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, Destination 2025. 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.-571500-1270The 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 QuarterQuadratic Equations & FunctionsDescriptive StatisticsOverview The units in this quarter emphasize key standards and big ideas that encompass the major work of the course. A variety of resources are included to supplement the units for the level of rigor needed for the TNReady Exam. The tasks illustrate the rigor and types of learning activities that should be utilized from a variety of sources to enhance the students’ procedural skills and fluency, conceptual understanding, and application of the various concepts outlined this quarter. In this quarter students will gain a deeper understanding of quadratic functions and how they can be used to model real-world phenomena. Lastly, students will become statisticians as they learn how to use descriptive statistics to analyze, interpret, and predict outcomes of various data sets. HYPERLINK ""Year at a Glance DocumentContent StandardType of RigorFoundational StandardsSample Assessment ItemsF-IF.A.4Conceptual Understanding 8.EE.C.7 a, b; 8.EE.C.8 a, b, cMath Shell : Sorting FunctionsS-ID.A.1, S-ID.A.2, S-ID.A.3Procedural Skills & Fluency , Conceptual Understanding8.EE.C.7 a, b; 8.EE.C.8 a, b, cIllustrative: Speed TrapS-ID.A.5Procedural Skills & Fluency , Conceptual Understanding8.F.A.1, 8.F.A.2,8.F.A.3Illustrative: Musical PreferencesS-ID.A.6Conceptual Understanding8.F.A.4, 8.F.A.5Math Shell: Interpreting Categorical and Quantitative DataS-ID.C.8, S-ID.C.9Procedural Skills & Fluency , Conceptual UnderstandingIllustrative: Coffee and Crime; Illustrative: Golf and Divorce; Illustrative: Math Test GradesTNReady High School Assessment BlueprintsAlgebra I Practice Test (you must login to your EdTools account)Fluency The high school standards do not set explicit expectations for fluency, but fluency is important in high school mathematics. Fluency in algebra can help students get past the need to manage computational and algebraic manipulation details so that they can observe structure and patterns in problems. Such fluency can also allow for smooth progress toward readiness for further study/careers in science, technology, engineering, and mathematics (STEM) fields. These fluencies are highlighted to stress the need to provide sufficient supports and opportunities for practice to help students gain fluency. Fluency is not meant to come at the expense of conceptual understanding. Rather, it should be an outcome resulting from a progression of learning and thoughtful practice. It is important to provide the conceptual building blocks that develop understanding along with skill toward developing fluency.The fluency recommendations for Algebra I listed below should be incorporated throughout your instruction over the course of the school year.A/G A-APR.A.1 A-SSE.A.1b Solving characteristic problems involving the analytic geometry of lines Fluency in adding, subtracting, and multiplying polynomials Fluency in transforming expressions and seeing parts of an expression as a single object References: STATE STANDARDSCONTENTINSTRUCTIONAL SUPPORT & RESOURCES Quadratic Functions and Equations (Allow approximately 3-4 weeks for instruction, review, and assessment) Domain: Interpreting Functions (F-IF)Cluster: Interpret functions that arise in applications in terms of the context.F-IF.A.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.★Domain: Interpreting Functions (F-IF)Cluster: Analyze functions using different representations.. F-IF.A.7a Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★Enduring Understanding(s):For any quadratic function in standard form, the values of a, b, and c provide key information about its graph.The vertex of a parabola will represent the maximum point of the functions, which will help to understand maximum and minimum values in real-world situations.The graph of a quadratic function always forms a parabola.The characteristics of quadratic functions and their representations are useful in solving real-world problems.Essential Question(s)What are the advantages of a quadratic function in vertex form?What are the advantages of a quadratic equation in standard form?How do you graph a quadratic function by finding a vertex and axis of symmetry?What are the characteristics of quadratics functions?Objective(s):Students will graph a quadratic function in standard and vertex form.Students will explore the key features of graphs of quadratic functions.Students will interpret zeros, y-intercepts, minimum and maximum values, positive and negative values for the function, increasing and decreasing intervals, and the graph’s end behavior.Students will determine an appropriate domain and range for a function’s graph and recognize restrictions on the domain.Use the following Lesson(s) and tasks to introduce concepts/build conceptual understanding. HYPERLINK ""engageny Algebra I Module 4, Topic A HYPERLINK ""Lesson 8HYPERLINK ""Lesson 9HYPERLINK ""Lesson 10 Inside Math Task: Printing TicketsInside Math Task: Quadratic Number Machine Quadratic Functions Task: What’s the Pattern? P. 13 Quadratic Functions Task: Table Tiles p. 20 Illustrative Math: HYPERLINK "" Throwing