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 opportunityIn 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. 42291023279100-571500-1270The 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: 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 judgment 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 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 QuarterAnalytic Geometry and the Conic SectionsAdditional Topics in AlgebraOverviewIn this quarter conic sections are presented from both an algebraic and a geometric point of view. Students address equations of conics in standard and general forms. Graphing is done by hand and using graphing technology. Students see that complex numbers can be represented in the Cartesian plane and that operations with complex numbers have a geometric interpretation. They connect their understanding of trigonometry and geometry of the plane to express complex numbers in polar form. In previous courses, students learned about arithmetic and geometric sequences and their relationships to linear and exponential functions, respectively. This quarter builds on students’ understandings of those sequences and extends students’ knowledge to include geometric series, both finite and infinite. Summation notation and properties of sums are also introduced. Additionally, students will examine other types of sequences and, if appropriate, proof by induction. They will use their knowledge of the characteristics of the types of sequences and the corresponding functions to compare scenarios involving different sequences.Finally, students review some of the basic topics in probability including the counting principles, permutations and combinations, and the Binomial Theorem and use these to solve real-world problems and make decisions.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 & RESOURCESAnalytic Geometry and the Conic Sections(Allow approximately 4 - 5 Weeks for instruction, review, and assessments )Domain: Conic SectionsCluster: Understand the properties of conic sections and apply them to model real-world phenomena.*A-C1. Display all of the conic sections as portions of a cone.Enduring Understanding(s)Conic sections are quadratic relations that can be expressed generally by the form ??2 + ?xy + ??2 + ?x + ?y + ? = 0 and the comparison of the coefficients ? and ? reveal the specific type of conic.All conic sections are defined by the relationship of their locus of points to fixed points known as foci.Different forms of equations provide different information about key characteristics of the conic sections. The characteristics of quadratic relations and their representations are useful in solving real-world problems.Essential Question(s):What information can be gathered from the equation of a circle, ellipse, hyperbola, or parabola? How do I determine the center and radius given an equation of a circle? How do quadratic relations model real-world problems and their solutions?Objective(s):Students will:Verify theorems from basic geometry involving the distance between two pointsVerify that points (x, y) are an equal distance from a given point and a given lineUse the defining characteristics of a conic section to find its equation10.1 Introduction to Analytic Geometry (Coburn)Additional Resource(s)engageny Precalculus and Advanced Topics Module 3, Topic A, Lesson 6: Curves in the Complex Plane HYPERLINK "" Algebra & Trigonometry (Coburn), 2nd Edition(Exercise Videos, Lecture Videos, Graphing Calculator Videos, PowerPoint Presentations) Examples of EllipseConic Sections (Khan Academy)Task(s)Conics Project:VocabularyMidpoint formula, distance formula, circle, ellipse, hyperbola, parabolaWriting in MathCompare and contrast the different types of conic equations and figures.Domain: Conic SectionsCluster: Understand the properties of conic sections and apply them to model real-world phenomena.*A-C2. From an equation in standard form, graph the appropriate conic section: ellipses, hyperbolas, circles, and parabolas. Demonstrate an understanding of the relationship between their standard algebraic form and the graphical characteristics. 