Grade 8



IntroductionIn 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 ready90% of students will graduate on time100% of our students who graduate college or career ready will enroll in a post-secondary opportunity42291021812250In 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. -537210152400The 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:The TN Mathematics StandardsThe Tennessee Mathematics Standards: HYPERLINK "" 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 Practice Mathematical Practice Standards 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 MapsThis 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 SupportShelby 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 MapsOverviewAn 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 ResourcesDistrict 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 QuarterProperties of ExponentsExpressions, Equations and InequalitiesLinear SystemsVarious Functions & Their GraphsRadical ExpressionsOverview 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 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: STATE STANDARDSCONTENTINSTRUCTIONAL SUPPORT & RESOURCESChapter 1 Essential Mathematics (McGraw-Hill Bridge Math)Chapter 1- Foundations of Algebra & Chapter 7 Exponents and Exponential Functions (Prentice Hall Algebra I)(Allow approximately 1.5 weeks for instruction, review, and assessment)Conceptual Category: HYPERLINK ""Ways of Looking: Revisiting ConceptsDomain: 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 sets and describe the relationships among sets and elements of sets.McGraw-Hill Bridge Math1-1The Language of Mathematics1-2 Real Numbers 1-3 Union and Intersection of SetsPrentice Hall Algebra 1Real Numbers and the Number LineTask(s):Math Shell: Real Numbers Novice TaskAdditional Resources:Brightstorm Video: Introduction to Real NumbersBrightstorm Video: Set Operations-IntersectionKhan Academy Video: Absolute Value and Number LinesKhan Academy Video: Set Operations-UnionVocabulary: square root, radical, perfect square, set, subset, element of a set, rational number, irrational number, natural number, integer, whole number, inequality, union, intersectionWriting 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. Conceptual Category: HYPERLINK ""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 ExponentsPrentice 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 PropertyLearnzillion Video: Division property of exponentsVocabulary: exponential form, base, exponent, distributive propertyWriting 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: HYPERLINK ""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.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.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 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.McGraw-Hill Bridge Math1-8 Exponents and Scientific NotationPrentice Hall Algebra 17-2 Scientific NotationTask(s):Math Shell: Estimating Length Using Scientific NotationAdditional Resources:Khan Academy Video: Exponent Properties Involving ProductsTI-84/Navigator LessonVocabulary: scientific notationWriting 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.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: HYPERLINK ""Making ConnectionsDomain: 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 relation is a function.Students will identify the domain and range of a relation.Students will represent mathematical relationships using graphs.McGraw-Hill Bridge Math2-2 The Coordinate Plane, Relations, and FunctionsPrentice Hall Algebra 1Review: Graphing in the Coordinate Plane p. 604-1 Using Graphs to Relate Two Quantities4-6 Formalizing Relations and FunctionsAdditional 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, rangeWriting 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: HYPERLINK ""Ways of Looking: Revisiting ConceptsDomain: 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: HYPERLINK ""Applications: Ways of Looking at the WorldDomain: Applications with Functions (A-AF)A-AF1. Solve problems involving applications of linear equations.Enduring Understanding(s):Functions describe situations where one quantity determines anotherThe 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 FunctionsPrentice Hall Algebra 11-8 An Introduction to EquationsConcept Byte: Using Tables to Solve Equations p.594-2 Patterns and Linear FunctionsTask(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 EquationsVocabulary: 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: HYPERLINK ""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.