 weeks for instruction, review, and assessment)Conceptual Category: Making ConnectionsDomain: Symbolic & Diagnostic Mathematics (M-SD)

M-SD2. Solve a linear inequality and provide an interpretation of the solution.

Conceptual Category: Ways of Looking: Revisiting ConceptsDomain: Diagrammatic Mathematics (W-DM)

W-DM1 Identify the graph of a linear inequality on the number line.

Enduring Understanding(s): An inequality is a mathematical

sentence that uses an inequality symbol to compare the values of two expressions.

The solution of an inequality can be represented on a number line.

The characteristics of linear inequalities and their representations are useful in solving real-world problems.

Essential Question(s): How is solving an inequality different

from solving an equation? Why is the inequality symbol reversed

when the inverse operation involves multiplying or dividing by a negative number?

When do you use inequalities? When do you not?

Objective(s): Students will solve linear inequalities by

using multiplication and division. Students will graph solutions of a linear

inequality on a number line.

McGraw-Hill Bridge Math2-6 Solve Inequalities in Multiplication and Division

Prentice Hall Algebra 13-1 Inequalities and Their Graphs3-3 Solving Inequalities Using Multiplication or Division

Task(s):Critique Reasoning and Solve Problems Using InequalitiesGeorgia DOE: Lucy's Linear Equations and Inequalities (pp.30-38)

Additional Resource(s):Bright Storm: Solving Inequalities Using Multiplication or DivisionLearnzillion Video Lesson: Solving inequalitiesKhan Academy: Plotting Inequalities on a Number LineKhan Academy: Solving Multi-Step Inequalities

Vocabulary: inequality, solution of inequality, Multiplication Property of Inequality

Writing in Math: Give a step-by-step series of instructions on

how to solve inequalities. Give a guide on the common errors found in attempts to solve inequalities.

Explain the circumstances under which the inequality symbol changes directions. Use examples to support your explanation.

Conceptual Category: Making Connections

Domain: Symbolic & Diagnostic Mathematics (M-SD)

Domain: Symbolic & Graphic Mathematics (M-SG)

M-SD2. Solve a linear inequality and provide an

Enduring Understanding(s): Many real-world mathematical problems can

be represented algebraically and graphically. A function that models a real-world situation can then be used to find algebraic solutions or make estimates and/or predictions about future occurrences.

Essential Question(s):

McGraw-Hill Bridge Math2-7 Solve Linear Inequalities

Prentice Hall Algebra 13-2 Solving Inequalities Using Addition or Subtraction3-4 Solving Multi-Step Inequalities

Task(s):

Vocabulary: system of inequalities

Writing in Math:Describe the difference between the solution of a system of linear equations and system of linear inequalities.

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESinterpretation of the solution.

M-SG2. Graphically represent the solution to a linear inequality and the solution to a system of linear inequalities in two variables.

Conceptual Category: Ways of Looking: Revisiting Concepts

Domain: W-DM Diagrammatic Mathematics

W-DM1. Identify the graph of a linear inequality on the number line.

When do you use inequalities? When do you not?

What can we do with a system of inequalities that we cannot do with a single inequality?

Objective(s): Students will solve an inequality in one or

two variables. Students will graph the solution of a system

of linear inequalities. Students will interpret the solution of a linear

inequality.

Inside Math: Reasoning with Equations and InequalitiesAchieve.org: Rabbit FoodLearnzillion: Graphing the Solution Set of an Inequality from Context (use with Learn Zillion video lessons)

Additional Resources:Learnzillion: Graphing inequalities on a number lineLearnzillion Video LessonsBetter Lesson: Solving Two Variable InequalitiesGraphing Linear InequalitiesSystem of Linear Inequalities

Conceptual Category: Making ConnectionsDomain: Symbolic & Graphic Mathematics (M-SG)

M-SG1. Graphically represent the solution to a linear equation and the solution to a system of linear equations in two variables.

Conceptual Category: Applications: Ways of Looking at the WorldDomain: Applications with Functions (A-AF)A-AF1. Solve problems involving applications of linear equations.

Domain: Diagnostic Mathematics (W-DM)W-DM3. Given an equation of a line, write an accurate definition of a line by determining the unique characteristic that defines it (i.e. slope and intercepts).

Enduring Understanding(s): Ratios (ex. Slope) can be used to show

a relationship between changing quantities such as vertical and horizontal change.

Essential Question(s): What are the advantages and

disadvantages of solving a system of linear equations graphically versus algebraically?

How can systems of equations be used to represent situations and solve problems?

Objective(s): Students will solve linear equations. Students will write the slope-intercept

form of an equation and graph the equation.