BaseballsUse the textbook resources to address procedural skill and fluency.PearsonChapter 9- Quadratic Functions & Equations9-1 Quadratic Graphs & Their Properties9-2 Quadratic FunctionsGlencoe9-1 Graphing Quadratic Functions9-2 Concept Byte Collecting Quadratic DataChoose from the following resources and use them?to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems. Additional ResourcesSorting FunctionsBuilding FunctionsPatchworkSidewalk Patterns Characteristics of Quadratic FunctionsQuadratic Sequence 1HYPERLINK ""Quadratic Sequence 2 Graphing a quadratic function using a table, y = ax2Graphing a quadratic function using a table, y = ax2 + c HS Flip Book with Examples of each StandardVocabularyQuadratic formula, standard form, parabola, axis of symmetry, vertex, maximum, minimum, symmetryWriting in Math/DiscussionProvide 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 pare & Contrast: How are the graphs of y = -?x2 and y = -?x2 + 1 similar? How are they different? What information do the numbers a, b, and c give you about the graph y = ax2 + c? Domain: Seeing Structure in Expressions (A-SSE)Cluster: Write expressions in equivalent forms to solve problems.A-SSE.A.3a Factor a quadratic expression to reveal the zeros of the function it defines.A-SSE.A.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.Domain: Reasoning with Equations and Inequalities (A-REI)Cluster: Solve equations and inequalities in one variable.. A-REI.A.4 Solve quadratic equations in one variable.A-REI.A.4a 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 solution. Derive the quadratic formula from this form.A-REI.A.4b 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. Enduring Understanding(s):There are multiple ways to solve a quadratic equation.Quadratic equations may have 0, 1, or 2 solutions.To find the zeros of a quadratic function, you must set the equation equal to zero.Regardless of the method you choose to solve a quadratic function for real solutions, you are always looking for where the graph of the function crosses the x-axis.The domain and range of a quadratic function can be relative to a contextual, real-world situation.Essential Question(s)How are the real solutions of a quadratic equation related to the graph of the related quadratic function?Objective(s):Students will rewrite quadratic equations given in standard form in the equivalent completed-square form.Students derive the quadratic formula by completing the square for a general quadratic equation in standard form.Students understand that the discriminant,?b2?- 4ac, can be used to determine whether a quadratic equation has one, two, or no real solutions.Students will solve quadratic equations by completing the square.Students will solve quadratic equations using the quadratic formula.Use the following Lesson(s) and tasks to introduce concepts/build conceptual understanding. engageny Algebra I Module 4, Topic BHYPERLINK ""Lesson 11HYPERLINK ""Lesson 12HYPERLINK ""Lesson 13HYPERLINK ""Lesson 14Lesson 15Lesson 16Lesson 17 Illustrative Math: Profit of a Company A-SSE.A.3Illustrative Math: Braking Distance A-REI.A.4bIllustrative Math: HYPERLINK "" Springboard Dive A-REI.A.4b Cutting Corners Pearson9-3 Solving Quadratic Equations Glencoe9-2 Solving Quadratic Equations by GraphingPearson9-4 Factoring to Solve Quadratic Equations9-5 Completing the SquareGlencoe9-4 Solving Quadratic Equations by Completing the SquarePearson9-6 The Quadratic Formula and the DiscriminantGlencoe9-5 Solving Quadratic Equations by Using the Quadratic FormulaChoose from the following resources and use them?to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.Additional ResourcesHYPERLINK ""Henley’s ChocolatesJust the Right BorderHYPERLINK ""ACME FireworksHYPERLINK ""Quadratic Fanatic and the Case of the Foolish Function HYPERLINK "" Solving Quadratic Equations by Factoring HYPERLINK "" Solving Quadratic Equations by Completing the Square HYPERLINK "" Solving Quadratic Equations Using Completing the Square When a Does Not Equal 1 HYPERLINK "" Solving Quadratic Equations Using the Quadratic Formula HYPERLINK "" Solving Real-World Problems Using the Quadratic Formula HYPERLINK "" Choosing the Appropriate Method to Solve Quadratic Equations HYPERLINK "" Solving Quadratic Equations by Taking Square Roots HYPERLINK "" Using the Discriminant to Find the Number of Solutions and Solve Problems HS Flip Book with Examples of each StandardVocabularyQuadratic equation, standard form of a quadratic equation, root of an equation, zero of a function, zero-product property, completing the square, quadratic formula, discriminantWriting in Math/DiscussionCompare & Contrast: When is it easier to solve a quadratic equation of the form ax2 + c = 0 using square roots than to solve it using graphing?Compare & Contrast: How is factoring the expression x2 – 6x + 8 similar to solving the equation x2 – 6x + 8 = 0? How is it different?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. Compare & Contrast: How is solving a quadratic equation using square roots like completing the square? How is it different?How can you use the discriminant to write a quadratic equation that has two solutions?Domain: Interpreting Functions (F-IF)Cluster: Analyze functions using different representations.. F-IF.A.