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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 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. 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.

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

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Focus

The 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 grades K–8, each grade's time spent in instruction must meet or exceed the following percentages for the major work of the grade. In grade 8, more than 80% of instructional time is spent on the major focus standards. 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.

Coherence

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 on to 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 the focus of the grade, these concepts serve the grade level focus. For example, instead of data displays as an end in themselves, they are an opportunity to do grade-level word problems.

Rigor

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. Students are given opportunities to practice core functions such as single-digit multiplication so that they have access to more complex concepts and procedures.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.

Problem Solving

Reasoning and Proof

CommunicationRepresentation

Connecton

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Curriculum and Instruction – Office of Mathematics3rd Nine Weeks Grade 8

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 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 Maps

This curriculum map is designed to help teachers make effective decisions about what mathematical content to teach so that our

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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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Curriculum and Instruction – Office of Mathematics3rd Nine Weeks Grade 8

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, as described above, in instruction for Mathematics.

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 standards and teaching practices that teachers should consistently access:

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The TNCore Mathematics StandardsThe Tennessee Mathematics Standards:https://www.tn.gov/education/article/mathematics-standards

Teachers 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 Teaching Practiceshttps://mathprojectsjournal.files.wordpress.com/2015/05/nctm-teaching-practices.pdf

NCTM – Mathematics Teaching Practices

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Curriculum and Instruction – Office of Mathematics3rd Nine Weeks Grade 8

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. 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 ESSENTIAL UNDERSTANDINGS CONTENT & TASKS CLIP CONNECTIONS

Topic: Parallel Lines, Transversals and Angles(3 weeks)

8.G.A.5: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles

Students use exploration and deductive reasoning to determine relationships that exist between the following: a) angle sums and exterior angle sums of triangles, b) angles created when parallel lines are cut by a transversal, and c) the angle-angle criterion for similarity of triangle.

Students can informally prove relationships with transversals.Examples:Show that m∡3+ m∡4+ m∡5= 180˚ if l and m are parallel lines and t1& t2 are transversals.∡1+ ∡2+ ∡3= 180˚. Angle 1 and Angle 5 are congruent because they are corresponding angles (∡5≅∡1). ∡1can be substituted for ∡5. ∡4≅∡2 because alternate interior angles are congruent. ∡4can be substituted for ∡2Therefore m∡3+ m∡4+ m∡5= 180˚

Students can informally conclude that the sum of a triangle is 180º (the angle-sum theorem) by applying their understanding of lines and alternate interior angles. In the figure below, line x is parallel to line yz:

Glencoe7-2A Explore Parallel Lines7-2B Lines7-3A Explore Triangles7-3B TrianglesHolt7-2 Parallel and Perpendicular Lines7-3 TrianglesTechnology Lab Exterior Angles of a Polygon p. 352

CMP CCSS Investigation 4 Geometry Topics

Special Angle Pairs Discovery Activity

Engage NY: 8.G.5

Math Shell: Identifying Similar Triangles

Illustrative Math Find the Missing Angle

Lunch Lines

Math Warehouse Interactive

Ohio DOE Lesson

MICA Sample Items for 8.G.A.5:IDs 24262, 42086, and 44202

Language Objectives:Students will explore and justify relationships that exist between angles created when parallel lines are cut by a transversal.

Students will discuss the relationship between exterior angles of triangles and angles formed when two parallel lines are cut by a transversal.

Vocabulary:transversal, parallel, exterior angles, alternate exterior angles, interior angles, alternate interior angles, angle-angle criterion, vertical angles, adjacent angles, supplementary and complementary angles, corresponding angles,

Graphic Organizer:When Two Parallel Lines are Cut by a Transversal

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TN STATE STANDARDS ESSENTIAL UNDERSTANDINGS CONTENT & TASKS CLIP CONNECTIONS

Solution: Angle a is 35º because it alternates with the angle inside the triangle that measures 35º. Angle c is 80º because it alternates with the angle inside the triangle that measures 80º. Because lines have a measure of 180º, and angles a + b + c form a straight line, then angle b must be 65 º (180 – 35 + 80 = 65). Therefore, the sum of the angles of the triangle are 35º + 65 º + 80 º

