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Major Content Supporting Content Additional Content Curriculum and Instruction – Mathematics Quarter 1 Grade 8 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 aligned instruction. The Tennessee State Standards provide a common set of expectations for what students will know and be able to do at the end of a grade. College and career readiness is rooted in the knowledge and skills students need to succeed in post- secondary study or careers. The TN State Standards represent three fundamental shifts in mathematics instruction: focus, coherence and rigor. Shelby County Schools 2016/2017 Revised 6/29/16 1 of 30

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Major Content Supporting Content Additional Content

Curriculum and Instruction – Mathematics Quarter 1 Grade 8

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

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In order to achieve these ambitious goals, we must collectively work to provide our students with high quality, college and career ready aligned instruction. The Tennessee State Standards provide a common set of expectations for what students will know and be able to do at the end of a grade. College and career readiness is rooted in the knowledge and skills students need to succeed in post-secondary study or careers. The TN State Standards represent three fundamental shifts in mathematics instruction: focus, coherence and rigor.

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The 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.

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Mathematical Practices(MP)

1. Make sense of problems and persevere in solving them

2. Reason abstractly and quatitatively

3. Construct viable arguments and

crituqe the reasoning of

others

4. Model with mathematics

5. Use appropriate tools strategically

6. Attend to precision

7. Look for and make use of

structure

8. Look for and express regularity

in repeated reasoning

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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:

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The TN 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.

Standards for Mathematical Practice

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Standards for Mathematical Practice https://drive.google.com/file/d/0B926oAMrdzI4RUpMd1pGdEJTYkE/view

Teachers 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.

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Purpose of the Mathematics Curriculum Maps

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This 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.

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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 judgement 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.

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Additional Instructional SupportShelby County Schools adopted our current math textbooks for grades 6-8 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.

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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 MapsShelby County Schools 2016/2017

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OverviewAn 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

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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”

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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, i-Ready lessons 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.

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Topics Addressed in QuarterDecimal Expansions & Irrational NumbersCompare Irrational NumbersInteger ExponentsSquare Roots and Cube Roots

Very Small & Very Large QuantitiesScientific NotationSolve Linear Equations in One Variable

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Overview During this quarter students will know that there are numbers that are not rational, and approximate them by rational numbers. Students should know that numbers that are not rational are called irrational and understand that every number has a decimal expansion. For rational numbers students should show that the decimal expansion repeats eventually. (8.NS.1) Students should also use rational approximations of irrational numbers to compare the size of irrational numbers and approximately locate them on a number line diagram.(8.NS.2) Students will apply properties of the law of exponents to simplify expressions. (8.EE.1) Students will understand the meaning behind square root and cubed root symbols. (8.EE.2) Numbers will be expressed in scientific notation so students can compare very large and very small quantities and compute with those numbers. (8.EE.3)

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Lastly, students will write linear and non-linear expressions leading to linear equations, which are solved using properties of equality (8.EE.C.7b). Students learn that not every linear equation has a solution. In doing so, students will learn how to transform given equations into simpler forms until an equivalent equation results in a unique solution, no solution, or infinitely many solutions (8.EE.C.7a).

Grade Level Standard Type of Rigor Foundational Standards Sample Assessment Items8.NS.1 Conceptual Understanding Learnzillion Assessment: 8.NS.1-28.NS.2 Conceptual Understanding

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8.EE.1 Conceptual Understanding 6.EE.1 Learnzillion Assessment: 8.EE.1-38.EE.2 Procedural Skill & Fluency 6.EE.5, 7.NS.38.EE.3 Procedural Skill & Fluency 4.OA.2, 5.NBT.2, 8.EE.18.EE.4 Procedural Skill & Fluency 7.EE.3, 8.EE.1 Math Shell Assessment Task: 100

People8.EE.7 Procedural Skill & Fluency 7.EE.1 TNCore Assessment Task: School

Fair

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Fluency NCTM Position

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Procedural fluency is a critical component of mathematical proficiency. Procedural fluency is the ability to apply procedures accurately, efficiently, and flexibly; to transfer procedures to different problems and contexts; to build or modify procedures from other procedures; and to recognize when one strategy or procedure is more appropriate to apply than another. To develop procedural fluency, students need experience in integrating concepts and procedures and building on familiar procedures as they create their own informal strategies and procedures. Students need opportunities to justify both informal strategies and commonly used procedures mathematically, to support and justify their choices of appropriate procedures, and to strengthen their understanding and skill through distributed practice.

