Shelby County Schools’ mathematics instructional maps are ...



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. Acknowledging the need to develop competence in literacy and language as the foundation for all learning, Shelby County Schools developed the Comprehensive Literacy Improvement Plan (CLIP). The CLIP ensures a quality balanced literacy approach to instruction that results in high levels of literacy learning for all students across content areas. Destination 2025 and the CLIP establish common goals and expectations for student learning across schools. CLIP connections are evident throughout the mathematics curriculum maps.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. While the academic standards establish desired learning outcomes, the curriculum provides instructional planning designed to help students reach these outcomes. Educators will use this guide and the standards as a roadmap for curriculum and instruction. The sequence of learning is strategically positioned so that necessary foundational skills are spiraled in order to facilitate student mastery of the standards.These standards emphasize thinking, problem-solving and creativity through next generation assessments that go beyond multiple-choice tests to increase college and career readiness among Tennessee students. In addition, assessment blueprints ( ) have been designed to show educators a summary of what will be assessed in each grade, including the approximate number of items that will address each standard. Blueprints also detail which standards will be assessed on Part I of TNReady and which will be assessed on Part II.Our collective goal is to ensure our students graduate ready for college and career. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation and 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: 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 McGraw-Hill or Holt 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 McGraw-Hill or Holt 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 STANDARDSExplanations/Examples/QuestionsCONTENT & TASKSCLIP CONNECTIONSTopic: ( 3 weeks)8.F.A.2: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).8.F.B.4: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.Students compare two functions from different representations.Examples:Compare the two linear functions listed below and determine which equation represents a greater rate of change.Function 1 Function 2:The function whose input x and output y are related by y = 3x + 7Compare the following functions to determine which has the greater rate of change.Function 1: Function 2:y = 2x + 4xy-1-60-323Solution: The rate of change for function 1 is 2; the rate of change for function 2 is 3. Function 2 has the greater rate of change.8.F.4Students identify the rate of change (slope) and initial value (y-intercept) from tables, graphs, equations or verbal descriptions to write a function (linear equation). Students understand that the equation represents the relationship between the x-value and the y-value; what math operations are performed with the x-value to give the y-value. Slopes could be undefined slopes or zero slopes.Tables:Students recognize that in a table the y-intercept is the y-value when x is equal to 0. The slope can be determined by finding the ratio y/x between the change in two y-values and the change between the two corresponding x-values..Graphs:Using graphs, students identify the y-intercept as the point where the line crosses the y-axis and the slope as the rise/run. Equations:In a linear equation the coefficient of x is the slope and the constant is the y-intercept. Students need to be given the equations in formats other than y = mx + b, such as y = ax + b (format from graphing calculator), y = b + mx (often the format from contextual situations), etc.Point and Slope:Students write equations to model lines that pass through a given point with the given slope.Glencoe5-1C Ordered Pairs and Relations5-2A Explore Patterns5-2B Analyze Tables5-2C Analyze Graphs5-2D Translate Tables and Graphs into Equations5-3B Functions5-3C Linear Functions6-1A Constant Rate of Change6-1B Explore Graphing Technology: Rate of Change6-1C Slope6-1D Constant Rate of Change6-1E Direct Variation6-2A Slope-InterceptCMP Thinking with Mathematical Models Investigations 1, 2 & 3CMP Say it With Symbols Investigation 4 Looking Back at FunctionsEngage NY Lessons: 8.F.2Engage NY Lesson: 8.F.4Math Shell