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 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 73% 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.While the academic standards establish desired learning outcomes, the curriculum provides instructional planning designed to help students reach these outcomes. Educators will use this guide and the standards as a roadmap for curriculum and instruction. The sequence of learning is strategically positioned so that necessary foundational skills are spiraled in order to facilitate student mastery of the standards.4530090115443000These standards emphasize thinking, problem-solving and creativity through next generation assessments that go beyond multiple-choice tests to increase college and career readiness among Tennessee students. In addition, assessment blueprints () have been designed to show educators a summary of what will be assessed in each grade, including the approximate number of items that will address each standard. Blueprints also detail which standards will be assessed on Part I of TNReady and which will be assessed on Part II.Our collective goal is to ensure our students graduate ready for college and career. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation and connectionsThe second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations) procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics and sensible, useful and worthwhile, coupled with a belief in diligence and one’s own efficacy). Throughout the year, students should continue to develop proficiency with the eight Standards for Mathematical Practice.How to Use the Mathematics Curriculum Maps135255-154940000This 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 instructional practice in alignment with the three College and Career Ready shifts, as described above, in instruction for Mathematics. 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 standards and teaching practices that teachers should consistently access:The TNCore 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.Mathematical Teaching Practices NCTM – Mathematics Teaching PracticesCurriculum Maps:Locate the TDOE Standards in the left column. Analyze the language of the standards and match each standard to an essential understanding in the second column. Consult your Pearson/Prentice Hall or Glencoe Algebra 1 Teachers’ Edition (TE) and other cited references to map out your week(s) of instruction.Plan your weekly and daily objectives, using the standards' explanations provided in the second column. Best practices tell us that making objectives measureable increases student mastery.Carefully review the web-based resources provided in the 'Content and Tasks' column and use them as you introduce or assess a particular standard or set of standards.Review the CLIP Connections found in the right column. Make plans to address the content vocabulary, utilizing the suggested literacy strategies, in your instruction.Examine the other standards and skills you will need to address in order to ensure mastery of the indicated standard.Using your Pearson/Prentice Hall or Glencoe TE and other resources cited in the curriculum map, plan your week using the SCS lesson plan template. Remember to include differentiated activities for small-group instruction and math stations.TN State StandardsEssential UnderstandingsContent & TasksCLIP ConnectionsQuadratic Functions & Modeling( 4.5 weeks) HYPERLINK "" A-CEDCreate equations that describe numbers orrelationships HYPERLINK "" F-IFUnderstand the concept of a function and use function notation HYPERLINK "" F-IFInterpret functions that arise in applications in terms of the context HYPERLINK "" F-IFAnalyze functions using different representations2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.★5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.★7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★a. Graph linear and quadratic functions and show intercepts, maxima, and minima.b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.9. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.Pearson 9-1: Quadratic Graphs & Their PropertiesGraphing a quadratic function using a table, y = ax^2Graphing a quadratic function using a table, y = ax^2 + cUsing a quadratic function to model the height of an object - Example 1Glencoe9-1: Graphing Quadratic FunctionsSorting Functions Task 9-2: Concept Byte Collecting Quadratic DataVocabulary: Quadratic formula, standard form, parabola, axis of symmetry, vertex, maximum, minimum, symmetryGraphic Organizers:Graphing in Standard FormGraphing in Vertex FormGraphing in Intercept FormJournal Prompt(s):Provide an example of a real-world situation that is best represented by a nonlinear function.Describe the features that are common to the graphs of all quadratic functions.Explain how to approximate the roots of a quadratic equation when the roots are not integers.Utilize Tasks to include the Standards for Mathematical Practice where students have to reason, justify, explain, construct & model their thinking. HYPERLINK "" A-CEDCreate equations that describe numbers or relationshipsA-REISolve equations and inequalities in one variable HYPERLINK "" A‐APRUnderstand the relationship between zeros and factors of polynomials HYPERLINK "" F-IFAnalyze functions using different representations 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.4. Solve quadratic equations in one variable.a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x –p)2 = q that has the same solutions. Derive the quadratic formula from this form. b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.3. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★a. Graph linear and quadratic functions and show intercepts, maxima, and minima.b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.Pearson9-3: Solving Quadratic EquationsSolving quadratic equations by graphingSolving quadratic equations using square rootsGlencoe9-2:Solving Quadratic Equations by GraphingConcept Byte: Finding Roots HYPERLINK "" Graphing Quadratic Equations ReviewSheet Graphing Quadratics Khan AcademyVocabulary:Double root, quadratic equation, standard form of a quadratic equation, root of an equation, zero of a functionCompare & ContrastWhen is it easier to solve a quadratic equation of the form ax2 + c = 0 using square roots than to solve it using a graph?Journal Prompt(s):Use a two-column algebraic proof to provide justifications and explanations when solving each equation and inequality.Utilize Tasks to include the Standards for Mathematical Practice where students have to reason, justify, explain, construct & model their thinking.A-CED (See Lesson 9-3)A-REI (See Lesson 9-3) HYPERLINK "" A-SSEWrite expressions in equivalent forms to solve problemsF-IF (See Lesson 9-3; F-IF 8)3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★a. Factor a quadratic expression to reveal the zeros of the function it defines.b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.Pearson9-4: Factoring to Solve Quadratic EquationsSolving quadratic equations by factoringGlencoe9-4:Solving Quadratic Equations by Completing the SquareVocabulary:Complete the square, zero product propertyCompare & ContrastHow is factoring the expression x2-6x+8 similar to solving the equation x2-6x+8=0? How is it different?How is solving a quadratic equation using square roots like completing the square? How is it different?Journal Prompt(s):Can you extend the Zero-Product Property to nonzero products of numbers? For example, if ab = 8, is it always true that a = 8 or b = 8? Explain.Pearson Algebra I Book Page 558 #34Use KNWS, SQRQCQ, or UPS√ StrategyLiteracy Strategies in Math (p. 22 )UPS√Use a two-column algebraic proof to provide justifications and explanations when solving each equation and inequality.Pearson9.5: Completing the SquareSolving quadratic equations using completing the squareSolving quadratic equations using completing the square when a does not equal 1 HYPERLINK "" Completing the Square Stations(see Math Tasks on C & I site)Tell whether you would use square roots, factoring, or completing the square to solve each equation. Explain your choice of method.a. k2 – 3k = 304 b. t2 – 6t + 16 = 0Pearson Algebra I Book Page 565 #32 & #33Use KNWS, SQRQCQ, or UPS√ StrategyLiteracy Strategies in Math (p. 22 )UPS√A-CED (See Lesson 9-3)A.REI (See Lesson 9-3)F-IF (See Lesson 9-3; F-IF 8)Pearson9-6: The Quadratic Formula and the DiscriminantSolving quadratic equations using the quadratic formulaSolving real-world problems using the quadratic formulaChoosing the appropriate method to solve quadratic equationsUsing the discriminant to find the number of solutions and solve problemsGlencoe9-5: Solving Quadratic Equations by Using the Quadratic formulaPearsonAlgebra II 4-8: Complex NumbersQuadratic TasksSimplifying the square root of negative numbersSimplifying imaginary numbersAdding complex numbersMultiplying complex numbersFinding complex solutionsVocabulary:Discriminant, quadratic formulaJournal Prompt(s):Explain how the discriminant of the equation ax2 + bx + c = 0 is related to the number of x-intercepts of the graph y = ax2 + bx + c.Pearson Algebra I Book Page 572 #22, #41, & #42Use KNWS, SQRQCQ, or UPS√ StrategyLiteracy Strategies in Math (p. 22 )UPS√Explain the difference between the additive inverse of a complex number and a complex conjugate.Pearson Algebra I Book Page 588 Tasks 1 & 2Use KNWS, SQRQCQ, or UPS√ StrategyLiteracy Strategies in Math (p. 22 )UPS√Utilize Tasks to include the Standards for Mathematical Practice where students have to reason, justify, explain, construct & model their thinking.A-REI (See Lesson 6-1)Solve systems of equations5. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.Pearson9-8: Systems of Linear and Quadratic EquationsVocabulary:Systems of linear equations, systems of quadratic equations, elimination, substitutionCompare & ContrastHow are solving systems of linear equations and solving systems of linear and quadratic equations alike? How are they different?Journal Prompt(s):Pearson Algebra I Book Page 586 #31 & #32Use KNWS, SQRQCQ, or UPS√ StrategyLiteracy Strategies in Math (p. 22 )UPS√Pearson Algebra I Book Page 588 Tasks 1 - 3Use KNWS, SQRQCQ, or UPS√ StrategyLiteracy Strategies in Math (p. 22 )UPS√Rational Expressions & Functions( 4.5 weeks) HYPERLINK "" A-CEDCreate equations that describe numbers or relationships2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.Pearson11-1: Simplifying Rational ExpressionsSimplifying a rational expressionSimplifying a rational expression by recognizing opposite factorsGlencoe11-3: Simplifying Rational Expressions Extra PracticeVocabulary:Rational expression, excluded valueJournal Prompt(s):When simplifying rational expressions, why may it be necessary to exclude values? Explain.Suppose neither the numerator not the denominator of a rational expression can be factored Is the expression necessarily in simplified form? Explain.Pearson Algebra I Book Page 656 #40Use KNWS, SQRQCQ, or UPS√ StrategyLiteracy Strategies in Math (p. 22 )UPS√ HYPERLINK "" A‐APRRewrite rational expressions.7. Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.Pearson11-2: Multiplying & Dividing Rational ExpressionsMultiplying rational expressions using factoringMultiplying rational expressions by polynomialsDividing rational expressions by rational expressions and polynomialsGlencoe 11-4: Multiplying & Dividing Rational Expressions Concept Byte:Dividing Polynomials Using Algebra Tiles HYPERLINK "" Multiplying and Dividing RationalExpressions PracticeVocabulary:Complex fraction, rational expression Compare & ContrastHow are multiplying rational expressions and multiplying numerical fractions similar? How are they different?Journal Prompts):Explain how to multiply a rational expression by a polynomial.Explain how to divide a rational expression by a polynomial.Pearson Algebra I Book Page 663 #59 & #60Use KNWS, SQRQCQ, or UPS√ StrategyLiteracy Strategies in Math (p. 22 )UPS√Pearson11-3: Dividing PolynomialsDividing a polynomial by a monomial HYPERLINK "" Dividing a polynomial by a binomialDividing polynomials with a zero coefficientGlencoe 11-5: Dividing PolynomialsVocabulary:Zero coefficient, degree of quotientJournal Prompt(s):What are the steps that you repeat performing polynomial long division?How is dividing polynomials like dividing real numbers? How is it different?Pearson Algebra I Book Page 670 #37Use KNWS, SQRQCQ, or UPS√ StrategyLiteracy Strategies in Math (p. 22 )UPS√Utilize Tasks to include the Standards for Mathematical Practice where students have to reason, justify, explain, construct & model their thinking.Pearson11-4: Adding & Subtracting Rational ExpressionsAdding rational expressions with like denominatorsSubtracting rational expression with like denominatorsAdding rational expressions with unlike monomial denominatorsAdding rational expressions with unlike polynomial denominatorsGlencoe 11-6: Adding & Subtracting Rational ExpressionsVocabulary:No new vocabularyCompare & ContrastHow is finding the least common denominator (LCD) of two rational expressions similar to finding the least common denominator (LCD) of two numerical fractions? How is it different?Journal Prompt(s):Suppose your friend was absent today. How would you explain to your friend how to add and subtract rational expressions?Your friend says she can always find a common denominator for two rational expressions by finding the product of two denominators.a. Is your friend correct? Explain.b. Will your friend’s method always give you the least common denominator (LCD)? Explain.Pearson Algebra I Book Page 676 #43 & #44Use KNWS, SQRQCQ, or UPS√ StrategyLiteracy Strategies in Math (p. 22 )UPS√A-REI Reasoning with Equations and InequalitiesSolve systems of equations HYPERLINK "" A-REIRepresent and solve equations and inequalities graphically6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.★Pearson11-7: Graphing Rational FunctionsGraphing a rational function using a vertical asymptoteGraphing a rational function using vertical and horizontal asymptotesDescribing the graph of different types of functions11-7: Concept Byte Graphing Rational FunctionsGlencoe 11-2: Rational Functions Vocabulary:Rational function, asymptoteCompare & ContrastHow are excluded values and a vertical asymptote of a rational function alike? How are they different?Journal Prompt(s):Pearson Algebra I Book Page 698 #23Use KNWS, SQRQCQ, or UPS√ StrategyLiteracy Strategies in Math (p. 22 )UPS√Pearson Algebra I Book Page 699 #24 & #31Pearson Algebra I Book Page 702 Tasks 1 - 3Utilize Tasks to include the Standards for Mathematical Practice where students have to reason, justify, explain, construct & model their thinking.RESOURCE TOOLBOXTextbook ResourcesPearsonmath Site - Textbook and ResourcesStandardsCCSS HYPERLINK "" Common Core Flip BookAchieve HYPERLINK "" TN Algebra I StandardsTN Department of Education Math StandardsVideos HYPERLINK "" Khan AcademyTeacher TubeMath TV The Futures ChannelThe Teaching ChannelIlluminations (NCTM)Discovery EducationGet The MathCalculator HYPERLINK "" \t "_blank" HYPERLINK "" Manipulatives Sites for Teaching Math Assessment Project (MARS Tasks)Dan Meyer's Three-Act Math TasksSCS Math Tasks (Algebra 1)CLIPLiteracy 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) ................
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