Curriculum and Instruction – Office of Mathematics

Quarter 1 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 – Office of Mathematics

Quarter 1 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

The Shelby County Schools curriculum maps are intended to guide planning, pacing, and sequencing, reinforcing the major work of the grade/subject. Curriculum maps are NOT meant to replace teacher preparation or judgment; however, it does serve as a resource for good first teaching and making instructional decisions based on best practices, and student learning needs and progress. Teachers should consistently use student data differentiate and scaffold instruction to meet the needs of students. The curriculum maps should be referenced each week as you plan your daily lessons, as well as daily when instructional support and resources are needed to adjust instruction based on the needs of your students.

How to Use the Mathematics Curriculum Maps

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 the 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 teachers' responsibility to examine the standards and skills needed in order to ensure student mastery of the indicated standard.

ContentWeekly and daily objectives/learning targets should be included in your plan. These 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 learning targets/objectives provide specific outcomes for that standard(s). Best practices tell us that making objectives measureable increases student mastery.

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Quarter 1 Bridge Math

Instructional Support and ResourcesDistrict and web-based resources have been provided in the Instructional Support and Resources column. The additional resources provided are supplementary and should be used as needed for content support and differentiation.

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Topics Addressed in Quarter Properties of Exponents Expressions, Equations and Inequalities Linear Systems Various Functions & Their Graphs Radical Expressions

Overview Students begin the quarter learning the precise definition of exponential notation and expand the definition of exponential notation to include what it means to raise a nonzero number to a zero power; Students discern the structure of exponents by relating multiplication and division of expressions with the same base to combining like terms using the distributive property, and by relating multiplying three factors using the associative property to raising a power to a power.

Students gradually shift to solving linear equations and inequalities and systems of linear equations and inequalities. Throughout middle school, students practiced the process of solving linear equations (6.EE.5, 6.EE.7, 7.EE.4, 8.EE.7) and systems of linear equations (8.EE.8). Now instead of just solving equations, they formalize descriptions of what they learned before (variable, solution sets, etc.) and are able to explain, justify, and evaluate their reasoning as they strategize methods for solving linear equations. Students take their experience solving systems of linear equations further as they prove the validity of the addition, substitution and elimination methods and 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.

After mastering solving of linear equations and inequalities, students apply related solution techniques and the properties of exponents to the creation and solution of simple exponential expressions and students end the quarter multiplying and dividing expressions that contain radicals to simplify their answers.

Fluency

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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.

References:

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

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESChapter 1 Essential Mathematics (McGraw-Hill Bridge Math)

Chapter 1- Foundations of Algebra & Chapter 7 Exponents and Exponential Functions (Prentice Hall Algebra I)

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES(Allow 1.5 weeks for instruction, review, and assessment)

Conceptual Category: Ways of Looking: Revisiting Concepts

Domain: Symbolic Mathematics (W-SM)W-SM2 Develop a thorough understanding of both rational and irrational numbers; make both historical and concrete connections between irrational numbers and the real world.

Domain: Numeric Mathematics (W-NM)W-NM1 Understand that there are numbers that are not rational numbers, called irrational numbers which together with the rational numbers form the real number system that satisfies the law of exponents.

Enduring Understanding(s): Rational and irrational numbers are a

natural extension of the way that we use numbers.

The rational numbers are a set of numbers that includes the whole numbers and integers as well as numbers that can be written as the quotient of two integers, a divided by b, where b is not zero. The irrational numbers are numbers that cannot be expressed as a quotient of two integers.

Rational and irrational numbers can be compared using a number line.

Essential Question(s): What are the definition, description, and

difference of rational and irrational numbers?

Why is it important for students to know the square root of a number?

Objective(s): Students will develop a thorough

understanding of both rational and irrational numbers; make both historical and concrete connections between irrational numbers and the real world.

Students will understand that there are numbers that are not rational numbers, called irrational numbers which together with the rational numbers form the real number system that satisfies the law of exponents.

Students will identify and graph real numbers.

Students will use math symbols to describe

McGraw-Hill Bridge Math1-1The Language of Mathematics1-2 Real Numbers1-3 Union and Intersection of Sets

Prentice Hall Algebra 11-3 Real Numbers and the Number Line

Task(s):Math Shell: Real Numbers Novice Task

Additional Resources:Brightstorm Video: Introduction to Real NumbersBrightstorm Video: Set Operations-IntersectionKhan Academy Video: Absolute Value and Number LinesKhan Academy Video: Set Operations-Union

Vocabulary: square root, radical, perfect square, set, subset, element of a set, rational number, irrational number, natural number, integer, whole number, inequality, union, intersection

Writing in Math:Have students respond to the following in their math journal or notebook.

