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 opportunity42291021812250In 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. -537210152400The 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 judgement 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, i-Ready lessons 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 QuarterProbability and Counting Rules Discrete Probability Distributions The Normal Distribution Overview In this quarter students extend their work in probability and statistics by applying statistics ideas to real-world situations. They link classroom mathematics and statistics to everyday life, work, and decision-making, by applying these standards in modeling situations. They choose and use appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. The basic concepts of probability are explained including probability experiments, sample spaces, the addition and multiplication rules, and the probabilities of complementary events. Students learn the rule for counting, the differences between permutations and combinations, and how to figure out how many different combinations for specific situations exist. Students take their understanding of probability further by studying expected values, interpreting them as long-term relative means of random variables, functions of the outcomes of a random process, with associated probabilities attached to their possible values. Random variables can be either discrete or continuous. Discrete variables and their distributions are explained and students explore probability distributions in general and a specific, often used distribution called the binomial distribution. Students also begin to discuss and explore the properties of a normal distribution and its applications. 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 4 - Probability and Counting Rules(Allow approximately 4 weeks for instruction, review, and assessment)Domain: Conditional Probability and the Rules of ProbabilityCluster: Understand and apply basic concepts of probability S-CP.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").S-CP.3 Demonstrate an understanding of the Law of Large Numbers (Strong and Weak).Enduring Understanding(s):Numbers, expressions, and measures can be compared by their relative values. Some questions can be answered by collecting and analyzing data, and the question to be answered determines the data that needs to be collected and how best to collect it.Essential Question(s):How to use the laws of probability and simulation to make informed decisions?How can large numbers based on a pattern be efficiently calculated to form probabilities? How can you model a simulation to represent a real life situation? How does theoretical probability relate to empirical probability? How do mutually exclusive events affect probability calculations? Objective(s)The student will:Determine sample spaces and find the probability of an event.Explain what is meant by the Law of Large Numbers.Elementary Statistics Textbook (Bluman)4-1 Sample Spaces and ProbabilityAdditional Resource(s)Elementary Statistics PowerPoint – Chapter 4HYPERLINK ""Against All Odds Videos (Against All Odds is a Video Series that introduces a statistical topic and illustrates it with a real-world example) HYPERLINK "" Khan Academy: ProbabilityLaw of Large Numbers AppletSTatistics Education WebTask(s) HYPERLINK "" SCS Math Task: Statistics Too Many Choices HYPERLINK "" Law of Large NumbersVocabulary (Chapter 4)classical probability, combination, complement of an event, compound event, conditional probability, dependent events, empirical probability, equally likely events, event, fundamental counting rule, independent events, law of large numbers, mutually exclusive events, outcome, permutation, probability, probability experiment, sample space, simple event, subjective probability, tree diagram, Venn diagramsElementary Statistics Textbook (Bluman)Statistics Today, pp. 182, 245Critical Thinking Challenges, p. 248Speaking of Statistics, p. 240Applying the Concepts, pp. 195, 203, 220, 232, 239Extending the Concepts, pp.198, 207, 224, 235Data Projects, p. 248TI-83/84 Step by Step, pp. 207, 235 Vocabulary (Chapter 4)classical probability, combination, complement of an event, compound event, conditional probability, dependent events, empirical probability, equally likely events, event, fundamental counting rule, independent events, law of large numbers, mutually exclusive events, outcome, permutation, probability, probability experiment, sample space, simple event, subjective probability, tree diagram, Venn diagramsElementary Statistics Textbook (Bluman)Statistics Today, pp. 182, 245Critical Thinking Challenges, p. 248Speaking of Statistics, p. 240Applying the Concepts, pp. 195, 203, 220, 232, 239Extending the Concepts, pp.198, 207, 224, 235Data Projects, p. 248TI-83/84 Step by Step, pp. 207, 235Domain: Conditional Probability and the Rules of ProbabilityCluster: Use the rules of probability to compute probabilities of compound events in a uniform probability model. HYPERLINK "" S-CP.4 Demonstrate an understanding of the addition rule, the multiplication rule, conditional probability, and independence.Objective(s)The student will:Find the probability of compound events using the addition rule of probabilityElementary Statistics Textbook (Bluman)4-2 The Addition Rules for ProbabilityAdditional Resource(s)Elementary Statistics PowerPoint – Chapter 4Khan Academy: ProbabilityDomain: Conditional Probability and the Rules of ProbabilityCluster: Use the rules of probability to compute probabilities of compound events in a uniform probability model. HYPERLINK "" S-CP.4 Demonstrate an understanding of the addition rule, the multiplication rule, conditional probability, and independence.Objective(s)The student will:Find the probability of compound events using the multiplication rule of probability.Find the conditional probability of an event.Discuss the concept of independenceElementary Statistics Textbook (Bluman)4-3 The Multiplication Rules and Conditional ProbabilityAdditional Resource(s)Elementary Statistics PowerPoint – Chapter 4HYPERLINK ""Against All Odds Videos Khan Academy: ProbabilityTask(s)SCS Math Task: Statistics- Independence Domain: Conditional Probability and the Rules of ProbabilityCluster: Use the rules of probability to compute probabilities of compound events in a uniform probability model. HYPERLINK "" S-CP.4 Demonstrate an understanding of the addition rule, the multiplication rule, conditional probability, and independence.S-CP.5 Apply the general?Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the modelObjective(s)The student will:Find the total number of outcomes in a sequence of events using the fundamental counting rule.Find the number of ways that r objects can be selected from n objects, using the permutation rule.Find the number of ways that r objects can be selected from n objects, without regard to order, using the combination rule.Elementary Statistics Textbook (Bluman)4-4 Counting rulesAdditional Resource(s)Elementary Statistics PowerPoint – Chapter 4HYPERLINK ""Against All Odds Videos HYPERLINK "" Khan Academy: The Counting PrincipleTask(s)SCS Math Task: Statistics- Too Many ChoicesDomain: Conditional Probability and the Rules of ProbabilityCluster: Understand and apply basic concepts of probability S-CP.2 Use permutations and combinations to compute probabilities of compound events and solve problems.Objective(s)The student will:Find the probability of an event using the counting rules.Elementary Statistics Textbook (Bluman)4-5 Probability and Counting RulesAdditional Resource(s)Elementary Statistics PowerPoint – Chapter 4HYPERLINK ""Against All Odds Videos HYPERLINK "" Khan Academy: The Counting PrincipleSTatistics Education WebTask(s)SCS Math Task: Statistics- M&Ms6Chapter 5 - Discrete Probability Distributions(Allow approximately 3 weeks for instruction, review, and assessment)Domain: Using Probability to Make Decisions Cluster: Understand and use the discrete probability distributions.S-MD.1 Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions Enduring Understanding(s):There are special numerical measures that describe the center and spread of numerical data sets. The chance of an event occurring can be described numerically by a number between 0 and 1 inclusive and used to make predictions about other events. Essential Question(s):What probability distribution patterns occur in real life situations? How do you distinguish when to use the three distributions (poison, binomial, geometric)? How do you apply your understanding of probability distribution to determine examples of it? Objective(s):The student will:Construct a probability distribution for a random variable.Elementary Statistics Textbook (Bluman)5-1 Probability DistributionsAdditional Resource(s) HYPERLINK "" Elementary Statistics PowerPoint – Chapter 5 HYPERLINK ""Against All Odds Videos HYPERLINK "" Khan Academy: Statistics and ProbabilitySTatistics Education WebTask(s)SCS Math Task: Statistics- GOFISHVocabulary (Chapter 5):Binomial distribution, binomial experiment, discrete probability distribution, expected value, hypergeometric distribution, multinomial distribution, Poisson distribution, random variable Elementary Statistics Textbook (Bluman)Statistics Today, pp. 252, 269, 295Critical Thinking Challenges, p. 296Speaking of Statistics, p.256, Applying the Concepts, pp. 276, 289 Extending the Concepts, pp. 259, 268, 279Data Projects, p. 297TI-83/84 Step by Step, pp. 269, 281, 291Domain: Using Probability to Make Decisions Cluster: Understand and use the discrete probability distributions.S-MD.2 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.HYPERLINK ""S-MD.6 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. S-MD.7 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.S-MD.8 Use probabilities to make fair decisionsObjective(s): The student will:Find the mean, variance, standard deviation, and expected value for a discrete random variable.Elementary Statistics Textbook (Bluman)5-2 Mean, Variance, Standard Deviation, and Expected ValueAdditional Resource(s) HYPERLINK "" Elementary Statistics PowerPoint – Chapter 5 Khan Academy-: Summarizing Spread of DistributionsAgainst All Odds Videos STatistics Education WebTask(s)SCS Math Task: Statistics- It’s To Be ExpectedSCS Math Task: Statistics- Collecting Pens Vocabulary (Chapter 5):Binomial distribution, binomial experiment, discrete probability distribution, expected value, hypergeometric distribution, multinomial distribution, Poisson distribution, random variable Elementary Statistics Textbook (Bluman)Statistics Today, pp. 252, 269, 295Critical Thinking Challenges, p. 296Speaking of Statistics, p.256, Applying the Concepts, pp. 276, 289 Extending the Concepts, pp. 259, 268, 279Data Projects, p. 297TI-83/84 Step by Step, pp. 269, 281, 291Domain: Using Probability to Make Decisions Cluster: Understand and use the discrete probability distributions.HYPERLINK ""S-MD.6 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.S-MD.8 Use probabilities to make fair decisionsThe student will:Construct a probability distribution for a random variable using a simulation. Find the expected value of the simulation.Elementary Statistics Textbook14-3 Simulation