Grade 8 - Shelby County Schools



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 standards-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 Ready Standards are 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. FocusCoherenceRigorThe 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 work of each grade 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 algebra 1, the major clusters, algebra and functions, account for about 75% of time spent on instruction.Supporting Content - information that supports the understanding and implementation of the major work of the grade.Additional Content - content that does not explicitly connect to the major work of the grade yet it is required for proficiency.Thinking across grades:The Standards are designed around coherent progressions from grade to grade. Learning is carefully connected across grades so that students can build new understanding onto 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 course, these concepts serve the course focus. For example, instead of data displays as an end in themselves, they are an opportunity to do grade-level word problems.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. While the high school standards for math do not list high school fluencies, there are suggested fluency standards for algebra 1, geometry and algebra 2.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.-571500-1270Standards 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 QuarterExponents and Exponential FunctionsPolynomials and FactoringOverview In this quarter students will extend their knowledge of functions and build upon their earlier experiences with functions by extending the function types to exponential functions. Students develop fluency in graphing, interpreting, and modeling exponential functions, and using them to solve problems. Students will also explore ways in which exponential functions can describe real-world situations. Finally, in this quarter students understand that polynomials form a system analogous to the integers and that polynomials can produce equivalent forms of an expression. Students classify polynomials, perform the basic operations on polynomials, and factor polynomials in order to solve problems involving polynomials.HYPERLINK ""Year at a Glance DocumentContent StandardType of RigorFoundational StandardsSample Assessment Items**A-APR.A.1Conceptual Understanding, Procedural Skills & Fluency8.EE.C.7 a, b; 8.EE.C.8 a, b, cMathshell: Arithmetic With Polynomials and Rational ExpressionsA-SSE.B.3.aConceptual Understanding 8.EE.C.7 a, b; 8.EE.C.8 a, b, cMathshell: Seeing Structure in ExpressionsF-IF.A.3Conceptual Understanding8.F.A.1, 8.F.A.2,8.F.A.3Mathshell: Interpreting FunctionsF-BF.A.1aConceptual Understanding8.F.A.4, 8.F.A.5Mathshell: Building Functions** TN Tasks are available at and can be accessed by Tennessee educators with a login and password. 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.The fluency recommendations for Algebra I listed below should be incorporated throughout your instruction over the course of the school year.A/G A-APR.A.1 A-SSE.A.1b Solving characteristic problems involving the analytic geometry of lines Fluency in adding, subtracting, and multiplying polynomials Fluency in transforming expressions and seeing parts of an expression as a single object References: STATE STANDARDSCONTENTINSTRUCTIONAL SUPPORT & RESOURCES Exponents and Exponential Functions (Allow 3.5 weeks for instruction, review, and assessment) Domain: Interpreting Functions (F-IF)Cluster: Understand the concept of a function and use function notationF-IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n + 1) = f(n) + f(n – 1), for n > 1.★Domain: Building Functions (F-BF)Cluster: Build a function that describes a relationship between two quantities. F-BF.A.1a Determine an explicit expression, a recursive process, or steps for calculation from a context.Enduring Understanding(s):Exponents are used to represent complex expressions.Linear functions have a constant difference, whereas exponential functions have a constant ratio.Real world situations can be represented symbolically and graphically.Essential Question(s)What are the characteristics of exponential functions?What are real world models of exponential growth and decay?How can one differentiate an exponential model from a linear model given a real world set of data?Objective(s):Students