Concept Development Lesson: Comparing Lines and Linear EquationsTNCore Task: Hexagon PuzzleTNCore Assessment Task: Javier's Bike, Cell Phone and/or Tanker TrucksTNCORE Assessment ItemsChoose items from pp. 51-71Growing Dots p. 3Holt3-4 Functions3-5 Equations, Tables and GraphsLab Explore Multiple Representations12-1 Graphing Linear Equations12-2 Slope of a Line12-3 Using Slopes and Intercepts Lab Graph Equations in Slope-Intercept Form12-4 Point-Slope form12-5 Direct VariationCMP Thinking with Mathematical Models Investigations 1, 2 & 3CMP Say it With Symbols Investigation 4 Looking Back at FunctionsEngage NY Lessons: 8.F.2Engage NY Lesson: 8.F.4Math Shell Concept Development Lesson: Comparing Lines and Linear EquationsTNCore Task: Hexagon PuzzleTNCore Assessment Task: Javier's Bike, Cell Phone and/or Tanker TrucksTNCORE Assessment ItemsChoose items from pp. 51-71Growing Dots p. 3Language Objectives:Students will translate values from a graph or table into equations.Students will compare and contrast relations and functions.Students will define constant rate of change and describe its meaning as it relates to the problem situation.Students will compare and contrast the various forms of linear functions.Students will work with a partner to create a table of data from a graph. They will find ratios of several points in the table and determine the constant rate of change.Vocabulary: linear relationship, rate of change, slope, initial value, y-intercept, x-intercept, function, x-value, y-valueJournal Prompt(s): How do you translate among the four representations (words, graphs, tables symbols) of a linear function? Define constant rate of change in yourGraphic Organizer:Have students record information about tables, graphs, words and equations in a Foldable study table.Dinah Zike's FoldablesTopic: Systems of Linear Equations(2 weeks)8.EE.C.8: Analyze and solve pairs of simultaneous linear equations.8.EE.C.8.a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.8.EE.C.8.b:. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection8.EE.C.8.c: Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.Systems of linear equations can also have one solution, infinitely many solutions or no solutions. Students will discover these cases as they graph systems of linear equations and solve them algebraically. A system of linear equations whose graphs meet at one point (intersecting lines) has only one solution, the ordered pair representing the point of intersection. A system of linear equations whose graphs do not meet (parallel lines) has no solutions and the slopes of these lines are the same. A system of linear equations whose graphs are coincident (the same line) has infinitely many solutions, the set of ordered pairs representing all the points on the line. By making connections between algebraic and graphical solutions and the context of the system of linear equations, students are able to make sense of their solutions. Students need opportunities to work with equations and context that include whole number and/or decimals/fractions.Examples:Find x and y using elimination and then using substitution.3x + 4y = 7-2x + 8y = 10Plant A and Plant B are on different watering schedules. This affects their rate of growth. Compare the growth of the two plants to determine when their heights will be the same. Let W = number of weeksLet H = height of the plant after W weeksPlant APlant BWHWH04(0,4)02(0,2)16(1,6)16(1,6)28(2,8)210(2,10)310(3,10)314(3,14)Given each set of coordinates, graph their corresponding lines.Solution:Write an equation that represent the growth rate of Plant A and Plant B.Solution:Plant A H = 2W + 4Plant B H = 4W + 2At which week will the plants have the same height?Solution:The plants have the same height after one week.Plant A: H = 2W + 4 Plant B: H = 4W + 2Plant A: H = 2(1) + 4 Plant B: H = 4(1) + 2Plant A: H = 6 Plant B: H = 6After one week, the height of Plant A and Plant B are both 6 inches.Glencoe6-3B Explore Graphing Technology: Systems of Equations6-3C Solve Systems of Equations by Graphing6-3D Solve Systems of Equations by SubstitutionTNCore Task Arc: Understanding and Solving Systems of Linear EquationsCMP Lessons: The Shapes of Algebra Investigations 2, 3, & 4Engage NY: 8.EE.8 Lessons 24-30Math Shell Concept Development Lesson: Classifying Solutions to Systems of EquationsMath Shell Problem Solving Lesson: Baseball Jerseys 8.EE.8cIllustrative Math Tasks: 8.EE.8a-cInside Math: On