Techniques and Expected ValueAdditional Resource(s)Khan Academy-: Summarizing Spread of DistributionsAgainst All Odds Videos Task(s) HYPERLINK "" SCS Math Task: Statistics- Distracted Driving Vocabulary (Section 14-3):Simulation technique, Monte Carlo methodElementary Statistics Textbook (Bluman)Applying the Concepts, pp. 742 HYPERLINK "" Domain: Using Probability to Make Decisions Cluster: Understand and use the discrete probability distributions.S-MD.2 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.HYPERLINK ""S-MD.6 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.S-MD.8 Use probabilities to make fair decisionsThe student will:Find the exact probability for X successes in n trials of a binomial experiment.Find the mean, variance, and standard deviation for the variable of a binomial distribution.Elementary Statistics Textbook5-3 The Binomial DistributionAdditional Resource(s) HYPERLINK "" Elementary Statistics PowerPoint – Chapter 5 Khan Academy: Binomial DistributionAgainst All Odds Videos STatistics Education WebTask(s)SCS Math Task: Statistics- Makin It Through Winter Vocabulary (Chapter 5):Binomial distribution, binomial experiment, discrete probability distribution, expected value, hypergeometric distribution, multinomial distribution, Poisson distribution, random variable Elementary Statistics Textbook (Bluman)Statistics Today, pp. 252, 269, 295Critical Thinking Challenges, p. 296Speaking of Statistics, p.256, Applying the Concepts, pp. 276, 289 Extending the Concepts, pp. 259, 268, 279Data Projects, p. 297TI-83/84 Step by Step, pp. 269, 281, 291 HYPERLINK "" Domain: Using Probability to Make Decisions Cluster: Understand and use the discrete probability distributions.S-MD.2 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.HYPERLINK ""S-MD.6 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.S-MD.8 Use probabilities to make fair decisionsThe student will:Find the probabilities for outcomes of variables, using Geometric, Poisson, hypergeometric, and multinomial distributions.Elementary Statistics Textbook5-4 Other Types of Distributions (optional) Additional Resource(s) HYPERLINK "" Elementary Statistics PowerPoint – Chapter 5 Against All Odds VideosSTatistics Education WebChapter 6-The Normal Distribution (Sections 1 & 2) (Allow approximately 2 weeks for instruction, review, and assessment)Domain: Using Probability to Make Decisions Cluster: Understand the normal probability distribution. S-MD.11 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.Enduring Understanding(s):Relationships between quantities can be represented symbolically, numerically, graphically and verbally in the exploration of real world situations.The results of statistical analysis must be interpreted and analyzed to determine if there is a significant evidence to justify conclusions about real world situations. Essential Question(s):What characteristics of a problem influence the choice of representation and analysis of the data? How can data be represented to best communicate important information about a problem?The student will:Identify distributions as symmetric or skewed. Identify the properties of a normal distribution.Find the area under the standard normal distribution, given various z values.Elementary Statistics Textbook6-1 Normal DistributionsAdditional Resource(s)HYPERLINK ""Elementary Statistics PowerPoint – Chapter 6 Khan Academy: Normal DistributionsAgainst All Odds VideosSTatistics Education WebVocabulary (Sections 6-1 & 6-2):Binomial distribution, binomial experiment, discrete probability distribution, expected value, hypergeometric distribution, multinomial distribution, Poisson distribution, random variable Elementary Statistics Textbook (Bluman)Statistics Today, p.300Applying the Concepts, p. 311, 324 Extending the Concepts, pp. 313, TI-83/84 Step by Step, pp. 313, 329Domain: Using Probability to Make Decisions Cluster: Understand the normal probability distribution. S-MD.11 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.The student will:Find probabilities for a normally distributed variable by transforming it into a standard normal variable.Elementary Statistics Textbook (Bluman)6-2 Applications of the Normal DistributionAdditional Resource(s)HYPERLINK ""Elementary Statistics PowerPoint – Chapter 6 Khan Academy: Normal DistributionsAgainst All Odds VideosSTatistics Education WebTask(s)The Normal DistributionIs Your Score NormalRESOURCE TOOLBOXTextbook ResourcesElementary Statistics 7th edition BlumanHYPERLINK ""Elementary Statistics PowerPoints (Bluman)Standards HYPERLINK "" Common Core Standards - Mathematics HYPERLINK "" Common Core Standards - Mathematics Appendix A HYPERLINK "" The Mathematics Common Core ToolboxLink to common core glossaryTennessee’s State Mathematics StandardsHYPERLINK ""State Academic Standards (Statistics) HYPERLINK "" \t "_top" Edutoolbox (formerly TNCore)Videos HYPERLINK "" Against All Odds Videos (with Study Guides) (A Video Series that introduces a statistical topic and illustrates it with a real-world example) HYPERLINK "" Khan Academy CalculatorTexas Instruments Education HYPERLINK "" ManipulativesStat Applet CollectionAdditional SitesThe Data and Story LibraryFed StatsBureau of Labor StatisticsEducational StatisticsNCTM Math IlluminationsUnited States Census BureauCore Math ToolsSTatistics Education WebMathematics Vision Project: Modeling DataLiteracyGlencoe- Reading and Writing in the Math ClassroomGraphic Organizers (9-12)Graphic Organizers (dgelman) ACTTN ACT Information & ResourcesACT College & Career Readiness Mathematics Standards ................
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