shelby county schools’ mathematics instructional maps are ... 8 q2 7_27_15_n… · web...
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Curriculum and Instruction – Office of Mathematics
Introduction
In 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 ready 90% of students will graduate on time
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100% of our students who graduate college or career ready will enroll in a post-secondary opportunity
In 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
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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
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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 (http://www.tn.gov/education/article/tnready-blueprints ) have been designed to show educators a summary of what will be assessed in
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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.
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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,
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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
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How to Use the Mathematic Curriculum Maps
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 instructional practice in alignment with the three College and Career Ready shifts in instruction for Mathematics. We should see these shifts in all classrooms:
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Mathematical Practices
Make sense of problems and persevere in solving them
Reason abstractly and quatitatively
Construct viable arguments and
crituqe the reasoning of
others
Model with mathematics
Use appropriate tools
strategically
Attend to precision
Look for and make use of
structure
Look for and express
regularity in repeated reasoning
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1) Focus2) Coherence3) Rigor
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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 each of the three shifts that teachers should consistently access:
The TNCore Mathematics StandardsThe Tennessee Mathematics Standards:https://www.tn.gov/education/article/mathematics-
Teachers can access the Tennessee State standards, which are featured throughout this curriculum map and
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standards represent college and career ready learning at reach respective grade level.
Mathematical ShiftsFocushttp://achievethecore.org/shifts-mathematics
The standards are focused on fewer topics so students can learn more
Coherence Topics within a grade are connected to support focus, and Shelby County Schools
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http://achievethecore.org/shifts-mathematics learning is built on understandings from previous grades
Rigorhttp://achievethecore.org/shifts-mathematics
The standards set expectations for a balanced approach to pursuing conceptual understanding, procedural fluency, and application and modeling
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Curriculum 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.
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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.
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS
Topic:( 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).
Students compare two functions from different representations.Examples:Compare the two linear functions listed below
Glencoe5-1C Ordered Pairs and Relations5-2A Explore
Holt3-4 Functions3-5 Equations,
Language Objectives:Students will translate values from a graph or table into equations.
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS
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
and determine which equation represents a greater rate of change.
Function 1
Patterns5-2B Analyze Tables5-2C Analyze Graphs5-2D Translate Tables and Graphs into Equations5-3B Functions5-3C Linear
Tables and GraphsLab Explore Multiple Representations12-1 Graphing Linear Equations12-2 Slope of a Line12-3 Using Slopes
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.
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONSin terms of the situation it models, and in terms of its graph or a table of values.
Functions6-1A Constant Rate of Change6-1B Explore Graphing Technology: Rate of Change6-1C Slope
and InterceptsLab Graph Equations in Slope-Intercept Form12-4 Point-Slope form12-5 Direct Variation
CMP Thinking with
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-value
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS6-1D Constant Rate of Change6-1E Direct Variation6-2A Slope-Intercept
CMP Thinking with Mathematical Models Investigations 1, 2 &
Mathematical Models Investigations 1, 2 & 3
CMP Say it With Symbols Investigation 4 Looking Back at Functions
Journal Prompt(s):How do you translate among the four representations (words, graphs, tables symbols) of a linear function?Define constant rate of change in your
Graphic Organizer:Shelby County Schools
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS3
CMP Say it With Symbols Investigation 4 Looking Back at FunctionsEngage NY Lessons: 8.F.2
Engage NY Lessons: 8.F.2Engage NY Lesson: 8.F.4
Math Shell Concept Development Lesson:
Have students record information about tables, graphs, words and equations in a Foldable study table.Dinah Zike's Foldables
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONSEngage NY Lesson: 8.F.4
Math Shell Concept Development Lesson: Comparing Lines and Linear Equations
Comparing Lines and Linear Equations
TNCore Task: Hexagon Puzzle
TNCore Assessment Task: Javier's Bike,
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONSTNCore Task: Hexagon Puzzle
TNCore Assessment Task: Javier's Bike, Cell Phone and/or Tanker Trucks
Cell Phone and/or Tanker Trucks
TNCORE Assessment ItemsChoose items from pp. 51-71Growing Dots
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONSTNCORE Assessment ItemsChoose items from pp. 51-71Growing Dots p. 3
p. 3
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS
Topic: 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
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.