The fluency standards for 8th grade listed below should be incorporated throughout your instruction over the course of the school year. Click Engage NY Fluency Support to access exercises that can be used as a supplement in conjunction with building conceptual understanding.

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8.EE.7 Solve one-variable linear equations, including cases with infinitely many solutions or no solutions. 8.G.9 Solve problems involving volumes of cones, cylinders, and spheres together with previous geometry work, proportional reasoning and multi-step

problem solving in grade 7

References:

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https://www.engageny.org/ http://www.corestandards.org/ http://www.nctm.org/ http://achievethecore.org/

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

Rational and Irrational Numbers

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(Allow approximately 2 weeks for instruction, review and assessment)Domain: The Number SystemCluster: Know that there are numbers that are not rational, and approximate them by rational numbers.

8.NS.A.1 : Know that numbers that are not

Enduring Understandings: Rational numbers can be represented in

multiple ways and are useful when examining situations involving numbers that are not whole.

The rational and irrational numbers allow

Glencoe1-1A Rational Numbers p. 282-3D Compare Real Numbers p. 135

Holt2-1 Rational Numbers p. 682-2 Comparing and Ordering Rational

Vocabulary: rational number, irrational number, truncated decimal

Writing in Math:Have students explain the process of writing a fraction as a repeated decimal and vice versa.

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESrational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

8.NS.A.2 : Use rational approximations of

us to solve problems that are not possible to solve with just whole numbers or integers.

Between any two rational numbers there are infinitely many rational and irrational numbers.

Essential Questions:

Numbers (This lesson only references comparing rational numbers to other rational numbers) p. 724-7 The Real Numbers p.195

Choose from the following resources and use them to ensure that the intended outcome and level of rigor of the standards

Allow students to define and discuss the differences between rational and irrational numbers.

Think/Pair/Share:Think: Locate the irrational number, √2, on a number line.

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESirrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2).

In what ways can rational numbers be useful?

Why is it important to be able to compare and approximate rational and irrational numbers?

Objectives: Students will classify real numbers as

are met.

Additional Lessons:Engage NY: Lesson 8 The Long Division AlgorithmEngage NY: Lesson 9 Decimal Expansions of FractionsEngage NY: Lesson 10 Converting Repeating

Pair: How do your solutions compare?Share: Justify your agreed upon solution to the whole group

Graphic Organizer(s):Create a Venn Diagram for Rational and Irrational Numbers.

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESrational and irrational.

Students will convert a repeating decimal into a fraction.

Students will convert a fraction into a repeating decimal.

Students will write approximations of irrational numbers as rational numbers.

Student will compare the sizes of irrational

Decimals toEngage NY: Lesson 11 Decimal Expansion of Some Irrational NumbersEngage NY: Lesson 13 Comparing Irrational Numbers

Tasks:Illustrative Math: Identifying Rational

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESnumbers by using rational approximations of irrational numbers.

Students will approximate the locations of irrational numbers on the number line by using rational approximations of irrational numbers.

Additional Information:

NumbersIllustrative Math: Converting Repeating Decimals to FractionsIllustrative Math: Converting Decimal Representations of Rational Numbers to Fraction RepresentationsIllustrative math: Repeating or Terminating?Illustrative Math: Calculating & Rounding

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES Students understand that real numbers

are either rational or irrational. They should recognize that rational numbers can be expressed as a fraction.