What are real numbers? Are there numbers that aren’t real? Compare and contrast the union of a set

and the intersection of a set.

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

sets and describe the relationships among sets and elements of sets.

Conceptual Category: Ways of Looking: Revisiting Concepts

Domain: Symbolic Mathematics (W-SM)

W-SM5: Skillfully manipulate formulas involving exponents.

W-SM6: Understand how mathematical properties yield equivalent equations and can be used in determining if two expressions are equivalent.

Enduring Understanding(s): The characteristics of exponential functions

and their representations are useful in solving real-world problems.

Two or more expressions may be equivalent, even when their symbolic forms differ.

Essential Question(s): How do exponential functions model real-

world problems and their solutions? How can you determine if two or more

expressions are equivalent? How can you generate equivalent expressions?

Objective(s): Students will use properties of exponents to

evaluate and simplify expressions. Students will use the distributive property to

evaluate and simplify expressions. Students will apply properties to

evaluate and simplify expressions.

McGraw-Hill Bridge Math1-7 Distributive Property and Properties of Exponents

Prentice Hall Algebra 11-7 The Distributive Property7-1 Zero and Negative Exponents7-3 Multiplying Powers With the Same Base7-4 More Multiplication Properties of Exponents7-5 Division Properties of Exponents

Task(s):Math Shell: Applying Properties of Exponents

Additional Resources:Khan Academy Video: Distributive Property Learnzillion Video: Division property of exponents

Vocabulary: exponential form, base, exponent, distributive property

Writing in Math:Describe how the distributive property can be used to simplify or expand an expression.

How does the property for powers of a power apply to positive and negative exponents?

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

W-SM1. Operate with numbers expressed in scientific notation.W-SM5. Skillfully manipulate formulas involving exponents.

Enduring Understanding(s): Exponential and scientific notation are

efficient ways to operate with numbers. Scientific notation is used to represent large

and small numbers.

Essential Question(s): Why is it important to understand how to

McGraw-Hill Bridge Math1-8 Exponents and Scientific Notation

Prentice Hall Algebra 17-2 Scientific Notation

Task(s):Math Shell: Estimating Length Using Scientific

Vocabulary: scientific notation

Writing in Math:Why and how is scientific notation useful in the real world?Describe what happens to a decimal when it is multiplied by 10n and 10-n.

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

W-SM6. Understand how mathematical properties yield equivalent equations and can be used in determining if two expressions are equivalent.

Conceptual Category: Applications: Ways of Looking at the WorldDomain: Applications with Numbers (A-AN)A-AN1: Solve problems using scientific notation.

write numbers in scientific notation? How does scientific notation differ from

standard notation? How does multiplying by a power of 10

affect the decimal?

Objective(s): Students will evaluate variable expressions

with negative exponents. Students will write numbers in scientific

notation. Students multiply and divide numbers

expressed in scientific notation.

Notation

Additional Resources:Khan Academy Video: Exponent Properties Involving ProductsTI-84/Navigator Lesson

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 1.5 weeks for instruction, review, and assessment)Conceptual Category: Making Connections

Domain: Symbolic & Numeric Mathematics (M-SM)

M-SM3. Recognize functions as mappings of an independent variable into a dependent variable.

Enduring Understanding(s): 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

McGraw-Hill Bridge Math2-2 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 Functions

Additional Resource(s):Functions and Their Graphs (section 3.1)

Vocabulary: coordinate plane, quadrant, ordered 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.

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESrelation is a function.

Students will identify the domain and range of a relation.

Students will represent mathematical relationships using graphs.

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 linear equations.

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?

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.

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: Modelling With a Linear Function

Additional Resource(s):Great Minds Module (pgs. 92-115, 267)Modelling With a Linear FunctionMath Shell: Matching Situations, Graphs and Linear Equations

Vocabulary: zero pairs, linear function, open sentenceWriting in Math: What are the differences between an expression

and an equation? Does a mathematical expression have a

solution? Explain.

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): Literal equations can be used to model

real-world situations. The properties of equality can be used

repeatedly to isolate any particular variable.