Balance Task Level E 8.EE.8c p. 7&18TNCore Assessment Task: Cross Country, Electric Cars, or Swimming PoolsNYC Common Core AssessmentSimultaneous-Linear-Equations-Mini-AssessmentHolt11-6 Systems of Equations12-7 Solving Systems of Linear Equations by GraphingTNCore Task Arc: Understanding and Solving Systems of Linear EquationsCMP Lessons: The Shapes of Algebra Investigations 2, 3, & 4Engage NY: 8.EE.8 Lessons 24-30Math Shell Concept Development Lesson: Classifying Solutions to Systems of EquationsMath Shell Problem Solving Lesson: Baseball Jerseys 8.EE.8cIllustrative Math Tasks: 8.EE.8a-cInside Math: On Balance Task Level E 8.EE.8c p. 7&18TNCore Assessment Task: Cross Country, Electric Cars, or Swimming PoolsNYC Common Core AssessmentSimultaneous-Linear-Equations-Mini-AssessmentLanguage Objectives:Students will discuss the meaning of the point of intersection of the graph of a system of linear equations.Students will describe cases where a system of linear equations has no solution, one solution or infinitely many solutions.Vocabulary: System of linear equations, Intersecting lines, parallel lines, same line, substitution, eliminationGraphic Organizer:Solving Systems of Linear Equations FoldableTopic: Qualitative Graphs(2 weeks)8.F.B.5: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.Given a verbal description of a situation, students sketch a graph to model that situation. Given a graph of a situation, students provide a verbal description of the situation.Examples:The graph below shows a John’s trip to school. He walks to his Sam’s house and, together, they ride a bus to school. The bus stops once before arriving at school.Describe how each part A – E of the graph relates to the story.Solution:A John is walking to Sam’s house at a constant rate.B John gets to Sam’s house and is waiting for the bus.C John and Sam are riding the bus to school. The bus is moving at a constant rate, faster than John’s walking rate.D The bus stops.E The bus resumes at the same rate as in part C.Describe the graph of the function between x = 2 and x = 5?Solution:The graph is non-linear and decreasing.Glencoe6-1C More About Graphs p. 349CMP Lessons: Thinking with Mathematical Models Investigation 2 Linear Models and EquationsCMP Lessons: Growing, Growing, Growing Investigations 1-4Engage NY Lessons: 8.F.5Math Shell Concept Development Lesson: Interpreting Distance-Time Lesson Qualitative GraphsTNCore Instructional Task: Flower PotTNCore Assessment Task: RollerbladingIllustrative Math Tasks: 8.F.5Understanding Graphs in Motion VideoLearn Zillion Lesson: Sketch Graphs by Interpreting SituationsHolt3-3 Interpreting GraphsCMP Lessons: Thinking with Mathematical Models Investigation 2 Linear Models and EquationsCMP Lessons: Growing, Growing, Growing Investigations 1-4Engage NY Lessons: 8.F.5Math Shell Concept Development Lesson: Interpreting Distance-Time Lesson Qualitative GraphsTNCore Instructional Task: Flower PotTNCore Assessment Task: RollerbladingIllustrative Math Tasks: 8.F.5Understanding Graphs in Motion VideoLearn Zillion Lesson: Sketch Graphs by Interpreting SituationsLanguage Objectives:Students will evaluate qualitative functions and write a description of a scenario that can be represented by the function.Vocabulary: qualitative graphGraphic Organizer:Have students use a foldable, or other graphic organizer to keep notes qualitative graphs.Qualitative Graphs Graphic Organizers pp. 15 & 16Topic: Transformations, Congruent and Similar Figures( 2 weeks)8.G.A: Understand congruence and similarity using physical models, transparencies, or geometry software.8.G.A.1: Verify experimentally the properties of rotations, reflections, and translations:a. Lines are taken to lines, and line segments to line segments of the same length.b. Angles are taken to angles of the same measure.c. Parallel lines are taken to parallel lines.8.G.A.2:Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.8.G.A.3: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.8.G.A.4: Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two dimensional figures, describe a sequence that exhibits the similarity between them.Students will use various tools and technology to explore figures created from translations. Lengths of line segments, angle measures and parallel linesUse tasks/exercises that require the use of coordinates in the coordinate plane.Tasks/exercises should elicit student understanding of the connection between congruence and