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★F-IF.A.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.Domain: Creating Equations (A-CED)Cluster: Create equations that describe numbers or relationships. A-CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.Enduring Understanding(s):The characteristics of quadratic functions and their representations are useful in solving real-world problems.Models are necessary to investigate, explain, and make mathematical predictions.Essential Question(s)How do quadratic functions model real-world problems and their solutions?Objective(s):Students make a connection between the symbolic and graphic forms of quadratic equations in the completed-square (vertex) form.?Students compare two different quadratic, square root, or cube root functions represented as graphs, tables, or equations. ?Students will graph, interpret, analyze, check results, draw conclusions, and apply key features of a quadratic function to real-life applications.Use the following Lesson(s) and tasks to enhance conceptual understanding, application, and modeling of quadratic functions that represent real-world situations.engageny Algebra I Module 4, Topic CHYPERLINK ""Lesson 21Lesson 22Lesson 23Lesson 24Illustrative Math: Identifying Graphs of Functions F-IF.7Illustrative Math: Throwing Baseballs F-IF.9Illustrative Math: Clea on an Escalator A-CED.2Illustrative Math: Silver Rectangle A-CED.2Choose from the following resources and use them?to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.Additional ResourcesProtein Bar Toss Parts 1 & 2Paula’s Peaches Parts 1 & 2 HYPERLINK "" Solving Quadratic Equations by Graphing HYPERLINK "" Math in BasketballDescriptive Statistics(Allow approximately 5-6 weeks for instruction, review, and assessment) S-ID.C.8 Compute and interpret the correlation coefficient of a linear fit. S-ID.C.9 Distinguish between correlation and causation. Enduring UnderstandingStatisticians summarize, represent, and interpret categorical and quantitative data in multiple ways since one method can reveal or create a different impression than another. Essential Question: How can the properties of data be communicated to illuminate its important features?Objectives:The students will interpret the correlation coefficient of a linear fit as a measure of how well the data fit the relationship.Use the following Lesson(s) and tasks to enhance conceptual understanding, application, and modeling of quadratic functions that represent real-world situations.engageny Module 2 Topic D Lesson 19engageny Module 2 Topic D Lesson 20Illustrative Math: Coffee and CrimeIllustrative Math: Math Test GradesPearson5-7 Scatter Plots and Trend LinesGlencoe4-5 Lab Scatter Plots and Lines of FitChoose from the following resources and use them?to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.Additional ResourcesIllustrative Math: Golf and DivorceDomain: Interpreting Categorical and Quantitative (S-ID)Cluster: Summarize, represent, and interpret data on a single count or measurement variable. S-ID.A.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).S-ID.A.2 Use 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.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).Enduring Understanding(s):There are several ways to collect data.The method in which data is collected, organized, and displayed influences interpretation.Represent both qualitative and quantitative data sets.Collecting, organizing, and displaying data helps to analyze information and make reasonable predictions and informed decisions.For each set of data, there is a number that best represents the center (mean, median, and mode) of the data.Measures of central tendency and spread (variation) can be used to describe data sets and justify conclusions.Find, analyze, and interpret measures of variation.Essential Question(s)Why is data collected and analyzed?How do people use data to influence others?How can predictions be made based on data?What kinds of questions can and cannot be answered from a graph?How does the type of data influence the choice of display?What are the three measures of central tendency?How does the spread (variation) of the data affect the shape of the histogram?How does the spread (variation) of the data affect the standard deviation?How do you analyze and interpret measures of variation?Objective(s):Students estimate the mean and median of a distribution represented by a dot plot or a histogram.Students indicate that the mean is a reasonable description of a typical value for a distribution that is symmetrical but that the median is a better description of a typical value for a distribution that is skewed.Students interpret the mean as a balance point of a distribution.Students indicate that for a distribution in which neither the mean nor the median is a good description of a typical value, the mean still provides a description of the center of a distribution in terms of the balance point.Use the following Lesson(s) and tasks to enhance conceptual understanding, application, and modeling of quadratic functions that represent real-world situations.HYPERLINK ""engageny Algebra I Module 2, Topic A HYPERLINK ""Lesson 1HYPERLINK ""Lesson 2HYPERLINK ""Lesson 3Illustrative Math: Understanding the Standard Deviation