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 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 QuarterNormal Distributions Confidence Intervals and Sample SizeHypothesis TestingOverview In this quarter students finish their study of normal distributions and continue to have the opportunity to apply concepts of probability and statistics to real-world situations. Students determine confidence intervals to begin to hypothesize if a large enough sample size has been taken to closely reflect the true mean of the population. Students classify the type of errors that can occur during experiments and will be able to make decisions on the hypothesis based on their own analysis of the data. Students will also be exposed to the level of significance and how this affects a decision to accept or deny a hypothesis. 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 6 ( Sections 3 & 4)Normal Distributions (Allow approximately 2 weeks for instruction, review, and assessment)Domain: Making Inferences and Justifying ConclusionsCluster: Know the characteristics of well-designed studies. HYPERLINK "" S-IC.6 Demonstrate an understanding of the Central Limit Theorem. Domain: Using Probability to Make Decisions Cluster: Understand the normal probability distribution. HYPERLINK "" 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):There are special numerical measures that describe the center and spread of numerical data sets. Essential Question(s):How do all Normal distributions relate to each other? How can we find examples of normal distribution in real world scenarios? Objective(s)The student will:Use the Central Limit Theorem to solve problems involving sample means for large samples.Elementary Statistics Textbook (Bluman)6-3 Central Limit TheoremAdditional Resource(s)Elementary Statistics PowerPoint – Chapter 6Khan Academy: Central Limit Theorem STatistics Education Web: Who Sends the Most Text Messages (This lesson provides an informal introduction to concepts surrounding the Central Limit Theorem.)Task(s) HYPERLINK "" SCS Math Task: Statistics - Cents & Central Limit Theorem HYPERLINK "" Statistics Applet-Sampling DistributionsAccelerated GSE Pre-Calculus Tasks: Unit 8: Inferences & Conclusions from DataColors of Skittles, p. 120Pennies, p.142The Gettysburg’s Address, p. 156Vocabulary (Sections 6-3 & 6-4)sampling distribution of sample means, Sampling error, standard error of the mean, central limit theorem, correction for continuityElementary Statistics Textbook (Bluman)Statistics Today, p. 350Critical Thinking Challenges, p. 352Applying the Concepts, pp. 338, 346Extending the Concepts, pp.340, 347Data Projects, p. 397Domain: 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. Domain: Using Probability to Make Decisions Cluster: Understand the normal probability distribution. HYPERLINK "" 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):There are special numerical measures that describe the center and spread of numerical data sets. Essential Question(s):How do all Normal distributions relate to each other? How can we find examples of normal distribution in real world scenarios? Objective(s)The student will:Use the normal approximation to compute probabilities for a binomial variableElementary Statistics Textbook (Bluman)6-4 The Normal Approximation to the Binomial DistributionAdditional Resource(s)Elementary Statistics PowerPoint – Chapter 6HYPERLINK ""Against All Odds Videos & Lessons: Normal Curves Against All Odds Videos & Lessons: Normal Calculations STatistics Education WebTask(s) HYPERLINK "" Statistics Applet: Normal to BinomialStatistics Applet: Normal to Binomial 2Chapter 7- Confidence Intervals and Sample Size(Allow approximately 3 weeks for instruction, review, and assessment)Domain: Making Inferences and Justifying ConclusionsCluster: Understand and use confidence intervals. HYPERLINK "" S-IC.14 Understand the meaning of confidence level, of confidence intervals, and the properties of confidence intervals. S-IC.15 Construct and interpret a large sample confidence interval for a proportion and for a difference between two proportions. S-IC.16 Construct the confidence interval for a mean and for a difference between two means. Domain: Using Probability to Make Decisions Cluster: Understand the normal probability distribution.S-MD.9 Analyze decisions and strategies using probability conceptsDomain: Making Inferences and Justifying ConclusionsCluster: Make inferences and justify conclusions from sample surveys, experiments, and observational studies(CCSS) S.IC.B.