Topic: Pythagorean Theorem

8.G.B: Understand and apply the Pythagorean Theorem. 8.G.B.6: Explain a proof of the Pythagorean Theorem and its converse. 8.G.B.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. 8.G.B.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Using models, students explain the Pythagorean Theorem, understanding that the sum of the squares of the legs is equal to the square of the hypotenuse in a right triangle.Braining Camp Pythagorean Theorem Model Math Open Reference: Pythagorean Theorem ModelStudents also understand that given three side lengths with this relationship forms a right triangle.

Students will apply the Pythagorean Theorem to calculate unknown side lengths for right triangles.Example(s):The Irrational Club wants to build a tree house. They have a 9-foot ladder that must be propped diagonally against the tree. If the base of the ladder is 5 feet from the bottom of the tree, how high will the tree house be off the ground?

Glencoe8-2A Explore Right Triangles Relationships8-2B The Pythagorean Theorem8-2C Use the Pythagorean Theorem8-2D Distance on the Coordinate Plane

HoltLab Explore Right Triangles p. 1994-8 The Pythagorean Theorem4-9 Applying the Pythagorean Theorem

CMP Lessons: Looking for Pythagoras Investigations 2, 3 & 4

Engage NY Lessons: 8.G. 6-7Engage NY: 8.G.6-7Engage NY: 8.G.7Engage NY: 8.G.8Engage NY: 8.G.7-8

Language Objective(s):Students will explain and discuss the proof of the Pythagorean Theorem and its converse with a partner.

Using the Pythagorean Theorem, student will write a quadratic equation for the length of a one side of a right triangle. Student will solve the quadratic equation for the unknown length.

Students will explain a proof of the Pythagorean Theorem and its converse verbally and in written form.

Students will analyze the given information about a triangle and utilize the Pythagorean Theorem to determine the dimensions of its missing sides.

Students will be able to explain the correspondence between two points and

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TN STATE STANDARDS ESSENTIAL UNDERSTANDINGS CONTENT & TASKS CLIP CONNECTIONSSolution:a2 + 52 = 92

a2 + 25 = 81a2 = 56 √a2 = √56a =√56 or ~7.5

Students will use the Pythagorean Theorem to calculate the distance between two points on a coordinate plane. Students build on work from 6th grade (finding vertical and horizontal distances on the coordinate plane) to determine the lengths of the legs of the right triangle drawn connecting the points. Students understand that the line segment between the two points is the length of the hypotenuse.

Use of the distance formula is not an expectation for this standard.

Examples:Find the length of line segment AB.

Solution: 1. Form a right triangle so that the given line segment is the hypotenuse.2. Use Pythagorean Theorem to find the distance (length) between the two points.

Illustrative Math Tasks: Pythagorean TheoremJane’s TVPatterns in PragueRugsPythagorean Lesson (Includes Writing Prompts)

TNCORE Non-Summative Assessment ItemsChoose from items p. 34-49Lesson 8.G.B.8

MICA Sample Items for 8.G.B.7 and 8:8.G.B.7: IDs 41075, 42089, and 441048.G.B.8: IDs 41712 and 42093MICA does not currently have items for 8.G.B.6.

calculate the distance between those points using the Pythagorean Theorem.

Journal/Writing Prompt(s):Explain a Pythagorean triple.Name and prove two different sets of Pythagorean triples.Explain how you know which side of a right triangle is the hypotenuse.

Vocabulary: right triangle, hypotenuse, legs, Pythagorean Theorem, Pythagorean Triple

Graphic Organizer:Pythagorean Theorem GO Samples

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TN STATE STANDARDS ESSENTIAL UNDERSTANDINGS CONTENT & TASKS CLIP CONNECTIONS

62 + 72 = c2

36 + 49 = c2

85 = c2

√85 = c

Find the distance between (-2, 4) and (-5, -6).Solution:The distance between -2 and -5 is the horizontal length; the distance between 4 and -6 is the vertical distance.Horizontal length: 3Vertical length: 10102 + 32 = c2

100 + 9 = c2

109 = c2

√109 =√c2 √109 = c

Topic: Unit Rate and Slope(4 weeks)

8.EE.B.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. 8.EE.B.6: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equationy = mx + b for a line intercepting the vertical axis at b.