3. Transform equations of conic sections to convert between general and standard form. Enduring Understanding(s):Ellipses arise from a locus of points that represent a constant sum of distances from two fixed points (foci).Different forms of equations provide different information about key characteristics of the conic sections. Essential Question(s):What information can be gathered from the equation of a circle or ellipse? How do I determine the center and radius given an equation of a circle? How can ellipses be defined in relation to their foci?How can I use the equation of a circle to determine if a point lies on the graph? How do quadratic relations model real-world problems and their solutions?Objective(s):Students will:Use the characteristics of a circle and its graph to understand the equation of an ellipseUse the equation of an ellipse to graph central and noncentral ellipsesLocate the foci of an ellipse and use the foci and other features to write the equationSolve applications involving the foci10.2 The Circle and The Ellipse (Coburn)10.1 The Ellipse (Blitzer)Additional Resource(s)engageny Precalculus and Advanced Topics Module 3, Topic A, Lesson 7: Curves from Geometry HYPERLINK "" Algebra & Trigonometry (Coburn), 2nd Edition(Exercise Videos, Lecture Videos, Graphing Calculator Videos, PowerPoint Presentations)Parabolas, Hyperbolas, Ellipses:Conic Sections (Khan Academy)Task(s)Accelerated Mathematics II, Unit 7 - Conic SectionsCircles, p. 11Is It Really an Ellipse?, p. 39VocabularyEllipse, foci (focus), center, radius, vertices (vertex), major axis, minor axis, standard form of the equation of a circle, standard form of the equation of an ellipse Writing in Math/DiscussionWrite an equation of the graph of a circle in standard form and describe how to graph it.Write an equation of the graph of an ellipse in standard form and describe how to graph it.Determine whether the following statements make sense or does not make sense and explain your reasoning.I graphed an ellipse with a horizontal major axis and foci on the y-axis.My graph of (x – 2)2 + (y + 5)2 = 36 is a circle with radius 6 centered at (-3, 5)Domain: Conic SectionsCluster: Understand the properties of conic sections and apply them to model real-world phenomena.*A-C2. From an equation in standard form, graph the appropriate conic section: ellipses, hyperbolas, circles, and parabolas. Demonstrate an understanding of the relationship between their standard algebraic form and the graphical characteristics. 3. Transform equations of conic sections to convert between general and standard form. Enduring Understanding(s):All conic sections are defined by the relationship of their locus of points to fixed points known as foci.Different forms of equations provide different information about key characteristics of the conic sections. The characteristics of quadratic relations and their representations are useful in solving real-world problems.Essential Question(s):What information can be gathered from the equation of a hyperbola? How do quadratic relations model real-world problems and their solutions?Objective(s):Students will:Use the equation of a hyperbola to graph central and noncentral hyperbolasDistinguish between the equations of a circle, ellipse, and hyperbolaLocate the foci of a hyperbola and use the foci and other features to write its equationSolve applications involving foci10.3 The Hyperbola (Coburn)10.2 The Hyperbola (Blitzer)Additional Resource(s) HYPERLINK "" engageny Precalculus and Advanced Topics Module 3, Topic A, Lesson 8; Curves from Geometry HYPERLINK "" Algebra & Trigonometry (Coburn), 2nd Edition(Exercise Videos, Lecture Videos, Graphing Calculator Videos, PowerPoint Presentations)Examples of HyperbolasConic Sections (Khan Academy)Task(s)Accelerated Mathematics II, Unit 7 - Conic SectionsHyperbolas, p. 41GSE Pre-Calculus Unit 6: ConicsOur Only Focus: Circles & Parabolas, p. 8The Focus is the Foci: Ellipses and Hyperbolas, p. 29VocabularyHyperbola, standard form of the equation of a hyperbola, branches, vertices, transverse axis, center, asymptotesWriting in Math/DiscussionHow can you distinguish an ellipse from a hyperbola by looking at their equations?Research a few applications of hyperbolas and report on these applications and the fields/occupations that use them.Domain: Conic SectionsCluster: Understand the properties of conic sections and apply them to model real-world phenomena.