will describe and interpret exponential functions that fit the patterns.Students will evaluate and graph exponential functions.Students will model exponential growth and decay. Use the following lessons first to introduce concepts/build conceptual understanding. HYPERLINK ""engageny Algebra I Module 3, Topic A HYPERLINK "" Lesson 1 HYPERLINK "" Lesson 2 HYPERLINK "" Lesson 3 HYPERLINK "" Lesson 4 HYPERLINK "" Lesson 5 HYPERLINK "" Lesson 6 HYPERLINK "" Lesson 7Use the textbook resources to address procedural skill and fluency.PearsonChapter 7- Exponents and Exponential Functions (Briefly review 7-1, 7-3, 7-4, & 7-5 as needed)7-6 Exponential Functions 7-7 Exponential Growth & Decay Glencoe7-6 Exponential Functions Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.Task(s)Illustrative Math: HYPERLINK "" Snake on a PlaneIllustrative Math: HYPERLINK "" College FundIllustrative Math: HYPERLINK "" Paper FoldingIllustrative Math: HYPERLINK "" Basketball BouncesIllustrative Math: HYPERLINK "" Exponential ParametersIllustrative Math: HYPERLINK "" Allergy MedicationIllustrative Math: HYPERLINK "" Boom TownInside Math: HYPERLINK "" FunctionsMath Shell - Short Tasks: Functions IIllustrative Math: Identifying Exponential Functions HYPERLINK "" Spread of DiseaseMath Shell: Representing Linear and Exponential Growth ( A Formative Assessment Lesson/Task) HYPERLINK "" \l "task436" Math Shell: Representing Polynomials GraphicallyMath Shell: Generating polynomials from PatternsLesson VideoExponentsAdditional Resource(s)HS Flip Book with examples of each Standard(This document is designed as a resource tool to assist teachers in deepening their understanding of what each standard means in terms of what students must know and be able to do. It outlines only a sample of instructional strategies and examples. Links to conceptual categories and specific standards in the document can be accessed from page 5 Mathematics Standards for High School.)ACT Practice (sample problems to prepare for the ACT)Pearson, pp.468-470Glencoe, pp.466- 467VocabularyExponential function, exponential growth, growth factor, compound interest, exponential decay, decay factorWriting in Math /Discussion How does the graph of y = bx change as the base b increase or decreases?How can you tell if an exponential function models growth or decay?Give an example of an exponential function in the form y = abx that is neither an exponential growth function nor an exponential decay function. Explain your reasoning.Explain how the recursive rule and the exponential rule are related?Polynomials & Factoring(Allow approximately 5.5 weeks for instruction, review, and assessment)Domain: Arithmetic with Polynomials and Rational Expressions (A-APR)Cluster: Perform arithmetic operations on polynomials A-APR.A.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.Domain: Seeing Structure in Expressions (A-SSE)Cluster: Write expressions in equivalent forms to solve problems A-SSE.B.3.a Factor a quadratic expression to reveal the zeros of the function it defines. Enduring Understanding(s):The properties of integers apply to polynomials.Factors are a subset of a product and with the distributive property allow options in solving polynomials.Multiplying and factoring polynomials are related.Solving polynomials involves the reversal of operations, the distributive property, and rules of exponents.Essential Question(s)How can polynomials be simplified and applied to solve problems?Can two algebraic expressions that appear to be different be equivalent?How are the properties of real numbers related to polynomials? What strategies can be used to perform arithmetic operations on polynomials?Objective(s):Explain the connection between the factored form of a quadratic expression and the zeros of the function it defines.Factor a quadratic expression to produce an equivalent form of the original expression. Use the following lessons first to introduce concepts/build conceptual understanding. HYPERLINK ""engageny Algebra I Module 1, Topic B HYPERLINK "" Lesson 8 HYPERLINK "" Lesson 9engageny Algebra I Module 4, Topic A HYPERLINK "" Lesson 1Lesson 2 HYPERLINK "" Lesson 3 HYPERLINK "" Lesson 4LearnZillion: Simplifying polynomial expressions by dividing by monomialsLearnZillion: Find Solutions of polynomials by Factoring HYPERLINK "" LearnZillion: Simplifying Polynomials by Adding and Subtracting Terms of Like DegreeHYPERLINK ""LearnZillion: Simplifying Polynomials by Multiplying and Then Combining Like TermsHYPERLINK ""LearnZillion: Identify the Zeros of a Quadratic Function in Standard Form By FactoringHYPERLINK ""LearnZillion: Find Zeros of Quadratic Functions Using Factored FormUse the textbook resources to address procedural skill and fluency. Pearson8-1 Adding and Subtracting Polynomials 8-2 Multiplying and Factoring8-3 Multiplying Binomials8-4 Multiplying Special Cases8-5 Factoring x2 + bx + c8-6 Factoring ax2 + bx + c8-7 Factoring Special CasesGlencoe7-5, 7-6, 7-7, 7-8, 8-3, 8-4, 8-5, 8-6Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.Task(s) HYPERLINK " O'rourke - Polynomial Farm.pdf" Polynomial Farm Polynomials TasksIllustrative: Non-negative Polynomials Illustrative Math: HYPERLINK "" Powers of 11 Math Shell: Arithmetic with Polynomials and Rational ExpressionsAdditional Resource(s):HS Flip Book with examples of each Standard HYPERLINK "" Adding and Subtracting Polynomials Practice Review Factoring-VocabularyBinomials Exit TicketsFactoring By GroupingOperations on PolynomialsLesson Videos:Exponents and Polynomials VideosVideo: Classifying polynomials using the degree and number of termsVideo: Adding polynomialsVideo: Subtracting polynomialsVideo: Multiplying a polynomial by a monomialVideo: Finding the GCF of a polynomialVideo: Factoring out a monomial using the GCFVideo: Multiplying two binomials using the distributive propertyVideo: Multiplying two binomials using FOILVideo: Applying the multiplication of polynomialsVideo: Multiplying a trinomial and binomialVideo: Squaring a binomialVideo: Squaring a binomial to find probabilityVideo: Finding the difference of squaresVideo: Factoring trinomials of the type x^2 + bx + c where b is positive HYPERLINK "" Video: Factoring trinomials of the type x^2 + bx + c where b is negative HYPERLINK "" Video: Factoring trinomials of the type x^2 + bx - cVideo: Factoring trinomials with two variablesVideo: Factoring perfect square trinomials with a = 1Video: Factoring perfect square trinomials with a not equal to 1Video: Factoring the difference of two squaresVideo: Factoring a four-term polynomial by groupingVideo: Factoring a trinomial by groupingVideo: Using factoring of trinomials in real-world situationsACT Practice (sample problems to prepare for the ACT)Pearson, pp.528-530Glencoe, pp.520-521VocabularyMonomial, degree of a monomial, polynomial, standard form of a polynomial, binomial, trinomial.Writing in Math /Discussion Compare & contrast the processes of adding monomials and adding polynomials. Suppose n is an integer. Is n2+n always, sometimes, or never an integer? Justify your answer.How is the degree of the product of two polynomials p(x) and q(x) related to the degrees of p(x) and q(x)?Explain why 2x2 + 7x+ 10 cannot be factored.Summarize the procedures for factoring a difference of squares and provide at least two examples.Graphic Organizer:Polynomials Graphic Organizer Review 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 ResourcesPearsonmath Site - Textbook and ResourcesStandardsCCSS (formerly ) Flip Book with Examples of Each Standard(This is designed as a resource tool to assist teachers in deepening their understanding of what each standard means in terms of what students must know and be able to do. It outlines only a sample of instructional strategies and examples. Links to conceptual categories and specific standards in the document can be accessed from page 5 Mathematics Standards for High School.)Achieve HYPERLINK "" TN Algebra I StandardsTN Department of Education Math StandardsVideos HYPERLINK "" Khan AcademyTeacher TubeMath TV The Futures ChannelThe Teaching ChannelIVEST Video LibraryIlluminations (NCTM)Get The MathCalculator HYPERLINK "" \t "_blank" HYPERLINK "" ResourcesNational Library of Virtual Manipulatives MAP Resources: 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. ?LiteracyLiteracy Skills and Strategies for Content Area Teachers(Math, p. 22)Formative Assessment Using the UPS StrategyGlencoe Reading & Writing in the Mathematics ClassroomGraphic Organizers (9-12)TasksMathematics Assessment Project (MARS/ Math Shell Tasks)Dan Meyer's Three-Act Math TasksIllustrative Math TasksUT Dana CenterInside Math TasksLearnZillionSCS Math Tasks (Algebra I)ACTTN ACT Information & ResourcesACT College & Career Readiness Mathematics Standards ................
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