Write a fraction a/b as a repeating decimal by showing, filling in, or otherwise producing the steps of a long division a/b.

Numbers 8.NS.A.1 Illustrative Math: Approximating Pi

Additional Resources:Station Activities for 8.NS.1 & 2 Refer to p. 1TNCORE Non-Summative Assessment Itemsp. 35 #3-5; p. 46 #6-7

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESExample(s): Write a given repeating decimal as a

fraction.

Change 0.4444… to a fraction.

Let x = 0.444444…..Multiply both sides so that the repeating digits

Correlated iReady Lesson(s) Rational and Irrational Numbers Approximating Rational Numbers

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESwill be in front of the decimal. In this example, one digit repeats so both sides are multiplied by 10, giving 10x = 4.4444444….

Subtract the original equation from the new equation.

10x = 4.4444444-x =0.4444444

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES9x = 4

Solve the equation to determine the equivalent fraction.

9 x9 = 4

9

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

X = 49

Additionally, students can investigate repeating patterns that occur when fractions have denominators of 9, 99, or 11.

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES Approximate the value of √5 to the nearest

hundredth.

Solution: Students start with a rough estimate based upon perfect squares. √5 falls between 2 and 3 because 5 falls between 22 = 4 and 32

= 9. The value will be closer to 2 than to 3.Students continue the iterative process with

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESthe tenths place value. √5 falls between 2.2 and 2.3 because 5 falls between 2.22 = 4.84 and 2.32 = 5.29. The value is closer to 2.2. Further iteration shows that the value of √5 is between 2.23 and 2.24 since 2.232 is 4.9729 and 2.242 is 5.0176.

Compare √2 and √3 by estimating their

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESvalues, plotting them on a number line, and making comparative statements.

Solution: Statements for the comparison could include:

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

√2 and √3 are between 1 and 2√3 is between 1.7 and 1.8√2 is less than √3Students will understand that the value of a square root can be approximated between integers and that non-perfect square roots are irrational.

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

Powers, Exponents and Roots( Allow approximately 3 weeks for instruction, review and assessment )

Domain: Expressions and EquationsCluster: Work with radicals and integer exponents.8.EE.A.1: Know and apply the properties of integer exponents to generate equivalent

Enduring Understandings:Algebraic expressions and equations are used to model real-life problems and represent quantitative relationships.

Glencoe2-1A Powers and Exponents p. 912-1B Multiply and Divide Monomials p.972-1C Powers of Monomials p. 1022-2A Negative Exponents 9.108

Vocabulary: power, base, exponent, monomial, laws of exponents, root, square root, cube root, perfect square, perfect cube, radical sign

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numerical expressions. For example, 32 x 3-5 = 1/33 = 1/27.8.EE.A.2 Use square roots and cube root symbols to represent solutions to equations of the form x2 = p and x3=p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small

Essential Questions: How do radicals and exponents influence

one’s understanding of other content, such as geometry and science?

What is the relationship between squares and square roots? Cube and cube roots?

Objectives:

2-3A Roots p. 124

Holt4-1 Exponents p.1624-2 Integer Exponents p. 1664-3 Properties of Exponents p. 1704-5 Square and Square Roots p. 1824-6 Hands-On Lab Explore Cube Roots p.

Writing in Math:Describe what it means to take the square root and cube root of a number.

Compare and contrast multiplying and dividing exponents with the same base.

Explain why the rules you discovered for

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perfect cubes. Know that √2 is irrational. Students will describe why a zero exponent produces a value of one.

Students will explain how a number raised to an exponent of -1 is the reciprocal of that number

Students will evaluate square roots of small perfect squares and cube roots of small perfect cubes.

192Additional Topic: Square Roots and Cube Roots p. AT5

Choose from the following resources and use them to ensure that the intended outcome and level of rigor of the standards are met.

multiplying and dividing exponents with the same base do or do not apply to multiplying and dividing exponents with different bases.