McGraw-Hill Bridge Math6-1 Slope of a Line and Slope-intercept Form

Prentice Hall Algebra 15-1 Rate of Change and Slope5-3 Slope-Intercept Form

Task(s):Achievement First: Systems of Equations (Task is embedded in this unit p. 5)Illustrative Math: Find a System

Additional Resources:Learnzillion: Finding the slope of a lineLearnzillion: Derive y = mx + bLearnzillion: Graph an equation in y = mx + b form

Vocabulary: slope, rate of change, parent function

Writing in Math: Is it true that a line with slope 1 always passes

through the origin? Explain your reasoning. Describe two ways to determine whether an

equation is linear.

Chapter 6 Linear Systems of Equations (CONTINUED)Chapter 6 Systems of Equations (PH Algebra I)

(Allow approximately 2 weeks for instruction, review, and assessment)Conceptual Category: Making ConnectionsDomain: Symbolic & Graphic Mathematics (M-SG)

Enduring Understanding(s): Systems of linear equations can be

used to model real-world problems and

McGraw-Hill Bridge Math6-4 Systems of Equations

Vocabulary: independent system, dependent system, solution of a system of linear equations, consistent system, inconsistent system

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESM-SG1. Graphically represent the solution to a linear equation and the solution to a system of linear equations in two variables.

Conceptual Category: Applications: Ways of Looking at the WorldDomain: Applications with Functions (A-AF)A-AF1. Solve problems involving applications of linear equations.A-AF3. Solve problems involving systems of equations such as mixture problems

they can be solved in multiple ways.

Essential Question(s): How do different linear functions with the

same variables interact? What is the best way to solve a particular

system of equations? What is the significance of the solution to a

system of linear equations?

Objective(s): Students will solve a system of equation by

graphing. Students will analyze a special system of

equations

Prentice Hall Algebra 16-1 Solving Systems by GraphingConcept Byte: Solving Systems Using Tables and Graphs (use after 6-1)

Task(s):Achievement First: Systems of Equations (Task is embedded in this unit p. 5)

Additional Resources:Learnzillion: Solve system of equation with graphingNCTM Illuminations: There has to be a System for this Sweet ProblemBetter Lesson: Mixture ProblemsSystems of Equations Mixture Problems

Writing in Math:Suppose you graph a system of linear equations. If a point is on only one of the lines, is it a solution of the system? Explain.

Conceptual Category: Making ConnectionsDomain: Symbolic & Graphic Mathematics (M-SG)M-SG1. Graphically represent the solution to a linear equation and the solution to a system of linear equations in two variables.

Conceptual Category: Applications: Ways of Looking at the WorldDomain: Applications with Functions (A-AF)A-AF1. Solve problems involving applications of linear equations.A-AF3. Solve problems involving systems of equations such as mixture problems.

Enduring Understanding(s):A system of equations can be solved in multiple ways, one being by substitution.Essential Question(s):When is the substitution method a better method than graphing for solving a system of linear equations?

Objective(s):Students will solve systems of equations using the substitution method.

McGraw-Hill Bridge Math6-5 Solve Systems by Substitution

Prentice Hall Algebra 16-2 Solving Systems Using Substitution

Task(s):TNCore Task Arc: Understanding and Solving Systems of Linear Equations

Additional Resources:Learnzillion: Solve system of equations using substitutionConcord Consortium: Solving Systems of Equations- Mixture Problems

Vocabulary: substitution method

Writing in Math:When is the substitution method a better method than graphing for solving a system of linear equations?

Conceptual Category: Making ConnectionsDomain: Symbolic & Graphic Mathematics (M-SG)M-SG1. Graphically represent the solution to a linear equation and the solution to a system of linear equations in two variables.

Enduring Understanding(s):A system of equations can be solved in multiple ways.Essential Question(s):When is it more appropriate to solve a system of linear equations by the

McGraw-Hill Bridge Math6-6 Solve Systems by Adding and Multiplying

Prentice Hall Algebra 16-3 Solving Systems Using EliminationConcept Byte: Matrices and Solving systems

Vocabulary: elimination method, multiplication and addition method

Writing in Math:How can someone tell when solving by elimination is appropriate and when solving by substitution is

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

Conceptual Category: Applications: Ways of Looking at the WorldDomain: Applications with Functions (A-AF)A-AF1. Solve problems involving applications of linear equations.A-AF3. Solve problems involving systems of equations such as mixture problems.

elimination method than by graphing or by substitution?

Objective(s):Students will solve a system of linear equations by adding or subtracting and multiplying to eliminate a variable.

(after 6-3)6-4 Applications of Linear Systems

Task(s):Utah Education Network: Systems of inequalities( Two Tasks - ‘Shopping for Cats and Dogs’and ‘Get to the Point’)

Additional Resources:Learnzillion: Solve system of equations using Linear CombinationLearnzillion: Solve system of equations using eliminationLearnzillion: Using systems of equations to solve word problems

appropriate?

Conceptual Category: Making ConnectionsDomain: Symbolic & Graphic Mathematics (M-SG)M-SG2. Graphically represent the solution to a linear inequality and the solution to a system of linear inequalities in two variables.

Enduring Understanding(s): The graph of a system of linear

inequalities is the region where the graphs of the individual inequalities overlap.