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.Enduring Understanding(s):Understand how to use statistics as a way of dealing with, but not eliminating, variability of results from experiments and inherent randomness. Understand how to use the margin of error to find a confidence interval.Essential Question(s):How do I interpret the margin of error of a confidence interval? How do I use a margin of error to find a confidence interval?Objective(s)The student will:Find the confidence interval for the mean when σ is known and sample size is large.Determine the minimum sample size for fining a confidence interval for the mean.Elementary Statistics Textbook (Bluman)7-1 Confidence Intervals for the Mean When σ is KnownAdditional Resource(s) HYPERLINK "" Elementary Statistics PowerPoint – Chapter 7HYPERLINK ""Against All Odds Videos & Lessons: Confidence Intervals HYPERLINK "" Khan Academy: Confidence IntervalsTask(s)SCS Math Task: Statistics- Confidence Interval Vocabulary (Chapter 7):chi-square distribution, confidence interval, confidence level, consistent estimator, degrees of freedom, estimation, estimator, interval estimate, maximum error of the estimate, point estimate, proportion, relatively efficient, estimator, t distribution, unbiased estimator Elementary Statistics Textbook (Bluman)Statistics Today, pp. 356, 395Critical Thinking Challenges, p. 397Speaking of Statistics, pp. 381, 385 Applying the Concepts, pp. 365, 373, 381, 390 Extending the Concepts, pp. 375, 383, 391Data Projects, p. 397TI-83/84 Step by Step, pp. 368, 376, 384, 391S-IC.14 (See 7-1) S-IC.15 S-IC.16 S-MD.9 S.IC.B.4 Objective(s)The student will:Find the confidence interval for the mean when σ is unknown and sample size is small.Elementary Statistics Textbook (Bluman)7-2 Confidence Intervals for the Mean When σ is UnknownAdditional Resource(s) HYPERLINK "" Elementary Statistics PowerPoint – Chapter 7HYPERLINK ""Against All Odds Videos & Lessons HYPERLINK "" Understanding Confidence Intervals VideoSTatistics Education WebTask(s)SCS Math Task: Statistics- SAT PerformanceS-IC.14 (See 7-1) S-IC.15 S-IC.16 S-MD.9 S.IC.B.4 Objective(s)The student will:Find the confidence interval for a proportion.Determine the minimum sample size for fining a confidence interval for a proportion.Elementary Statistics Textbook (Bluman)7-3 Confidence Intervals and Sample Size for ProportionsAdditional Resource(s) HYPERLINK "" Elementary Statistics PowerPoint – Chapter 7HYPERLINK ""Against All Odds Videos & Lessons STatistics Education WebTask(s) HYPERLINK "" SCS Math Tasks: Statistics: M&Ms CI1SCS Math Tasks: Statistics: M&Ms CI2S-IC.14 (See 7-1) S-IC.15 S-IC.16 S-MD.9 S.IC.B.4 Objective(s)The student will:Find the confidence interval for a variance and a standard deviation using Chi-Square.Elementary Statistics Textbook (Bluman)7-4 Confidence Intervals for Variances and Standard DeviationsAdditional Resource(s) HYPERLINK "" Elementary Statistics PowerPoint – Chapter 7HYPERLINK ""Against All Odds Videos & Lessons STatistics Education WebTask(s)Accelerated GSE Pre-Calculus Tasks: Unit 8: Inferences & Conclusions from DataHow Confident are You?, p. 177Chapter 8 - Hypothesis Testing(Allow approximately 4 weeks for instruction, review, and assessment)Domain: Making Inferences and Justifying ConclusionsCluster: Understand and evaluate random processes underlying statistical experiments(CCSS) S.IC.A.