transformations i.e., tasks may provide two congruent figures and require the description of a sequence of transformations that exhibits the congruence or tasks may require students to identify whether two figures are congruent using a sequence of transformations.Is Figure A congruent to Figure A’? Explain how you know.Describe the sequence of transformations that results in the transformation of Figure A to Figure A’.Describe the sequence of transformations that results in the transformation of Figure A to Figure A’.For items involving dilations, tasks/exercises must state the center of dilation.Elicit student understanding of the connection between similarity and transformationsGlencoe8-1A Investigation: Similar Triangles 8-1B Similar Polygons 8-1C Extend Similar Triangles8-3A Translations8-3B Reflections8-3C Rotational Symmetry8-3D Rotations8-3E DilationsAdditional Lesson 8 Congruence and Transformation p. 800-804Additional Lesson 9 p. 805-810 Similarity of Transformations8-3F Composition of TransformationsCMP CCSS Investigations 3 & 4 Transformations, Geometry TopicsCMP Kaleidoscopes, Hubcaps & Mirrors (KHM) Investigations 1-5CMP KHM AnswersEngage NY Lessons: 8.G.1Engage NY Lessons: 8.G.2 Engage NY Lessons: 8.G.3Engage NY Lessons: 8.G.4Math Shell: Representing and Combining TransformationsMath Shell: Identifying Similar TrianglesMath Shell: Aaron's Design 8.G.3Illustrative Mathematics Tasks: 8.G.1-5TasksCoordinating ReflectionsSimilar TrianglesWindow "Pain"Dilations in the Coordinate Plane Learnzillion 8.G.A.3UEN Lesson Angles, Triangles, Distance Section 10.1HoltHands-On Lab Explore Similarity 5-55-5 Similar FiguresHands-On Lab 5-65-6 Dilations5-6A Explore Dilations7-6 Congruence7-7 Transformations Hands-On Lab Combine Transformation CMP CCSS Investigations 3 & 4 Transformations, Geometry TopicsCMP Kaleidoscopes, Hubcaps & Mirrors (KHM) Investigations 1-5CMP KHM AnswersEngage NY Lessons: 8.G.1Engage NY Lessons: 8.G.2 Engage NY Lessons: 8.G.3Engage NY Lessons: 8.G.4Math Shell: Representing and Combining TransformationsMath Shell: Identifying Similar TrianglesMath Shell: Aaron's Design 8.G.3Illustrative Mathematics Tasks: 8.G.1-5TasksCoordinating ReflectionsSimilar TrianglesWindow "Pain"Dilations in the Coordinate PlaneLearnzillion 8.G.A.3UEN Lesson Angles, Triangles, Distance Section 10.1Language ObjectivesStudents will define and describe the properties of rotations, reflections and translations.Students will describe the similarities and differences among the different types of transformations.Students will identify and explain orally the relationship between an image and pre-image using the properties of rotation.Vocabulary: congruent figures, congruence (≈), A’ is read “A Prime”, similar figures, transformation, reflection, rotation, translation, dilation, clockwise, counterclockwise, center of rotation, pre-image, imageGraphic Organizers:Have students make flash cards with symbols and/or pictures of the concepts related to congruence, transformations, and similar figures. Have students identify the symbols or pictures on each flashcard with a partner.Have students create a word web listing the terms they already know or think they know about transformations. Foldable: TransformationsRESOURCE TOOLBOXTextbook ResourcesGlencoe my.Tennessee StandardsState StandardsTN CoreCCSS Tool BoxVideosKhan Academy: Grade 8 GeometryRutherford Grade 8 PB WorksVirtual NerdTeacher TubeThe Futures ChannelCalculatorTexas Instruments EducationCasio EducationTI-Inspire for Middle GradesTI-Inspire Activity ExchangeInteractive ManipulativesNational Library of Interactive ManipulativesGlencoe Virtual ManipulativesRational vs Irrational GameShodor ManipulativesPythgorville MapAdditional SitesMath Connects, Course 3 Text ResourcesInternet 4 ClassroomsKuta SoftwareIlluminationsSTEM ResourcesCLIP ResourcesPolya’s Model Polya's Model Video Polya's Model Problem SolvingK-N-W-SSQRQCQ Three-level GuideStrategies to improve problem solvingWord Problem Roulette RouletteVideo: Roulette ProcessProcess LogRAFTRAFT StrategyVenn DiagramFrayer ModelCommon Core 360Mathematics Assessment ProjectNew York Common Core LibraryIllustrative MathematicsLearn ZillionHoward County Schools ResourcesCommon Core Curriculum 8th Grade Math Resources HYPERLINK "" Lessons for Learning North Carolina Public SchoolsAlbuquerque Public SchoolsInside Mathematicsmath8commoncore. ................
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