Graphic Organizer(s):Have students create various graphic organizers for some of the vocabulary words.Exponent Rules Foldable

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES Students will use square root and cube root

symbols to solve and represent solutions of equations.

Students will apply the properties of integer exponents to generate equivalent numerical expressions.

Additional Information:

Additional Lessons:Engage NY: Lesson 1 Exponential NotationEngage NY: Lesson 2 Multiplication of Numbers in Exponential FormEngage NY: Lesson 3 Numbers in Exponential Form Raised to a PowerEngage NY: Lesson Square and Cube Roots

Additional Graphic Organizer Ideas

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESInteger (positive and negative) exponents are further developed to generate equivalent numerical expressions when multiplying, dividing or raising a power to a power.

Students will generate equivalent expressions by using numerical bases and the laws of exponents.

Engage NY: Lesson Use Factors to Simplify Square RootsLearnzillion Lesson: 8.EE.2CMP CCSS Investigations: Investigation 1 ExponentsMath Shell Lesson: Applying Properties of Exponents

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Example(s): (23)/(52) = 8/25

(22)/(26) = 22-6 = 2-4 = 1/16

70 = 1 Students understand this relationship from examples such as 62/62.

CMP Lesson: Investigation 5- Patterns with Exponents Summary

The following links support CMP Investigation 5CMP: Inv 5 Lesson PlanCMP: Inv 5 Problem 1 Lab SheetCMP: Inv 5 Problem 1 Student PagesCMP: Problem 5.2 Operating with

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESThis expression could be simplified as 36/36 = 1. Using the laws of exponents, this expression could also be written as 62–2 = 60. Combining these gives 60 = 1.

(32)(33) = (32+3) = 35 = 243 (42)3 = 42x3 = 46

Exponents Lesson PlanCMP: Inv 5 Problem 2 Student PagesCMP: Inv 5 Application, Connection, Extension Problems (#56, 57, 60)

Tasks:Math Shell:100 PeopleIllustrative Math: Definition of Exponents

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Students recognize perfect squares and cubes. They should also recognize that squaring a number and taking the square root of a number are inverse operations; likewise for cubing and taking the cube root.

Illustrative Math: Raising to the Zero and Negative Power 8.EE.1Smarter Balance Performance Task 8.EE.2Smarter Balance Task 2 8.EE.2Illustrative Math: Estimating Square RootsIllustrative Math: Calculating the Square Root of 2Cube Hotel

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Additional Resources:Station Activities Refer to p.9 & 24

Correlated iReady Lessons Properties of Integer Exponents Square Roots and Cube Roots

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESScientific Notation

( Allow approximately 2 week(s) for instruction, review and assessment )Domain: Expressions and EquationsCluster: Work with radicals and integer8.EE.A.3: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as

Enduring Understandings: Real world situations involving exponential

relationships can be solved using multiple representations.

Essential Questions:

The following Glencoe & Holt lessons do not address expressing how many times as much one number written in scientific notation is than the other, so please refer to some of the additional lessons and tasks below.

Vocabulary: scientific notation, power, exponent, integer

Writing in Math:Why are numbers expressed in scientific notation more efficient?

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much one is than the other.8.EE.A.4: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small

Why would you want to use scientific notation to compare very large or very small numbers?

Objectives: Students will express numbers as a single

digit times an integer power of ten. Students will use scientific notation to

Glencoe2-2B Scientific Notation p. 1132-2C Compute with Scientific Notation p.118

Holt

4-4 Scientific Notation p. 174

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quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

estimate very large and/or very small quantities

Students will perform operations with numbers expressed in scientific notation and a mix of scientific notation and decimal notation.

Students will choose appropriate unit of measure when using scientific notation.

Additional Topic: Scientific Notation Operations p. AT2Scientific Notation Lab p. 179

Choose from the following resources and use them to ensure that the intended outcome and level of rigor of the standards are met.