S-ID.A.2engageny Algebra I Module 2, Topic BLesson 4HYPERLINK ""Lesson 5HYPERLINK ""Lesson 6 Illustrative Math: Describing Data Sets with Outliers S-ID.A.3Glencoe12-2 Frequency and Histograms12-3 Measures of Central Tendency and DispersionChoose from the following resources and use them?to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.Additional ResourcesHYPERLINK ""Fruit Loops & Cheerios: S-ID.A.1 McDonald’s Franchise TaskHYPERLINK ""The Basketball StarArchery HYPERLINK "" VocabularyFrequency, frequency table, histogram, cumulative frequency table, measure of central tendency, outlier, mean, median, mode, measure of dispersion, range of a set of data, standard deviationWriting in Math/DiscussionCompare & Contrast: What is the difference between a symmetric histogram and a skewed histogram?How might a frequency table help a store owner determine the busiest business hours?How is the range of a data set affected by an outlier? How do mean, median, and mode describe central tendency of a data set? Why are three different measures needed?Domain: Interpreting Categorical and Quantitative (S-ID)Cluster: Summarize, represent, and interpret data on a single count or measurement variable. S-ID.A.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).S-ID.A.2 Use 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.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).Enduring Understanding(s):The method in which data is collected, organized, and displayed influences interpretation.Collecting, organizing, and displaying data helps to analyze information and make reasonable predictions and informed decisions.Essential Question(s)How do you construct a box and whiskers plot?Objective(s):Students will construct and interpret box-and-whiskers plots.Students will find and interpret the interquartile range (IQR).Students will identify outliers in a data distribution.Students will construct a dot plot from a data set.Students will describe the shape, center, and variability of a distribution based on a dot plot, histogram, or box plot.Use the following Lessons and tasks to introduce concepts/build conceptual understanding.engageny Algebra I Module 2, Topic BHYPERLINK ""Lesson 7HYPERLINK ""Lesson 8Illustrative Math: HYPERLINK "" Hair Cut Costs S.ID.A.1-3Pearson12-3 Measures of Central Tendency and Dispersion12-3 Concept Byte Standard Deviation12-4 Box-and-Whiskers PlotsGlencoe0-12 Measures of Center and Variation0-13 Representing DataChoose from the following resources and use them?to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.Additional ResourcesHYPERLINK ""Box-and-Whiskers Activity HYPERLINK ""Data Collection & Analysis ActivityVocabularyQuartile, interquartile range, box-and-whisker plot, percentile, percentile rankWriting in Math/DiscussionAbout what percent of the data in a data set falls between the minimum value and the third quartile? Explain.Explain the difference between range and interquartile range.Must the third quartile of a data set be less than the maximum value? Explain. Can you find the mean, median, and mode of a data set by looking at a box-and-whisker plot? Explain.Domain: Interpreting Categorical and Quantitative (S-ID)Cluster: Summarize, represent, and interpret data on two categorical and quantitative variables. S-ID.A.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.Enduring Understanding(s):Find conditional probabilities using a formula or two-way frequency table.Essential Question(s)How can categorical data for two categories be summarized?How can we analyze data to make inferences and/or predictions based on probabilities?How can you recognize possible associations and trends between two categories of categorical data?Objective(s):Students will summarize data on two categorical variables from a sample using a two-way frequency table.Given a two-way frequency table, students construct a relative frequency table and interpret relative frequencies.Students will calculate and interpret conditional relative frequencies from two-way frequency tables.Students will evaluate conditional relative frequencies as an indication of possible association between to variables.Students will explain thy association does not imply causation.Use the following Lessons to introduce concepts/build conceptual understanding of two-way frequency tables and conditional probabilities.HYPERLINK ""engageny Algebra I Module 2, Topic C HYPERLINK ""Lesson 9HYPERLINK ""Lesson 10HYPERLINK ""Lesson 11Illustrative Math: Musical PreferenceIllustrative Math: Support for a Longer School Day? Choose from the following resources and use them?to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.Additional Resources HYPERLINK "" Public Opinions & Leisure Time VocabularyQuantitative data, qualitative data (categorical data), two-way frequency table, relative frequency, joint relative frequency, marginal relative frequency, conditional relative frequencyWriting in Math/DiscussionExplain how you can use joint and marginal frequencies to check your relative frequency table.What does it mean to say there is an association between characteristics in a two-way frequency table?How can you use two-way frequency data to recognize possible associations between the two categories of categorical data? Can a joint relative frequency be higher than either of the conditional relative frequencies associated with it?Domain: Interpreting Categorical and Quantitative (S-ID)Cluster: Summarize, represent, and interpret data on two categorical and quantitative variables. S-ID.A.