As part of your review of these standards you may use the following resources.Shmoop.com 8.EE.5Shmoop.com: 8.EE.6Better Lessons: 8.EE.5Better Lessons: 8.EE.6Learnzillion Lesson: 8.EE.6Khan Academy: 8.EE (Choose Desired Video Lesson)TnCore Assessment Task: Buying ToolsNYC Schools: Slippery Slopes Performance TaskMICA Sample Items for 8.EE.B.5 and 6:8.EE.B.5: IDs 42024 and 440788.EE.B.6: IDs 36760 and 42132

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TN STATE STANDARDS ESSENTIAL UNDERSTANDINGS CONTENT & TASKS CLIP CONNECTIONS

Topic: Solving Linear Equations

8.EE.C.7.a: Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). 8.EE.C.7.b: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

As part of your review of these standards you may use the following resources.Better Lessons: 8.EE.7Shmoop.com 8.EE.7mathworksheetsland.com 8.EE.7amathworksheetsland.com 8.EE.7b3 Act Math Tasks: 8.EE.7MICA Sample Items for 8.EE.C.7:8.EE.C.7a: ID 420298.EE.C.7b: IDs 42031 and 44092

Topic: Functions 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.

As part of your review of these standards you may use the following resources.Conjecturing about Functions Lesson 8.F.2Linear Graphing Lesson 8.F.4Learnzillion: Distance-Time Graphs 8.F.2Learnzillion Video Lessons and Practice 8.F 2 & 4Lesson Module: 8.F.1-3 NJcore.org Math Content 8.F.4 ResourcesTNCore Task: Workers and Earnings 8.F.2 & 8.EE.5MICA Sample Items for 8.F.A.2 and 8.F.B.4:8.F.A.2: IDs 24227 (assesses 8.F.A.1 & 2), 42043, 42045, and 242268.F.B.4: IDs 41076 and 42056

Topic: Systems of Linear Equations

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 8.EE.C.8.c: Solve real-world and mathematical problems leading to two linear

As part of your review of these standards you may use the following resources.Khan Academy Video Lessons: 8.EE.8Better Lessons: 8.EE.8Shmoop.com 8.EE.8

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TN STATE STANDARDS ESSENTIAL UNDERSTANDINGS CONTENT & TASKS CLIP CONNECTIONS

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.

Cpalms.org 8.EE.8 ResourcesShade Trees TaskSwimming Pools TaskThe Intersection of Two LinesCell Phone PlansKimi & JordanHow Many Solutions?Fixing the FurnaceCarbon Dioxide TaskQuinoa Pasta 1Summer SwimmingTNCORE Assessment ItemsChoose items from pp. 73-83MICA Sample Items for 8.EE.C.8.b and c.:8.EE.C.8b: IDs 24230 and 439098.EE.C.8c: IDs 12444, 36746, and 42153MICA Performance Task: ID 45289 (also assesses 8.EE.7 and 8.F.B.4)

Topic: Volume of Cylinders, Cones and Spheres(2 weeks, includes the TNReady Part Testing Window, Feb 29-Mar 4, 2016)

8.G.C: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.8.G.C.9: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Students build on understandings of circles and volume from 7th grade to find the volume of cylinders, finding the area of the base Πr2 and multiplying by the number of layers (the height).

V=πr2hStudents understand that the volume of a cylinder is 3 times the volume of a cone having the same base area and height or that the

volume of a cone is 13

the volume of a cylinder

Glencoe7-4A Explore 3D Figures7-4B Properties of 3D Figures

HoltHands-On Lab Construct Nets p. 4108-5 Volume of Prisms and Cylinders8-5 Hands on Lab8-6 Volume of Pyramids and Cones8-6 Hands on Lab8-9 SpheresEngage NY Lessons 9-11 for 8.G.9MatchsticksComparing Snow ConesFlower Vases

Language Objectives:Students will describe the attributes of cylinders, cones and spheres.Students will analyze and discuss the relationship between the volume of a cylinder and the volume of a cone.Students will discuss the process of using the volume formulae to solve real-world problems.Vocabulary: sphere, cone, volume, cylinder , Pi, height, radiusJournal/Writing PromptsUnit Starter- Write everything you know about the volume of 3-dimensional figures. (Have students write a similar entry at the end of the unit, and then have them compare this with their initial entry.)