*A-C2. From an equation in standard form, graph the appropriate conic section: ellipses, hyperbolas, circles, and parabolas. Demonstrate an understanding of the relationship between their standard algebraic form and the graphical characteristics. 3. Transform equations of conic sections to convert between general and standard form. Enduring Understanding(s):All conic sections are defined by the relationship of their locus of points to fixed points known as foci.Different forms of equations provide different information about key characteristics of the conic sections. The characteristics of quadratic relations and their representations are useful in solving real-world problems.Essential Question(s):What role does the focus play in determining the shape of the parabola? How does the orientation of the parabola affect the equation of the parabola?Objective(s):Students will:Graph parabolas with a horizontal axis of symmetryIdentify and use the focus-directrix from of the equation of a parabolaSolve nonlinear systems involving the conic sectionsSolve applications of the analytic parabola10.4 The Analytic Parabola(Coburn) 10.3 The Parabola (Blitzer)Additional Resource(s)Engageny Algebra II Module 1, Topic C, Lesson 33, The Definition of a Parabola HYPERLINK "" Algebra & Trigonometry (Coburn), 2nd Edition(Exercise Videos, Lecture Videos, Graphing Calculator Videos, PowerPoint Presentations)Video on Graphing ParabolasConic Sections (Khan Academy)Parabola Word ProblemTask(s)Accelerated Mathematics II, Unit 7 - Conic SectionsParabolas, p. 25 GSE Pre-Calculus Unit 6: ConicsDeriving the General Equation of a Parabola, p.53Parabolas in Other Directions, p. 64Writing the Equations of Parabolas, p. 72A Conic Application, p.Culminating Task: Dr. Cone’s New House, p. 84Dana Center; Conic SectionsVocabularyParabola, focus, directrix, axis of symmetry, standard form of the equation of a parabola, Writing in Math/DiscussionHow can you distinguish parabolas from other conic sections by looking at their equations?Research a few applications of parabolas and report on these applications and the fields/occupations that use them.Domain: Conic SectionsCluster: Understand the properties of conic sections and apply them to model real-world phenomena.*A-C2. From an equation in standard form, graph the appropriate conic section: ellipses, hyperbolas, circles, and parabolas. Demonstrate an understanding of the relationship between their standard algebraic form and the graphical characteristics. 3. Transform equations of conic sections to convert between general and standard form. Enduring Understanding(s):Polar equations are used to analyze distance and motion.Essential Question(s):What are polar coordinates and how can they be used to simplify circular functions?How can we find distances using polar coordinates?How can we relate polar and rectangular form?Objective(s):Students will:Plot points given in polar formConvert from rectangular form to polar formConvert from polar form to rectangular formSketch basic polar graphs using an r-value analysisUse symmetry and families of curves to write a polar equation given a polar graph or information about the graph10.5 Polar Coordinates, Equations and Graphs (Coburn) Additional Resource(s) HYPERLINK "" Algebra & Trigonometry (Coburn), 2nd Edition(Exercise Videos, Lecture Videos, Graphing Calculator Videos, PowerPoint Presentations)Polar Coordinates 1 (Khan Academy) HYPERLINK "" Polar Coordinates 2 (Khan Academy)HYPERLINK ""Polar Coordinates 3 (Khan Academy)VocabularyPolar coordinates, rectangular form, polar form, r-value analysis, polar symmetryWriting in Math/DiscussionExplain how to convert a point from polar to rectangular coordinates. Provide an example with your explanation.Domain: Conic SectionsCluster: Understand the properties of conic sections and apply them to model real-world phenomena.*A-C2. From an equation in standard form, graph the appropriate conic section: ellipses, hyperbolas, circles, and parabolas. Demonstrate an understanding of the relationship between their standard algebraic form and the graphical characteristics. 