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.S-ID.A.6a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.S-ID.A.6b Informally assess the fit of a function by plotting and analyzing residuals.S-ID.A.6c Fit a linear function for a scatter plot that suggests a linear association. Enduring Understanding(s):Scatterplots are one way to compare and find relationships between two variables.Two sets of numerical data can be graphed as ordered pairs. If two sets of data are related, a regression equation can be used to estimate or predict values.Although scatter plots and regression equations reveal a pattern, the relationship of the variables may indicate correlation, but not causation.Essential Question(s)How do we make predictions and informed decisions based on current numerical data?How do you use patterns to understand and model real-world situations?What are the advantages and disadvantages of analyzing data by hand versus by using technology?What types of relationships show a positive correlation? Negative correlation? No correlation?Objective(s):Students will distinguish between scatter plots that display a relationship that can be reasonably modeled by a linear equation and those that should be modeled by a nonlinear equation.Students will determine the least-squares regression line from a given set of data using technology.Students will use the least-squares regression line to make predictions.Students will use technology to determine the value of the correlation coefficient for a given data set.Students will interpret the value of the correlation coefficient as a measure of strength and direction of a linear relationship.Students will explain why correlation does not imply causation.To model a data set choose a function that most closely matches the pattern in the data or graph.Use the following Lessons and tasks to introduce concepts/build conceptual understanding of scatter plots and regression equations.engageny Algebra I Module 2, Topic DHYPERLINK ""Lesson 13 HYPERLINK ""Lesson 15HYPERLINK ""Lesson 16HYPERLINK ""Lesson 17HYPERLINK ""Lesson 18HYPERLINK ""Illustrative Math: Olympic Men’s 100-meter Dash HYPERLINK "" Illustrative Math: Laptop Battery Charge Pearson9-7 Linear, Quadratic, and Exponential ModelsChoose from the following resources and use them?to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.Additional ResourcesHYPERLINK ""Tuition Cost ActivityHYPERLINK ""The Number of Starbucks StoresVocabularyScatter plot, line of best fit, linear regression, two-variable data, correlation, correlation coefficient, interpolation, extrapolation, residual, residual plot, quadratic regression, exponential regressionWriting in Math/DiscussionWhy are the points in a scatter plot not connected in the same way plots of linear equations are?How does a scatter plot help you make predictions from two-variable data?Does causation always imply linear correlation? Explain. How can you use statistical methods to find relationships between sets of data?RESOURCE TOOLBOXThe Resource Toolbox provides additional support for comprehension and mastery of subject-level skills and concepts. While some of these resources are embedded in the map, the use of these categorized materials can assist educators with maximizing their instructional practices to meet the needs of all students.?Textbook ResourcesPearsonmath Site - Textbook and ResourcesStandardsCCSS (formerly ) HYPERLINK "" TN Algebra I StandardsTN Department of Education Math StandardsHS Flip Book with examples of each Standard(Designed as a resource tool to assist teachers in deepening their understanding of what each standard means in terms of what students must know and be able to do. It outlines only a sample of instructional strategies and examples. Links to conceptual categories and specific standards in the document can be accessed from page 5 Mathematics Standards for High School.)Videos HYPERLINK "" Khan AcademyTeacher TubeMath TV The Futures ChannelThe Teaching ChannelIVEST Video LibraryIlluminations (NCTM)Get The MathCalculator HYPERLINK "" \t "_blank" HYPERLINK "" ResourcesNational Library of Virtual Manipulatives HYPERLINK "" EdugoodiesNWEA MAP Resources: in and Click the Learning Continuum Tab – this resources will help as you plan for intervention, and differentiating small group instruction on the skill you are currently teaching. (Four Ways to Impact Teaching with the Learning Continuum) These Khan Academy lessons are aligned to RIT scores. ?LiteracyLiteracy Skills and Strategies for Content Area Teachers(Math, p. 22)Formative Assessment Using the UPS StrategyGlencoe Reading & Writing in the Mathematics ClassroomGraphic Organizers (9-12)TasksMathematics Assessment Project (MARS Tasks)Dan Meyer's Three-Act Math TasksIllustrative Math TasksUT Dana CenterInside Math TasksLearnZillionSCS Math Tasks (Algebra I)ACTState ACT ResourcesACT College & Career Readiness Mathematics Standards ................
................

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

Google Online Preview   Download