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES Students will interpret scientific notation

that has been generated by technology.

Additional Information:Students use scientific notation to express very large or very small numbers. Students compare and interpret scientific notation quantities in the context of the situation,

Additional Lessons:Engage NY Lessons: 8.EE.3 & 4Engage NY Lessons 7-8 deal with powers of 10 and Large Number Quantities. Lessons 9-13 deal with writing numbers in scientific notation and quantitative reasoning with scientific notation

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESrecognizing that if the exponent increases by one, the value increases 10 times. Likewise, if the exponent decreases by one, the value decreases 10 times.Students solve problems using addition, subtraction or multiplication, expressing the answer in scientific notation.

Math Shell Lesson: Scientific NotationMath Shell: Generalizing Patterns 8.EE.3

Tasks:Illustrative Math Tasks: 8.EE1- 4Illustrative Math: Ants vs Humans 8.EE.4 &

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Example(s): Write 75,000,000,000 in scientific notation 7.5 x 1010

Write 0.000592 in scientific notation 5.92 x 10-4

Express 4.76 x 102 in standard form

8.EE.1

Additional Resource(s):Station Activities Refer to p.24

Correlated iReady Lessons: Scientific Notation Operations with Numbers Expressed

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476 Compare 7.5 x 1010 and 5.92 x 10-4

7.5x1010 is larger because it has the larger value exponent

Students will begin to see scientific expressed

in Scientific Notation

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differently on various calculators and other technology. E or EE is often used for scientific notation and ^ is used as the exponent symbol.3.21E+6 is 3.21 x 106 and 3.21E-4 is 3.21 x 10 -4.

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Students will add and subtract with scientific notation. They will also use laws of exponents to multiply and divide numbers written in scientific notation, writing the product or quotient in proper scientific notation.

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(6.45x1011)(3.2x104) = (6.45x3.2)(1011 x 104) = 20.64 x 1015 = 2.064 x 1016

3.45 x 105

6.7 x 102 = 3.456.7 x 105-2 = 0.515 x 103

= 5.15 x 102

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESLinear Equations

( Allow approximately 2 weeks for instruction, review and assessment )Domain: Expressions and EquationsCluster: Analyze and solve linear equations and pairs of simultaneous linear equations.8.EE.C.7: Solve linear equations in one variable.

Enduring Understanding(s): Algebraic equations are used to model real-

life problems and represent quantitative relationships.

Essential Question(s):

The following Glencoe & Holt lessons address solving linear equations but do not address equations with infinitely many solutions or no solutions and equations whose solutions require expanding

Vocabulary: linear equation, one solution, infinite solutions, no solution, coefficient, like terms, (inconsistent ), one –step and two –step equation

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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

Why is it important to know whether a linear equation has one solution, infinitely many solutions, or no solution?

Objectives: Students will give examples of linear

equations in one variable with one solution and show that the given example equation

expressions using the distributive property and collecting like terms.

Glencoe3-1B Write Equations p. 1563-1C/1D Solve one step equation using addition, subtraction, multiplication and

Explain why showing the steps to solve an equation is equally important as showing the correct answer.

Graphic Organizer(s):Students can use graphic organizers to show the steps used to isolate the variable, and provide written explanation justifying their

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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.

has one solution by successively transforming the equation into an equivalent equation of the form x=a

Students will give examples of linear equations in one variable with infinitely many solutions and show that the given example has infinitely many solutions by successively transforming the equation into an equivalent

division. P. 1613-2A Two-step Equations p. 1713-2B Solve two-step equations p. 1723-2C Write two-step equations p.1774-1B The Distributive Property p. 2254-1C Simplify Algebraic Expressions p. 2314-2B Solve Equations with Variables on Both Sides p. 241

work.Multi-step Equations Graphic Organizer

Have students create a flow chart, similar to the one below, for solving linear equations.