3. Transform equations of conic sections to convert between general and standard form. Objective(s):Students will:Graph conics that have nonvertical and nonhorizontal axes (rotated conics) Identify conics using the discriminant of the polynomial form: the invariant B2 – 4ACWrite the equation of a conic section in polar formSolve applications involving the conic sections in polar form10.6 More on Conic Sections: Rotation of Axes and Polar Form (Coburn)10.4 Rotation of Axes (Blitzer)10.6 Conic Sections in Polar Coordinates (Blitzer)Additional Resource(s)HYPERLINK ""Algebra & Trigonometry (Coburn), 2nd Edition(Exercise Videos, Lecture Videos, Graphing Calculator Videos, PowerPoint Presentations)Video: Rotation of Conic SectionsBetter Lesson: Rotated Conic Sections, Day 1Better Lesson: Rotated Conic Sections, Day 2Writing in Math/DiscussionHow do you obtain the angle of rotation so that a general second-degree equation has no x′y′-term in a rotated x′y′-system?Domain: Conic SectionsCluster: Understand the properties of conic sections and apply them to model real-world phenomena.*A-C2. From an equation in standard form, graph the appropriate conic section: ellipses, hyperbolas, circles, and parabolas. Demonstrate an understanding of the relationship between their standard algebraic form and the graphical characteristics. 3. Transform equations of conic sections to convert between general and standard form. Enduring Understanding(s):Parametric equations, and polar coordinates are useful in solving real-world problems. Essential Question(s):Why are functions and relations represented by parametric equations? Objective(s):Students will:Sketch the graph of a parametric equationWrite parametric equations in rectangular formGraph curves from the cycloid familySolve applications involving parametric equations10.7 Parametric Equations and Graphs (Coburn)10.5 Parametric Equations (Blitzer)Additional Resource(s) HYPERLINK "" Algebra & Trigonometry (Coburn), 2nd Edition(Exercise Videos, Lecture Videos, Graphing Calculator Videos, PowerPoint Presentations)Better Lesson: Introduction to Parametric EquationsBetter Lesson: Parametric Equations, Day 1 HYPERLINK "" Better Lesson: Parametric Equations, Day 1VocabularyParameter, parametric equationWriting in Math/DiscussionWhat does it mean to eliminate the parameter? What useful information can be obtained by doing this?Explain how the rectangular equation y = 5x can have infinitely many sets of parametric equations.Additional Topics in Algebra(Allow approximately 4-5 Weeks for instruction, review, and assessments )Domain: Sequences and SeriesCluster: Understand and use sequences and series.HYPERLINK ""A-S 1. Demonstrate an understanding of sequences by representing them recursively and explicitly. 2. Use sigma notation to represent a series; expand and collect expressions in both finite and infinite settings. Enduring Understanding(s):All arithmetic and geometric sequences can be expressed recursively and explicitly. Some other sequences also can be expressed in both ways but others cannot. Arithmetic sequences are identifiable by a common difference and can be modeled by linear functions. Infinite arithmetic series always diverge. Geometric sequences are identifiable by a common ratio and can be modeled by exponential functions. Infinite geometric series diverge if │r │≥1 and converge is │r │<1. The sums of finite arithmetic and geometric series can be computed with easily derivable formulas.Identifiable sequences and series are found in many naturally occurring objects. Essential Question(s):What is a sequence? What is a series? How are sequences & series related? What is an arithmetic sequence/series? What is a geometric sequence/series? What is sigma (the summation symbol)? How does the binomial theorem apply? What are the types of real-life situations where sequences & series can be used as models and prediction tools? Objective(s):Students will:Write out the terms of a sequence given the general or nth termWork with recursive sequences and sequences involving factorialFind the partial sum of a seriesUse summation notation to write and evaluate seriesUse sequences to solve applied problems11.1 Sequences and Series (Coburn)11.1 Sequences and Summation Notation (Blitzer)Additional Resources: HYPERLINK "" Algebra & Trigonometry (Coburn), 2nd Edition(Exercise Videos, Lecture Videos, Graphing Calculator Videos, PowerPoint Presentations)Sequences & Series (Khan Academy Videos)VocabularySequence, series, recursion