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

Prentice Hall Algebra 12-2 Solving Two-Step Equations2-3 Solving Multi-Step Equations

Vocabulary: literal equation

Writing in Math:Explain the steps used to solve multi-step equations.

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

Essential Question(s):How can a formula be rearranged to highlight a quantity of interest using the same reasoning as in solving equations?

Objective(s): Students will rewrite and use literal

equations and formulas Students will use multiplication

properties of equality to solve equations.

Concept Byte: Modeling Equations With Variables on Both Sides2-4 Solving Equations With Variables on Both Sides

Task(s):Multi-Step Equations

Additional Resources:CCSS Video Lesson: Solve a multi-step equationCCSS Video Lesson: Solve an equation with variables on both sidesCCSS Video Lesson: Solving word problems

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 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

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 Inequalities

Additional Resource(s):Solving Inequalities Using Multiplication or DivisionCCSS Video Lesson: Solving inequalities

Vocabulary: inequality, solution of inequalityWriting 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.

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESnumber?

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.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 interpretation 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.

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): 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.

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):http://www.insidemathematics.org/assets/common-core-math-tasks/graphs %282006%29.pdf Rabbit Food Graphing the Solution Set of an Inequality from Context (use with Learn Zillion video lessons)

Additional Resources:CCSS Video Lesson: Graphing inequalities on a number lineLearnzillion Video Lessons

Vocabulary: system of inequalities

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

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

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):

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

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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.

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).

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.

Systems of Equations (Task is embedded in this unit p. 5)

Additional Resources:CCSS Video Lesson: Finding the slope of a lineCCSS Video Lesson: Derive y = mx + bCCSS Video Lesson: Graph an equation in y = mx + b form

equation is linear.

Chapter 6 Linear Systems of Equations (CONTINUED)/Chapter 6 Systems of Equations (PH Algebra I)(Allow 3 weeks for instruction, review, and assessment)

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): Systems of linear equations can be

used to model real-world problems and 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

McGraw-Hill Bridge Math6-4 Systems of Equations

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

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

Additional Resources:CCSS Video Lesson: Solve system of equation with graphingSystems of Equations Mixture Problems

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

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.

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?

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

Vocabulary: substitution method

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

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESConceptual 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.

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

Systems of Linear Equations

Additional Resources:CCSS Video Lesson: Solve system of equations using substitution

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.Essential Question(s):When is it more appropriate to solve a system of linear equations by the 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.

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

Task(s):TASK: Systems of inequalities(Shopping for Cats and Dogs, pages 29,30and Can You Get to the Point, page 33)

Additional Resources:CCSS Video Lesson: Solve system of equations using Linear CombinationCCSS Video Lesson: Solve system of equations using eliminationCCSS Video Lesson: Using systems of equations to solve word problems

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 appropriate?

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

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

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)

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 ofy< 5x + 1. Explain your reasoning.

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESordered 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.

Task(s):Graphing the Solution Set of an Inequality from Context (use with Learn Zillion video lessons)

Additional Resource(s):Learnzillion Video Lessons

Radicals, Radicals Expressions, and Radical EquationsBridge Math Chapter 10

Prentice Hall Algebra I – Chapter 10(Allow 1.5 weeks for instruction, review, and assessment)

Conceptual 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

Additional Resources:Math Shell: Evaluating Statements About Radicals Radicals and Radical Expressions (lessons and performance tasks)Lessons on Simplifying RadicalsSimplifying Radicals WorksheetLesson for Operation with Radical Expressions

Lesson 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.

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Quarter 1 Bridge Math

RESOURCE TOOLBOXNWEA 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 Lessonswww.learnzillion.comTennessee State StandardsTennessee’s Bridge Math Standards

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

Additional SitesIlluminations (NCTM)Stem Resourceshttp://www.explorelearning.comht t p: / / j c - s c hools.n e t / d y n a m i c / m a th / math12.ht m l

Interactive Manipulatives & TasksNational Math ResourcesMARS Course 2NASA Space MathMath Vision ProjectUT Dana CenterMars TasksInside Math TasksMath Vision Project Tasks Better 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

CalculatorMath nspiredTexas 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

Shelby County Schools 2016/2017Revised 6/6/16

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Curriculum and Instruction – Office of Mathematics

Quarter 1 Bridge Math

Shelby County Schools 2016/2017Revised 6/6/16

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