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. 45720022929850The 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. -571500457200Throughout 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 Standards for Mathematical Practice 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 ics Addressed in Quarter 3Applications of DifferentiationApplications of IntegrationOverviewStudents have previously studied two types of elementary functions, algebraic functions and trigonometric functions. During this quarter students study the properties, derivatives, and antiderivatives of logarithmic and exponential functions that have bases other than e. Students also study inverse trigonometric functions and find their derivatives and antiderivatives. Students study integration and a variety of applications associated with integration. They find the area of a region bounded by two curves, and find the volume of a solid of revolution by disk and shell methods. Students study Riemann Sums and definite integrals, the Fundamental Theorem of Calculus, and integration by substitution and by using the Trapezoidal Rule. Students investigate applications of differentiation and integration throughout the quarter.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 5: Logarithmic, Exponential, and Other Transcendental FunctionsChapter 6: Differential Equations (Allow approximately 4 - 5 weeks for instruction, review, and assessment)Domain: Calculate and Apply IntegralsCluster: Apply techniques of differentiationI-AIDevelop facility with finding antiderivatives that follow directly from derivatives of basic functions (power, exponential, logarithmic, and trigonometric). Enduring Understandings: Derivatives and anti-derivatives have an inverse relationship to each other. The area under the curve is the geometric meaning of anti-derivatives. The anti-derivative has both theoretical and real life applications. Essential Questions: How are the rules for differentiation used to develop the basic rules of integration? How can we use the measure of area under a curve to discuss net change of a function over time? How are area under the curve and the definite integral related? Objectives:Students will:Integrate exponentials that have bases other than e.Use exponential functions to model compound interest and exponential growth.Integrate functions whose antiderivatives involve inverse trigonometric functions.5.5: Bases Other than e and Applications5.7: Inverse Trigonometric Functions: IntegrationAdditional Resource(s)HYPERLINK ""Larson Calculus Videos – Section 5.5 Larson Calculus Videos Visual Calculus TutorialsHYPERLINK ""Video – Bases Other than e and Applications Video - Inverse Trigonometric Functions: Integration Khan Academy Calculus VideosCalculus Activities Using the TI-84Precalculus & Calculus TasksChapter 5 Vocabulary (5-5 & 5-7)Base, exponential function to the base a, logarithmic function to the base a, separation of variablesDomain: Calculate and Apply IntegralsCluster: Apply integrals to solve problemsI-AIUse integrals to solve a variety of problems (e.g., distance traveled by a particle along a line, exponential growth/decay).Objectives:Students will:Use separation of variables to solve a simple differential equation.Use exponential functions to model growth and decay in applied problems.6.2: Differential EquationsAdditional Resource(s)Larson Calculus Videos – Section 6.2 Visual Calculus TutorialsKhan Academy (Differential equations)Differential EquationsVideo: Differential Equations: Growth & DecayCalculus Activities Using the TI-84Precalculus & Calculus TasksVocabularyExponential growth, exponential decayWriting in Math/DiscussionSuppose an insect population increases by a constant number each month. Explain why the number of insects can be represented by a linear function.Suppose an insect population increases by a constant percentage each month. Explain why the number of insects can be represented by an exponential function.Chapter 7: Applications of Integration (Allow approximately 4-5 weeks for instruction, review, and assessment)Domain: Calculate and Apply IntegralsCluster: Apply techniques of differentiationI-AIDevelop facility with finding antiderivatives that follow directly from derivatives of basic functions (power, exponential, logarithmic, and trigonometric). Objectives:Students will:Find the area of a region between two curves using integration.Find the area of a region between intersecting curves using integration.Describe integration as an accumulation process.7.1: Area of a Region Between Two CurvesAdditional Resource(s)Visual Calculus TutorialsHYPERLINK ""Larson Calculus Videos – Section 7.1Calculus Tutorial VideosKhan Academy (Integrals)Calculus Activities Using the TI-84Precalculus & Calculus TasksChapter 7 Vocabulary (7-1, 7-2, 7-3) Representative rectangle, solid of revolution, axis of revolution, disk method, outer radius, inner radius, shell methodWriting in Math/ DiscussionHave students write how they use rectangles to find the approximate area between two curves.Domain: Calculate and Apply IntegralsCluster: Apply integrals to solve problemsI-AIUse a definite integral to find the volume of a solid formed by rotating around a given axis.Objectives:Students will:Find the volume of a solid of revolution using the disk method.Find the volume of a solid of revolution using the washer method.Find the volume of a solid with a known cross section.Find the volume of a solid of revolution using the shell pare the uses of the disk method