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 2, the major clusters, account for 65% 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.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 connections.The 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 Mathematic Curriculum MapsThis 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 in instruction for Mathematics. We should see these shifts in all classrooms:FocusCoherenceRigorThroughout 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 each of the three shifts that teachers should consistently access:The TNCore Mathematics StandardsThe Tennessee Mathematics Standards: standardsTeachers 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 ShiftsFocus standards are focused on fewer topics so students can learn moreCoherence within a grade are connected to support focus, and learning is built on understandings from previous gradesRigor standards set expectations for a balanced approach to pursuing conceptual understanding, procedural fluency, and application and modelingCurriculum Maps:Locate the TDOE Standards in the left column. Analyze the language of the standards and match each standard to a learning target in the second column.Consult your Pearson/Prentice Hall or Glencoe Algebra 2 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 ConnectionsChapter 11(Allow 2.5 weeks)S-IC Making Inferences & Justifying ConclusionsUnderstand and evaluate random processes underlying statistical experiments.S-IC Making Inferences & Justifying ConclusionsMake inferences and justify conclusions from sample surveys, experiments, and observational studies.2. Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.4. Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.Pearson11-1 Permutations and CombinationsUsing permutationsEvaluating combinations11.2 Probability – SimulationFinding experimental probabilityFinding theoretical and geometric probabilityGlencoe 12.4 Probability and Probability DistributionsTextbook Resourcesmath Site - Textbook and ResourcesTASKSRock, Paper, ScissorsRoad Trip Shorts and ShirtsA Fair Game Stick or Switch Charity FairMath Nspired: Birthday ProblemVocabularyFundamental Counting Principle, permutation, n factorial, combination, experimental, probability, simulation, sample space , equally likely outcomes, theoretical probabilityJournaling/PromptExplain the difference between experimental probability and theoretical probability.Utilize Tasks to include the Standards for Mathematical Practice where students have to reason, justify, explain, construct & model their thinking. HYPERLINK "" S.ID.A.2Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.S.ID.A.3Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).Pearson11.5 Analyzing DataMaking a box-and-whisker plotPearson11-6 Standard Deviation Finding standard deviation Using standard deviationGlencoe 12.6 Hypothesis TestingTASKVariety of Word ProblemsVocabularyMeasure of central tendency, mean, median, mode, bimodal, outlier, range, quartile, interquartile range, box-and-whisker plot,Percentile, measure of variation, variance, standard deviationJournaling/PromptExplain the difference between measures of central tendency and measures of variation.What is the effect on an outlier on the standard deviation of a data set?Utilize Tasks to include the Standards for Mathematical Practice where students have to reason, justify, explain, construct & model their thinking.S-IC Making Inferences & Justifying ConclusionsUnderstand and evaluate random processes underlying statistical experiments.2. Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.Pearsonp.724 Describing DataS-IC Making Inferences & Justifying ConclusionsUnderstand and evaluate random processes underlying statistical experiments.1. Understand statistics as a process for making inferences about population parameters based on a random sample from that population.HYPERLINK ""S.IC.B.4Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.Pearson11.7 Samples and SurveysUsing margin of errorGlencoe 12.1 Experiments, Surveys, and Observational StudiesTextbook Resourcesmath Site - Textbook and ResourcesTASKClick ItVocabularyPopulation, sample, convenience sample, self-selected sample, systematic sample, random sample, bias, observational study, controlled experiment, surveyJournaling/PromptWhat does it mean to have an unbias sample? Why does it matter?Utilize Tasks to include the Standards for Mathematical Practice where students have to reason, justify, explain, construct & model their thinking.S-ID Interpreting Categorical and Quantitative DataSummarize, represent, and interpret data on a single count or measurement variable.4. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.Pearson11.9 Normal DistributionUsing a normal distributionUsing the standard normal curveGlencoe 12.5 Normal DistributionTASKSMath Vision Project 2014- Module and statistics (various)Is This Your Normal?VocabularyDiscrete probability distribution, continuous probability distribution, normal distributionJournaling/PromptDescribe how you can use a normal distribution to approximate a binomial distribution. Draw a binomial histogram and a normal curve to help with your explanation.Utilize Tasks to include the Standards for Mathematical Practice where students have to reason, justify, explain, construct & model their thinking.Chapter 13(Allow 5.5 weeks)N-Q Quantities★Reason quantitatively and use units to solve problems.F-TF Trigonometric FunctionsModel periodic phenomena with trigonometric functions.2. Define appropriate quantities for the purpose of descriptive modeling. 5. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.*Pearson13-1 Exploring Periodic DataIdentifying cycles and periodsFinding amplitude of a periodic functionVocabularyPeriodic function, cycle, period, amplitudeJournaling/PromptFunctions that repeat over time are common in everyday life. The English language has many words that stand for periods of time. Name a few terms and state the period of time from which the term is derived. Utilize Tasks to include the Standards for Mathematical Practice where students have to reason, justify, explain, construct & model their thinking.F-TF Trigonometric FunctionsExtend the domain of trigonometric functions using the unit circle.1. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. 2. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. TF.A.3 Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for?x, π +?x, and 2π -?x?in terms of their values for?x, where?x?is any real number.TF.A.4 Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.13-2 Angles and the Unit Circle Glencoe 13.2 Angles and Angle Measure13.3 Trigonometric Functions of General Angles13.6 Circular FunctionsMeasuring and sketching an angle in standard positionUsing the unit circle to find the cosine and sine of an angleUsing the unit circle to find exact values of cosine and sineTASKSTrigonometric FunctionsGraphs from the unit circleUnit CircleVocabularyStandard position, initial side, terminal side, coterminal angles, unit circle, cosine of Θ, sine of ΘJournaling/PromptSummarize how the quadrant in which the terminal side of an angle lies affects the sign of the sine and cosine of that angle.Utilize Tasks to include the Standards for Mathematical Practice where students have to reason, justify, explain, construct & model their thinking.F-TF-APearson13-3 Radian MeasureConverting between radians and degreesFinding cosine and sine of radian measuresFinding the length of an arcTASKRolling into RadiansVocabularyCentral angle, intercepted arc, radianJournaling/PromptTwo angles are measured in radians. Explain how to tell whether the angles are coterminal without rewriting their measures in degrees.Utilize Tasks to include the Standards for Mathematical Practice where students have to reason, justify, explain, construct & model their thinking.F-IF Interpreting FunctionsInterpret functions that arise in applications in terms of the contextAnalyze functions using different representationsF-BF Building FunctionsBuild new functions from existing functions S-ID Interpreting Categorical and Quantitative Data Summarize, represent, and interpret data on two categorical and quantitative variables4. 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.★e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. 9. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).3. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. a. Fit a function to the data; use functions fitted to data to solve problems in the context of the dataPearson13-4 The Sine Function Estimating sine values in radiansFinding the amplitude of a sine curveSketching sine functionsGraphing sine functions Glencoe 13.7 Graphing Trigonometric FunctionsTASKSeeing MusicVocabularySine function, sine curveJournaling/PromptTwo angles are measured in radians. Explain how to tell whether the angles are coterminal without rewriting their measures in degrees.Utilize Tasks to include the Standards for Mathematical Practice where students have to reason, justify, explain, construct & model their thinking.See Section 13-4Pearson13-5 The Cosine Function Graphing cosine functionsSolving trigonometric functionsGlencoe 13.7 Graphing Trigonometric FunctionsTASKSWord ProblemsVocabularyCosine functionJournaling/PromptExplain how you can apply what you know about solving cosine equations to solving sine equations. Use -1 = 6 sin 2t as an example.Utilize Tasks to include the Standards for Mathematical Practice where students have to reason, justify, explain, construct & model their thinking.See Section 13-4Pearson13-6 The Tangent Function Graphing a tangent functionUsing the tangent function to solve problemsGlencoe 13.7 Graphing Trigonometric FunctionsTASKSatelliteVocabularyTangent of Θ, tangent functionJournaling/PromptExplain how you can write a tangent function that has the same period as y = sin 4Θ.Utilize Tasks to include the Standards for Mathematical Practice where students have to reason, justify, explain, construct & model their thinking.See Section 13-4Pearson13-7 Translating Sine and Cosine Functions Graphing single translations of trigonometric functionsGraphing combined translations of trigonometric functionsGraphing translations of y = sin 2xWriting an equation to describe the translation of a trig functionGlencoe 13.8 Translations of Trigonometric GraphsVocabularyPhase shiftJournaling/PromptHow is a phase shift and a translation the same? How are they different?Utilize Tasks to include the Standards for Mathematical Practice where students have to reason, justify, explain, construct & model their thinking.See Section 13-4Pearson13-8 Reciprocal Trigonometric Functions Evaluating reciprocal trigonometric functionsSketching reciprocal trigonometric functionsGraphing reciprocal trigonometric functionsUsing reciprocal trigonometric functions to solve problemsGlencoe 13.9 Inverse Trigonometric FunctionsTASKSSine Graph With TransformationTrig for solving problemsMica PracticeVocabularyCosecant, secant, cotangentJournaling/PromptCompare and contrast the graphs y = sec x and y = csc x.Utilize Tasks to include the Standards for Mathematical Practice where students have to reason, justify, explain, construct & model their thinking.Chapter 14( 1 week)Pearson14-1 Trigonometric Identities Verifying trigonometric identities Glencoe 14.1 Trigonometric Identities TASKSTrig Ratios and the Pythagorean TheoremProve Pythagorean IdentityFerris Wheel Task-nyc schoolsVocabularyTrigonometric IdentityJournaling/PromptDevelop your own trigonometric identity. Hint: Start with a simple trigonometric expression and work backwards.Utilize Tasks to include the Standards for Mathematical Practice where students have to reason, justify, explain, construct & model their thinking.PearsonPg. 661 Systems of ConicsGlencoe10.7 Solving Quadratic SystemsTASKConic Sections and Solar SystemsTextbook ResourcesPearson Tools:math ( ELL, Enrichment, Re-teaching, Quizzes/Tests, Think About a Plan, Test Prep, Extra Practice, Find the Errors, Activities/Games/Puzzles, Video Tutor, Chapter Project, Performance Task, and Student Companion)Glencoe Tools:Student EditionTeacher EditionProblem SolvingVocabulary Puzzle Maker Core State Standards InitiativeCommon Core Standards - MathematicsCommon Core Standards - Mathematics Appendix ATN CoreThe Mathematics Common Core ToolboxTennessee Blueprints HYPERLINK "" PARCC Blueprints and Test Specifications FAQCCSS ToolboxNYC tasks New York Education Department TasksPARCC High School Math TN Department of Education Math StandardsHYPERLINK ""Algebra 2 TN State StandardsVideosBrightstormTeacher TubeThe Futures ChannelKhan AcademyMath TVLamar University TutorialCalculatorMath nspiredTexas Instrument ActivitiesCasio ActivitiesInteractive ManipulativesKuta Software- worksheet generator Illuminations (NCTM) Stem Resources National Math ResourcesMARS Course 2NASA Space Math Math Vision ProjectUT Dana CenterMars TasksPurple MathAdditional Sites Dana Center Algebra 2 AssessmentsIllinois State Assessment strategiesSCS Math Tasks (Algebra II)CLIP:Literacy Skills and Strategies for Content Area Teachers(Math, p. 22)Glencoe Reading & Writing in the Mathematics ClassroomGraphic Organizers (9-12)Graphic Organizers (dgelman) ................
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