formula, factorial notation, summation notationWriting in Math/DiscussionExplain the “how to” of breaking down sequences and series into equations. Explain the difference between a “normal” variable and the nth term.Domain: Sequences and SeriesCluster: Understand and use sequences and series.HYPERLINK ""A-S 3. Derive and use the formulas for the general term and summation of finite or infinite arithmetic and geometric series, if they exist. a. Determine whether a given arithmetic or geometric series converges or diverges.c. Find the sum of a finite arithmetic series.4. Understand that a series represents the approximation of a number when truncated; estimate truncation error in specific examples. Objective(s):Students will:Identify an arithmetic sequence and its common differenceFind the nth term of an arithmetic sequenceFind the nth partial sum of an arithmetic sequenceSolve applications involving arithmetic sequences11.2 Arithmetic Sequences (Coburn)11.2 Arithmetic Sequences (Blitzer)Additional Resource(s) HYPERLINK "" Algebra & Trigonometry (Coburn), 2nd Edition(Exercise Videos, Lecture Videos, Graphing Calculator Videos, PowerPoint Presentations)Sequences & Series (Khan Academy Videos)Better Lesson: Arithmetic SequencesTask(s) HYPERLINK "" Better Lesson: Patio ProblemVocabularyArithmetic sequence, common difference, partial sumWriting in Math/DiscussionExplain how to find the sum of the first nth term of an arithmetic sequence without having to add up all the terms.Domain: Sequences and SeriesCluster: Understand and use sequences and series.HYPERLINK ""A-S 3. Derive and use the formulas for the general term and summation of finite or infinite arithmetic and geometric series, if they exist. a. Determine whether a given arithmetic or geometric series converges or diverges.c. Find the sum of a finite arithmetic series.4. Understand that a series represents the approximation of a number when truncated;Objective(s):Students will:Identify a geometric series and its common ratioFind the nth term of a geometric sequenceFind the nth partial sum of a geometric sequenceFind the sum of an infinite geometric seriesSolve applications involving geometric sequences and series11.3 Geometric Sequences (Coburn)11.3 Geometric Sequences and Series (Blitzer)Additional Resource(s)HYPERLINK ""Algebra & Trigonometry (Coburn), 2nd Edition(Exercise Videos, Lecture Videos, Graphing Calculator Videos, PowerPoint Presentations)Sequences & Series (Khan Academy Videos)Better Lesson: Geometric SequencesVocabularyArithmetic sequence, common ratioWriting in Math/DiscussionWhat is the difference between a geometric series and an infinite geometric series? Give an example of each.Objective(s):Students will:Use subscript notation to evaluate and compose functionsApply the principle of mathematical induction to sum formulas involving natural numbersApply the principle of mathematical induction to general statements involving natural numbers11.4 Mathematical Induction (Coburn & Blitzer)Additional Resource(s)HYPERLINK ""Algebra & Trigonometry (Coburn), 2nd Edition(Exercise Videos, Lecture Videos, Graphing Calculator Videos, PowerPoint Presentations) HYPERLINK "" Khan Academy Videos: InductionBetter Lesson: Mathematical InductionVocabularyMathematical inductionWriting in Math/DiscussionExplain how to use mathematical induction to prove that a statement is true for every positive integer n.Provide a real-world example not used in class that describes mathematical induction.StatisticsDomain: Conditional Probability and the Rules of ProbabilityCluster: Understand and apply basic concepts of probabilityS-CP.A.2Use permutations and combinations to compute probabilities of compound events and solve problemsDomain: Using Probability to Make DecisionsCluster: Understand and use discrete probability distributionsS.MD.2Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.S.MD.8Use probabilities to make fair decisions S.MD.9Analyze decisions and strategies using probability concepts Enduring Understanding(s)Understand how to calculate probabilities using the General Multiplication Rule and interpret the results in context. Understand how to use permutations and combinations in conjunction with other probability methods to calculate probabilities of compound