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population.Domain: Using Probability to Make Decisions Cluster: Use probability to evaluate outcomes of decisions(CCSS) S.MD.B.7 Analyze decisions and strategies using probability concepts. Enduring Understanding(s):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):How do you use statistical ideas to test assumptions about data? How are results of hypothesis testing used for statistical inference? How do we test the differences between two population parameters? Objective(s):The student will:Understand the definitions used in hypothesis testing.State the null and alternative hypotheses.State the five steps used in hypothesis testing.Elementary Statistics Textbook (Bluman)8-1 Steps in Hypothesis Testing—Traditional MethodAdditional Resource(s)HYPERLINK ""Elementary Statistics PowerPoint – Chapter 8 HYPERLINK ""Against All Odds Videos & Lessons HYPERLINK ""Khan Academy: Simple Hypothesis TestingSTatistics Education WebVocabulary (Chapter 8):α (alpha) alternative, hypothesis β (beta) chi-square test, critical or rejection region, critical value, hypothesis testing, left-tailed test, level of significance, noncritical or nonrejection region, null hypothesis, one-tailed test, power of a test, P-value, research hypothesis, right-tailed test, statistical hypothesis, statistical test, test value, t test, two-tailed test, type I error, type II error, z test Elementary Statistics Textbook (Bluman)Statistics Today, pp. 400, 465Critical Thinking Challenges, p. 467Speaking of Statistics, pp. 414, 433 Applying the Concepts, pp. 412, 421, 433, 441, 453, 460 Extending the Concepts, pp. 424, 443Data Projects, p. 468TI-83/84 Step by Step, pp. 426, 236, 444, 456(CCSS) S.IC.A.1 (See 8-1)(CCSS) S.MD.B.7Objective(s): The student will:Test means when σ is known and sample size is large, using a z-test.Elementary Statistics Textbook (Bluman)8-2 z-Test for a MeanAdditional Resource(s)HYPERLINK ""Elementary Statistics PowerPoint – Chapter 8 HYPERLINK ""Against All Odds Videos & Lessons STatistics Education Web (CCSS) S.IC.A.1 (See 8-1)(CCSS) S.MD.B.7The student will:Test means when σ is unknown and sample size is small, using a t-test.Elementary Statistics Textbook8-3 t-Test for a MeanAdditional Resource(s)HYPERLINK ""Elementary Statistics PowerPoint – Chapter 8 HYPERLINK ""Against All Odds Videos & Lessons STatistics Education Web(CCSS) S.IC.A.1 (See 8-1)(CCSS) S.MD.B.7The student will:Test proportions, using a z-test.Elementary Statistics Textbook8-4 z Test for a ProportionAdditional Resource(s)HYPERLINK ""Elementary Statistics PowerPoint – Chapter 8 HYPERLINK ""Against All Odds Videos & Lessons STatistics Education Web (CCSS) S.IC.A.1 (See 8-1)(CCSS) S.MD.B.7The student will:Find the probabilities for outcomes of variables, using Geometric, Poisson, hypergeometric, and multinomial distributions.Elementary Statistics Textbook8-5 Chi Square Test for a Variance and a Standard Deviation Additional Resource(s)HYPERLINK ""Elementary Statistics PowerPoint – Chapter 8 HYPERLINK ""Against All Odds Videos & Lessons STatistics Education Web(CCSS) S.IC.A.1 (See 8-1)(CCSS) S.MD.B.7The student will:Explain the relationship between Type I and Type II errors and the power of a test.Elementary Statistics Textbook8-6 Additional Topics Regarding Hypothesis TestingAdditional Resource(s)HYPERLINK ""Elementary Statistics PowerPoint – Chapter 8 HYPERLINK ""Against All Odds Videos & Lessons STatistics Education WebTask(s) HYPERLINK "" SCS Math Task: Statistics- Types of ErrorsRESOURCE 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 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 WebSCS Math Tasks: StatisticsLiteracyGlencoe- Reading and Writing in the Math ClassroomGraphic Organizers (9-12)Graphic Organizers (dgelman) ACTTN ACT Information & ResourcesACT College & Career Readiness Mathematics Standards ................
................

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

Google Online Preview   Download