Glencoe6-3B Explore Graphing Technology: Systems
Holt11-6 Systems of Equations12-7 Solving Systems
Language Objectives:Students will discuss the meaning of the point of intersection of the graph of a system of linear equations.
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS
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 inspection
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
of Equations6-3C Solve Systems of Equations by Graphing6-3D Solve Systems of Equations by Substitution
of Linear Equations by Graphing
TNCore Task Arc: Understanding and Solving Systems 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, elimination
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS
8.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.
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
TNCore Task Arc: Understanding and Solving Systems of Linear Equations
CMP Lessons: The Shapes of Algebra Investigations 2, 3, &
CMP Lessons: The Shapes of Algebra Investigations 2, 3, & 4
Engage NY: 8.EE.8 Lessons 24-30
Graphic Organizer:Solving Systems of Linear Equations Foldable
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONSto 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
4
Engage NY: 8.EE.8 Lessons 24-30
Math Shell Concept Development Lesson: Classifying Solutions
Math Shell Concept Development Lesson: Classifying Solutions to Systems of Equations
Math Shell Problem
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS-2x + 8y = 10
Plant 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 weeks
to Systems of Equations
Math Shell Problem Solving Lesson: Baseball Jerseys 8.EE.8c
Solving Lesson: Baseball Jerseys 8.EE.8c
Illustrative Math Tasks: 8.EE.8a-c
Inside Math: On
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONSLet H = height of the plant after W weeks
Plant AW H0 4 (0,4)1 6 (1,6)2 8 (2,8)3 10 (3,10)
Illustrative Math Tasks: 8.EE.8a-c
Inside Math: On Balance Task Level E 8.EE.8c p. 7&18
TNCore Assessment
Balance Task Level E 8.EE.8c p. 7&18
TNCore Assessment Task: Cross Country, Electric Cars, or Swimming Pools
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS
Given each set of coordinates, graph their corresponding lines.Solution:
Task: Cross Country, Electric Cars, or Swimming Pools
NYC Common Core Assessment
Simultaneous-Linear-
NYC Common Core Assessment
Simultaneous-Linear-Equations-Mini-Assessment
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONSEquations-Mini-Assessment
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS
Topic: 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
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.
Glencoe6-1C More About Graphs p. 349
Holt3-3 Interpreting Graphs
CMP Lessons:
Language Objectives:Students will evaluate qualitative functions and write a description of a scenario that can be represented by the function.
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS
features of a function that has been described verbally.
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
CMP Lessons: Thinking with Mathematical Models Investigation 2 Linear Models and Equations
CMP Lessons:
Thinking with Mathematical Models Investigation 2 Linear Models and Equations
CMP Lessons: Growing, Growing,
Vocabulary: qualitative graph
Graphic Organizer:Have students use a foldable, or other graphic organizer to keep notes qualitative graphs.
Qualitative Graphs Graphic Organizers pp. 15
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONSrelates to the story. Growing, Growing,
Growing Investigations 1-4
Engage NY Lessons: 8.F.5
Math Shell Concept
Growing Investigations 1-4
Engage NY Lessons: 8.F.5
Math Shell Concept Development Lesson:
& 16
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONSDevelopment Lesson: Interpreting Distance-Time Graphs
Learner.org Lesson Qualitative Graphs
TNCore Instructional
Interpreting Distance-Time Graphs
Learner.org Lesson Qualitative Graphs
TNCore Instructional Task: Flower Pot
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONSTask: Flower PotTNCore Assessment Task: Rollerblading
Illustrative Math Tasks: 8.F.5
Understanding
TNCore Assessment Task: Rollerblading
Illustrative Math Tasks: 8.F.5
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONSGraphs in Motion Video
Learn Zillion Lesson: Sketch Graphs by Interpreting Situations
Understanding Graphs in Motion Video
Learn Zillion Lesson: Sketch Graphs by Interpreting Situations
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS
Topic: 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
Students will use various tools and technology to explore figures created from translations. Lengths of line segments, angle measures and parallel lines
Glencoe8-1A Investigation: Similar Triangles8-1B Similar
HoltHands-On Lab Explore Similarity 5-55-5 Similar Figures
Language ObjectivesStudents will define and describe the properties of rotations, reflections and translations.Students will describe the similarities and
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS
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.
Use 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
Polygons8-1C Extend Similar Triangles8-3A Translations8-3B Reflections8-3C Rotational Symmetry
Hands-On Lab 5-65-6 Dilations5-6A Explore Dilations7-6 Congruence7-7 TransformationsHands-On Lab
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,
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS
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.