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TN STATE STANDARDS ESSENTIAL UNDERSTANDINGS CONTENT & TASKS CLIP CONNECTIONShaving the same base area and height.

V=13π r2h

A sphere can be enclosed with a cylinder, which has the same radius and height of the sphere (Note: the height of the cylinder is twice the radius of the sphere). If the sphere is

flattened, it will fill 23

of the cylinder. Based on

this model, students understand that the

volume of a sphere is 23

the volume of a

cylinder with the same radius and height. The height of the cylinder is the same as the diameter of the sphere or 2r. Using this information, the formula for the volume of the sphere can be derived in the following way:

Students find the volume of cylinders, cones and spheres to solve real world and mathematical problems. Answers could also be given in terms of Pi.Examples:James wanted to plant pansies in his new planter. He wondered how much potting soil he should buy to fill it. Use the measurements

GlassesShipping Rolled OatsTNCORE Non-Summative Assessment ItemsChoose items from pp. 84-95Video Tutorial and Mini Quiz 8.G.9

Performance Task Bank 8.G.9

Yummymath: Pack It In 8.G.9

MICA Sample Items for 8.G.C.9:IDs 36789, 42094, 42095, and 42097.

Graphic Organizers:Create a Venn Diagram comparing 2 dimensional and 3 dimensional shapes/figures.Graphic Organizer for 8.G.9 Foldable 8.G.9 Nets for Various 3D Figures

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Curriculum and Instruction – Office of Mathematics3rd Nine Weeks Grade 8

TN STATE STANDARDS ESSENTIAL UNDERSTANDINGS CONTENT & TASKS CLIP CONNECTIONS

in the diagram below to determine the planter’s volume.

How much yogurt is needed to fill the cone below? Express your answers in terms of Pi.

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RESOURCE TOOLBOXTextbook ResourcesGlencoe http://connected.mcgraw-hill.com

Holt my.hrw.com

Tennessee Standards

State Standards

TN Core

CCSS Tool Box

Common Core 360

Mathematics Assessment Project

New York Common Core Library

Illustrative Mathematics

Learn Zillion

Howard County Schools Resources

Common Core Curriculum 8th Grade Math Resources

Lessons for Learning North Carolina Public Schools

Albuquerque Public Schools

Inside Mathematicsmath8commoncore.weebly.com

Videos

Khan Academy

Calculator

Texas Instruments Education Casio Education

Interactive Manipulatives

Illuminations Balance

Repeating Decimals

Math Play: Comparing and Ordering

Building Equations

One-Step Equations Game

Using Inverse Operations

Understanding Functions

Additional Sites

http://www.onlinemathlearning.com/math-word-problems.html Math Connects

Holt, Course 3 Text Resources

Virtual Nerd

Khan Academy

Internet 4 Classrooms

Teacher Tube

Kuta Software

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Curriculum and Instruction – Office of Mathematics3rd Nine Weeks Grade 8

RESOURCE TOOLBOXFunction Machine

Kuta - 2 Step EQ

Equations, Tables, and Graphs for Real World Situations

Create Verbal Descriptions of Functions

Illuminations

TI-Inspire for Middle Grades

TI-Inspire Activity Exchange

The Futures Channel

STEM Resources

CLIP StrategiesPolya’s Moldel Polya's Model Video Polya's Model Problem SolvingK-N-W-SSQRQCQ Three-level Guide

CLIP StrategiesStrategies to Improve Problem SolvingWord Problem Roulette Roulette Video: Roulette ProcessProcess LogRAFT RAFT StrategyVenn DiagramFrayer Model

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