Essential Question(s): How can you determine whether an

ordered pair is a solution of a system of linear inequalities?

Objective(s): Students will model a real-world situation

using systems of linear inequalities. Use graphing to solve a system of linear

inequalities.

McGraw-Hill Bridge Math6-8 Systems of Inequalities

Prentice Hall Algebra 16-5 Linear Inequalities6-6 Systems of Linear InequalitiesConcept Byte: Graphing Linear Inequalities (after 6-6)

Task(s):Achievement First Unit: (Includes several tasks)Activate Instruction : Linear Inequalities Activity - 'The Obama Project Lesson Plan'

Additional Resource(s):Learnzillion : Graph Solutions of Inequalities as a Half PlaneGraphing the Solution Set of an Inequality from Context (use with Learn Zillion video lessons)

Vocabulary: linear inequality, system of linear inequality, solution of system of linear inequality

Writing in Math:Write an inequality that describes the region of the coordinate plane not included in the graph of y< 5x + 1. Explain your reasoning.

Radicals, Radicals Expressions, and Radical EquationsBridge Math Chapter 10

Prentice Hall Algebra I – Chapter 10(Allow approximately 2 weeks for instruction, review, and assessment)

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Curriculum and Instruction – Mathematics

Quarter 2 Bridge Math

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESConceptual Category: Ways of Looking: Revisiting Concepts

Domain: Verbal Mathematics (W-VM)W-VM5. Multiply, divide, and simplify radicals.

Domain: Symbolic Mathematics (W-SM)W-SM8. Demonstrate fluency with techniques needed to simplify radical expressions and calculate with them, including addition, subtraction, and multiplication.

Domain: Graphic Mathematics (W-GM)W-GM5. Operate (add, subtract, multiply, divide, simplify, powers) with radicals and radical expressions including radicands involving rational numbers and algebraic expressions.

Enduring Understanding(s): Properties of real numbers can be used

to perform operations with radical expressions.

Essential Question(s): How are radical expressions simplified?

Objective(s): Students will simplify sums, differences,

products and quotients of radical expressions.

Students will identify extraneous solutions to when solving radical expressions.

McGraw-Hill Bridge math10-1 Irrational Numbers

Prentice Hall Algebra 110-2 Simplifying Radicals10-3 Operations with Radical Expressions10-4 Solving Radical Equations

Tasks:Radicals and Radical Expressions (lessons and performance tasks)

Additional Resources:Math Shell: Evaluating Statements About Radicals Learnzillion: Lessons on Simplifying RadicalsKhan Academy: Simplifying Radical ExpressionsLesson for Operation with Radical ExpressionsLesson on Solving Radical Equations

Vocabulary: radical expression, like radicals, unlike radicals, radicand, extraneous solution

Writing in Math:Explain how you can tell whether a radical expression is in simplified form.

Explain the difference between squaring √ x−1 and √ x – 1.

RESOURCE TOOLBOX

NWEA MAP Resources: https://teach.mapnwea.org/assist/help_map/ApplicationHelp.htm#UsingTestResults/MAPReportsFinder.htm - Sign in and Click the Learning Continuum Tab – this resources will help as you plan for intervention, and differentiating small group instruction on the skill you are currently teaching. (Four Ways to Impact Teaching with the Learning Continuum)https://support.nwea.org/khanrit - These Khan Academy lessons are aligned to RIT scores.

Textbook Resourceshttp://www.connected.mcgraw-hill.com/http://www.pearsonsuccessnet.com/

StandardsCom m on Core S tand a rds - Math e matics Com m on Core S tand a rds - Math e matics A pp e ndix A Edutoolbox (formerly TNCore)ht t p: / /ww w . cc ss t oolbo x . o r g / Common Core LessonsTennessee State StandardsTennessee’s Bridge Math StandardsCCSS Flip Book with Examples of each Standard

VideosBrightstormTeacher TubeThe Futures ChannelKhan AcademyMath TVLamar University TutorialShmoop - We Speak Students

Additional SitesIlluminations (NCTM)

Interactive Manipulatives & TasksNational Math Resources

CalculatorMath Nspired

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Curriculum and Instruction – Mathematics

Quarter 2 Bridge Math

Stem Resourcesht t p: / / j c - s c hools.n e t / d y n a m i c / m a th / math12.ht m l www.learnzillion.com

MARS Course 2NASA Space MathMath Vision ProjectUT Dana CenterMars TasksInside Math TasksMath Vision Project Tasks SCS TasksBetter LessonNational Math Resourcesht t p: / /ww w .i l ov e math.o r g / i nd e x .ph p ? opt i on =c om_docm a n http://www.mathopenref.comSMARTboard Lessons

Texas Instrument ActivitiesCasio Activities

LiteracyGlencoe- Reading and Writing in the Math ClassroomGraphic Organizers (9-12)Graphic Organizers (dgelman)

ACTTN ACT Information & ResourcesACT College & Career Readiness Mathematics Standards

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