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.
8-3D Rotations8-3E DilationsAdditional Lesson 8 Congruence and Transformation p. 800-804Additional Lesson 9
Combine Transformation
CMP CCSS Investigations 3 & 4 Transformations, Geometry Topics
transformation, reflection, rotation, translation, dilation, clockwise, counterclockwise, center of rotation, pre-image, image
Graphic Organizers:Have students make flash cards with symbols and/or pictures of the concepts related to congruence, transformations, and similar
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS
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 Describe the sequence of transformations that
p. 805-810 Similarity of Transformations8-3F Composition of TransformationsCMP CCSS Investigations 3 & 4 Transformations,
CMP Kaleidoscopes, Hubcaps & Mirrors (KHM) Investigations 1-5CMP KHM Answers
Engage NY Lessons: 8.G.1
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: Transformations
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS
rotations, reflections, translations, and dilations; given two similar two dimensional figures, describe a sequence that exhibits the similarity between them.
results in the transformation of Figure A to Figure A’.
Geometry Topics
CMP Kaleidoscopes, Hubcaps & Mirrors (KHM) Investigations 1-5CMP KHM Answers
Engage NY Lessons: 8.G.2
Engage NY Lessons: 8.G.3
Engage NY Lessons: Shelby County Schools
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONSEngage NY Lessons: 8.G.1
Engage NY Lessons: 8.G.2
Engage NY Lessons: 8.G.3
8.G.4
Math Shell: Representing and Combining TransformationsMath Shell: Identifying Similar
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS
Engage NY Lessons: 8.G.4
Math Shell: Representing and Combining Transformations
Triangles
Math Shell: Aaron's Design 8.G.3
Illustrative Mathematics Tasks: 8.G.1-5
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS
Math Shell: Identifying Similar Triangles
Math Shell: Aaron's Design 8.G.3
TasksCoordinating ReflectionsSimilar TrianglesWindow "Pain"
Dilations in the
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONSIllustrative Mathematics Tasks: 8.G.1-5
TasksCoordinating Reflections
Coordinate Plane
Learnzillion 8.G.A.3
UEN Lesson Angles, Triangles, Distance Section 10.1
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONSSimilar TrianglesWindow "Pain"
Dilations in the Coordinate Plane
Learnzillion 8.G.A.3
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONSUEN Lesson Angles, Triangles, Distance Section 10.1
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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS
Describe the sequence of transformations that Shelby County Schools 2015/2016 Revised 7/27/15(CSH)
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RESOURCE TOOLBOXTextbook Resources
Glencoe http://connected.mcgraw-hill.com Holt my.hrw.com
Tennessee Standards
State Standards
TN Core
CCSS Tool Box
Videos
Khan Academy: Grade 8 Geometry
Rutherford Grade 8 PB Works
Virtual Nerd
Teacher Tube
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Curriculum and Instruction – Office of Mathematics
The Futures Channel
Calculator
Texas Instruments Education
Casio Education
TI-Inspire for Middle Grades
Interactive Manipulatives
National Library of Interactive Manipulatives
Glencoe Virtual Manipulatives
Rational vs Irrational Game
Additional Sites
Math Connects
http://www.onlinemathlearning.com/math-word-problems.html Holt, Course 3 Text Resources
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Curriculum and Instruction – Office of Mathematics
TI-Inspire Activity Exchange Shodor Manipulatives Pythgorville Map
Internet 4 Classrooms
Kuta Software
Illuminations
STEM Resources
CLIP Resources Common Core 360
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Curriculum and Instruction – Office of Mathematics
Polya’s Model
Polya's Model Video Polya's Model Problem Solving
K-N-W-S
SQRQCQ Three-level Guide
Strategies to improve problem solving
Mathematics Assessment Project
New York Common Core Library
Illustrative Mathematics
Learn Zillion
Howard County Schools Resources
Common Core Curriculum 8th Grade Math
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Curriculum and Instruction – Office of Mathematics
Word Problem Roulette Roulette Video: Roulette Process
Process Log
RAFTRAFT Strategy
Venn DiagramFrayer Model
Resources
Lessons for Learning North Carolina Public Schools
Albuquerque Public Schools
Inside Mathematicsmath8commoncore.weebly.com
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