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESequation of the form a=a

Students will give examples of linear equations in one variable with no solution and show that the given example has no solution by successively transforming the equation into an equivalent equation of the form b=a, where a and b are different numbers.

4-2C Solve Multi-step Equations p. 246

Holt1-8: Solving Equations by Adding or Subtracting p. 381-9: Solving Equations by Multiplying or Dividing2-7: Solving Equations with Rational Numbers

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES Students will solve linear equations with

rational number coefficients. Students will solve equations whose

solutions require expanding expressions using the

distributive property and/or collecting like terms.

2-8: Solving Two-Step Equations

Choose from the following resources and use them to ensure that the intended outcome and level of rigor of the standards are met.

Additional Lessons:

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES Additional Information:When the equation has one solution, the variable has one value that makes the equation true as in 12 - 4y =16. The only value for y that makes this equation true is -1.

When the equation has infinitely many solutions, the equation is true for all real

Engage NY: Writing and Solving Linear Equations 8.EE.7a Read the Module 4, Topic A overview (pdf) to find out what students will learn during each of the 9 lessons. Or you may just do lessons 6, 7 & 9.

Engage NY:Writing and Solving Linear Equations 8:EE.7b

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESnumbers as in 7x + 14 = 7(x+2). As this equation is simplified, the variable terms cancel leaving 14 = 14 or 0 = 0. Since the expressions are equivalent, the value for the two sides of the equation will be the same regardless which real number is used for the substitution.

(Lessons 1-5, 8)CMP CCSS Investigation 2: FunctionsConnected Math: Say It with Symbols Inv. 1-4Say it With Symbols ResourcesConnected Math: Thinking with math Models Inv. 2Thinking with Math Models Answers Inv. 2

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESWhen an equation has no solutions it is also called an inconsistent equation. This is the case when the two expressions are not equivalent as in 5x - 2 = 5(x+1). When simplifying this equation, students will find that the solution appears to be two numbers that are not equal or -2 = 1. In this case, regardless which real number is used for the substitution,

Tasks:TNCore Task Arc: Equations and Linear Functions 8.EE.7TNCore Assessment Tasks: Currency Conversion, Dog Park & School FairInside Math: Squares and Circles Task 8.EE.7bInside Math: Squares and Circles Task

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESthe equation is not true and therefore has no solution.

8.EE.7bMath Shell Formative Assessment Lesson: 8.EE.7Illustrative Math: The Sign of SolutionsIllustrative Math: Coupon versus DiscountIllustrative Math: Sammy’s Chipmunk & Squirrel ObservationsIllustrative Math: Solving Equations

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESIllustrative Math: The Sign of Solutions

Additional Resources:Correlated iReady Lessons:

Solving Linear Equations Solving Linear Equations with

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESRational Coefficients

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RESOURCE TOOLBOXNWEA MAP Resources: https://teach.mapnwea.org/assist/help_map/ApplicationHelp.htm#UsingTestResults/MAPReportsFinder.htm - Sign 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)https://support.nwea.org/khanrit - These Khan Academy lessons are aligned to RIT scores.

Textbook Resources TN Core/CCSS Videos

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www.my.hrw.comwww.connected.mcgraw-hill.comHolt, Course 3 Text Resources

TNReady Math StandardsTNCoreAchieve the Core

Khan AcademyWatch Know LearnLearnZillionVirtual NerdMath PlaygroundStudyJams

Calculator ActivitiesGreatest Common Factor Calculator

Interactive ManipulativesNational Library of Interactive Manipulatives

Additional SitesTeacher Tube

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TI-73 ActivitiesCASIO ActivitiesTI-Inspire for Middle GradesTI-Inspire Activity Exchange

Glencoe Virtual Manipulatives Rational vs Irrational Activity Rational vs Irrational Game Irrational Numbers on the Number Line

The Futures ChannelSTEM Resources

http://community.ksde.org/LinkClick.aspx?fileticket=F2AYEhO1ZMs%3d&tabid=5646&mid=13290

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