and the shell method.7.2: Volume: The Disk Method7.3: Volume: The Shell MethodAdditional Resource(s)HYPERLINK ""Larson Calculus Videos – Section 7.2HYPERLINK ""Larson Calculus Videos – Section 7.3Volume of a Solid RevolutionVisual Calculus Tutorials HYPERLINK "" Khan Academy Calculus VideosEngageNY Precalculus and Advanced Topics Module 3, Topic A, Lesson 9: Volume and Cavalieri’s PrincipleCalculus Activities Using the TI-84Precalculus & Calculus TasksSection Project (after 7.3)The Oblateness of SaturnSee engageny Lesson for Exit Ticket/Discussion Questions.Domain: Understanding IntegralsCluster: Demonstrate understanding of a Definite IntegralI-UI Define the definite integral as the limit of Riemann sums and as the net accumulation of change. Correctly write a Riemann sum that represents the definition of a definite integral.Objectives:Students will:Understand the definition of Riemann sums.Evaluate a definite integral using limits.Evaluate a definite integral using properties of definite integrals.4.3: Riemann Sums and Definite IntegralsAdditional Resource(s)Visual Calculus TutorialsHYPERLINK ""Larson Calculus Videos – Section 4.3Calculus Tutorial VideosVideo: Riemann Sums and Definite Integrals HYPERLINK "" Khan Academy Calculus VideosCalculus Activities Using the TI-84Precalculus & Calculus TasksWriting in Math/DiscussionGive an example of a function that is integrable on the interval [-1, 1], but not continuous on [-1, 1]Domain: Understanding IntegralsCluster: Understand and apply the Fundamental Theorem of CalculusI-UI Evaluate definite integrals using the Fundamental Theorem of Calculus. Use the Fundamental Theorem of Calculus to represent a particular antiderivative of a function and to understand when the antiderivative so represented is continuous and differentiable.Apply basic properties of definite integrals.Objectives:Students will:Evaluate a definite integral using the Fundamental Theorem of Calculus.Understand and use the Mean Value Theorem for integrals.Find the average value of a function over a closed interval.Understand and use the Second Fundamental Theorem of Calculus.4.4: The Fundamental Theorem of CalculusAdditional Resource(s)Visual Calculus TutorialsHYPERLINK ""Larson Calculus Videos – Section 4.4Calculus Tutorial VideosVideo: The Fundamental Theorem of Calculus HYPERLINK "" Khan Academy Calculus VideosCalculus Activities Using the TI-84Precalculus & Calculus TasksWriting in Math/DiscussionResearch and prepare a report on the Fundamental Theorem of Calculus and the mathematicians Isaac Newton and Gottfried Leibniz. Domain: Calculate and Apply IntegralsCluster: Apply techniques of antidifferentiation I-AI Develop facility with finding antiderivatives that follow directly from derivatives of basic functions (power, exponential, logarithmic, and trigonometric). Use substitution of variables to calculate antiderivatives (including changing limits for definite integrals).Find specific antiderivatives using initial conditions.Objectives:Students will:Use pattern recognition to find an indefinite integral.Use change of variables to find an indefinite integral.Use the general power rule for integration to find an indefinite integral.Use a change of variables to evaluate a definite integral.Evaluate a definite integral involving an even or odd function.4.5: Integration by SubstitutionAdditional Resource(s)Visual Calculus TutorialsHYPERLINK ""Larson Calculus Videos – Section 4.5Calculus Tutorial VideosVideo: Integration by Substitution HYPERLINK "" Khan Academy Calculus VideosCalculus Activities Using the TI-84Precalculus & Calculus TasksDomain: Understanding IntegralsCluster: Demonstrate understanding of a Definite Integral I-UI 3. Use Riemann sums (left, right, and midpoint) and trapezoidal sums to approximate definite integrals of functions, represented graphically, numerically, and by tables of values.Objectives:Students will:Approximate a definite integral using the Trapezoidal Rule.4.6: Numerical Integration Additional Resource(s)Visual Calculus TutorialsHYPERLINK ""Larson Calculus Videos – Section 4.6Calculus Tutorial VideosVideo: Numerical Integration HYPERLINK "" Khan Academy Calculus VideosCalculus Activities Using the TI-84Precalculus & Calculus TasksRESOURCE 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 ResourcesLarson/Edwards Calculus of a Single Variable ? 2010Larson CalculusStandardsCommon Core Standards - MathematicsCommon Core Standards - Mathematics Appendix (formerly TN Core)The Mathematics Common Core ToolboxTennessee’s State Mathematics StandardsState Academic Standards (Calculus) VideosLarson Calculus Videos HYPERLINK "" KhanAcademyHippocampusBrightstormPre-Calculus Review University of Houston VideosCalculatorCalculus Activities Using the TI-84 HYPERLINK "" Texas Instruments EducationCasio EducationTI EmulatorInteractive Manipulatives HYPERLINK "" Interactive ExamplesAdditional Sites Calculus Tutorials HYPERLINK "" Lamar University Tutorial Precalculus & Calculus Tasks PowerPoint LecturesAlgebra Cheat SheetTrigonometry Cheat SheetOnline Algebra and Trigonometry TutorialStudy Tips for Math CoursesLiteracyGlencoe Reading & Writing in the Mathematics ClassroomLiteracy Skills and Strategies for Content Area Teachers(Math, p. 22)Graphic Organizers (dgelman)Graphic Organizers (9-12)Lessons/Tasks/Resourcesengageny Lessons (Precalculus & Advanced Topics)Precalculus & Calculus TasksLesson WorksheetsResource PageCalculus LinksMath Forum Calculus ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download