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 formulasStudents will use multiplication properties of equality to solve equations.McGraw-Hill Bridge Math2-5 Solve Multi-Step EquationsPrentice 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 SidesTask(s):Multi-Step EquationsAdditional Resources:CCSS Video Lesson: Solve a multi-step equationCCSS Video Lesson: Solve an equation with variables on both sidesCCSS Video Lesson: Solving word problemsVocabulary: literal equationWriting in Math:Explain the steps used to solve multi-step equations. Chapter 2 Essential Algebra (CONTINUED) & Chapter 6 Linear Systems of Equations Chapter 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: HYPERLINK ""Making ConnectionsDomain: Symbolic & Diagnostic Mathematics (M-SD)M-SD2. Solve a linear inequality and provide an interpretation of the solution. Conceptual Category: HYPERLINK ""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 DivisionPrentice Hall Algebra 13-1 Inequalities and Their Graphs3-3 Solving Inequalities Using Multiplication or DivisionTask(s):Critique Reasoning and Solve Problems Using InequalitiesAdditional Resource(s):Solving Inequalities Using Multiplication or DivisionCCSS Video Lesson: Solving inequalitiesVocabulary: 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. Conceptual Category: HYPERLINK ""Making ConnectionsDomain: 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: HYPERLINK ""Ways of Looking: Revisiting ConceptsDomain: W-DM Diagrammatic MathematicsW-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 InequalitiesPrentice Hall Algebra 13-2 Solving Inequalities Using Addition or Subtraction3-4 Solving Multi-Step InequalitiesTask(s): %282006%29.pdfRabbit FoodGraphing 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 LessonsVocabulary: system of inequalitiesWriting in Math:Describe the difference between the solution of a system of linear equations and system of linear inequalities.Conceptual Category: HYPERLINK ""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 FormPrentice Hall Algebra 15-1 Rate of Change and Slope5-3 Slope-Intercept FormTask(s):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 formVocabulary: slope, rate of change, parent functionWriting 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 3 weeks for instruction, review, and assessment)Conceptual Category: HYPERLINK ""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 problemsEnduring 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 equationsMcGraw-Hill Bridge Math6-4 Systems of EquationsPrentice 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 ProblemsVocabulary: independent system, dependent system, solution of a system of linear equations, consistent system, inconsistent systemWriting 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: HYPERLINK ""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 SubstitutionPrentice Hall Algebra 16-2 Solving Systems Using SubstitutionTask(s):TNCore Task Arc: Understanding and Solving Systems of Linear EquationsAdditional Resources:CCSS Video Lesson: Solve system of equations using substitutionVocabulary: substitution methodWriting in Math:When is the substitution method a better method than graphing for solving a system of linear equations?Conceptual Category: HYPERLINK ""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 MultiplyingPrentice Hall Algebra 16-3 Solving Systems Using EliminationConcept Byte: Matrices and Solving systems (after 6-3)6-4 Applications of Linear SystemsTask(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 problemsVocabulary: elimination method, multiplication and addition methodWriting in Math:How can someone tell when solving by elimination is appropriate and when solving by substitution is appropriate? Conceptual Category: HYPERLINK ""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 InequalitiesPrentice Hall Algebra 16-5 Linear Inequalities6-6 Systems of Linear InequalitiesConcept Byte: Graphing Linear Inequalities (after 6-6)Task(s):Graphing the Solution Set of an Inequality from Context (use with Learn Zillion video lessons)Additional Resource(s):Learnzillion Video LessonsVocabulary: linear inequality, system of linear inequality, solution of system of linear inequalityWriting 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 10Prentice Hall Algebra I – Chapter 10(Allow approximately1.5 weeks for instruction, review, and assessment)Conceptual Category: HYPERLINK ""Ways of Looking: Revisiting ConceptsDomain: 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 NumbersPrentice Hall Algebra 110-2 Simplifying Radicals10-3 Operations with Radical Expressions10-4 Solving Radical EquationsAdditional 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 ExpressionsLesson on Solving Radical EquationsVocabulary: radical expression, like radicals, unlike radicals, radicand, extraneous solutionWriting 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 TOOLBOXNWEA MAP Resources: - 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) - These Khan Academy lessons are aligned to RIT scores.Textbook Resources Core Standards - MathematicsCommon Core Standards - Mathematics Appendix A HYPERLINK "" \t "_top" Edutoolbox (formerly TNCore) Core LessonsTennessee State StandardsTennessee’s Bridge Math StandardsVideosBrightstormTeacher TubeThe Futures ChannelKhan AcademyMath TVLamar University TutorialShmoop - We Speak StudentsAdditional SitesIlluminations (NCTM) Stem Resources Interactive Manipulatives & TasksNational Math Resources MARS Course 2NASA Space Math Math Vision ProjectUT Dana CenterMars TasksInside Math TasksMath Vision Project TasksSCS TasksBetter LessonNational Math Resources LessonsCalculatorMath NspiredTexas Instrument ActivitiesCasio ActivitiesLiteracyGlencoe- 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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