events and solve problems. Essential Question(s)How do I use the General Multiplication Rule to calculate probabilities? How do I determine when to use a permutation or a combination to calculate a probability? How do I use expected values to make decisions? How do I explain the decisions I make using expected values?Objective(s):Students will:Count possibilities using lists and tree diagramsCount possibilities using the fundamental principle of countingQuick-count distinguishable permutationsQuick-count nondistinguishable permutationsQuick-count using combinationsDefine an event on a sample spaceCompute elementary probabilitiesUse certain properties of probabilityCompute probabilities using quick-counting techniquesCompute probabilities involving nonexclusive events11.5 Counting Techniques (Coburn)11.6 Introduction to Probability (Coburn)11.6 Counting Principles, Permutations, and Combinations (Blitzer)11.7 Probability (Bllitzer)Additional Resource(s)HYPERLINK ""Algebra & Trigonometry (Coburn), 2nd Edition(Exercise Videos, Lecture Videos, Graphing Calculator Videos, PowerPoint Presentations)HYPERLINK ""Khan Academy Videos; Probability and CombinatoricsTask(s)GSE Pre-Calculus Unit 8: ProbabilityChoose from the tasks described on pp. 9-10VocabularyTree diagram, Fundamental Counting Principle, permutation, combination, theoretical probability, independent events, mutually exclusiveWriting in Math/DiscussionDefine probability, combination, and permutation. Explain in your own words when to use a combination and when to use a permutation.Create a probability word problem whose answer is one of the following fractions: 1/6 or 1/4 or 1/3.Give an example of two events that are not mutually exclusive.Domain: Sequences and SeriesCluster: Understand and use sequences and series.HYPERLINK ""A-S 5. Know and apply the Binomial Theorem for the expansion of (x+y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle. Enduring Understanding(s)The Binomial Theorem can be used to expand polynomials and to determine the probability of an event.?The Binomial Theorem can be applied easily using tools like Pascal’s Triangle and the combination function.Essential Question(s)What is the nature of the combination function, and how does it relate to binomial expansion?How can the coefficients of an expanded binomial be found?Objective(s):Students will:Using Pascal’s Triangle to find (a + b)nFind binomial coefficients using notationUse the binomial theorem to find (a + b)nFind a specific term of a binomial expansion11.7 The Binomial Theorem Summary andConcept Review (Coburn)11.5 The Binomial Theorem (Blitzer)Additional Resource(s)HYPERLINK ""Algebra & Trigonometry (Coburn), 2nd Edition(Exercise Videos, Lecture Videos, Graphing Calculator Videos, PowerPoint Presentations)Khan Academy Videos: Binomial TheoremTask(s) HYPERLINK "" Sequences, Induction, BinomialTheoremVocabularyPascal’s Triangle, Binomial TheoremWriting in Math/DiscussionExplain how to write out the terms of Pascal’s triangle.RESOURCE TOOLBOXThe Resource Toolbox provides additional support for comprehension and mastery of subject-level skills and concepts. While some of these resources are embedded in the map, the use of these categorized materials can assist educators with maximizing their instructional practices to meet the needs of all students.?Textbook Resources Core Standards - MathematicsCommon Core Standards - Mathematics Appendix A (formerly ) Core LessonsTennessee's State Mathematics Standards HYPERLINK "" TN Advanced Algebra & Trigonometry StandardsVideosBrightstormTeacher TubeThe Futures ChannelKhan AcademyMath TVLamar University TutorialCalculator Interactive Manipulatives HYPERLINK "" EdugoodiesAdditional Sites Cheat SheetOnline Algebra and Trigonometry TutorialLiteracyGlencoe Reading & Writing in the Mathematics ClassroomGraphic Organizers (9-12)Literacy Skills and Strategies for Content Area Teachers(Math, p. 22)ACTTN ACT Information & ResourcesACT College & Career Readiness Mathematics StandardsTasks/LessonsUT Dana CenterMars TasksInside Math TasksMath Vision Project Tasksengageny Lessons (Precalculus & Advanced Topics)Better Lesson HYPERLINK "" TN TasksNYC tasksSCS Math Tasks (Advanced Algebra & Trigonometry) ................
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