Shelby County Schools’ mathematics instructional maps are ...



IntroductionIn 2014, the Shelby County Schools Board of Education adopted a set of ambitious, yet attainable goals for school and student performance. The District is committed to these goals, as further described in our strategic plan, Destination2025. By 2025,80% of our students will graduate from high school college or career ready90% of students will graduate on time100% of our students who graduate college or career ready will enroll in a post-secondary opportunityIn order to achieve these ambitious goals, we must collectively work to provide our students with high quality, college and career ready 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. 4572002628900The 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. -571500457200Throughout the year, students should continue to develop proficiency with the eight Standards for Mathematical Practice.This curriculum map is designed to help teachers make effective decisions about what mathematical content to teach so that, ultimately our students, can reach Destination 2025. To reach our collective student achievement goals, we know that teachers must change their practice so that it is in alignment with the three mathematics instructional shifts. Throughout this curriculum map, you will see resources as well as links to tasks that will support you in ensuring that students are able to reach the demands of the standards in your classroom. In addition to the resources embedded in the map, there are some high-leverage resources around the content standards and mathematical practice standards that teachers should consistently access:The TN Mathematics StandardsThe Tennessee Mathematics Standards: can access the Tennessee State standards, which are featured throughout this curriculum map and represent college and career ready learning at reach respective grade level.Standards for Mathematical Practice Standards for Mathematical Practice can access the Mathematical Practice Standards, which are featured throughout this curriculum map. This link contains more a more detailed explanation of each practice along with implications for instructions.Purpose of the Mathematics Curriculum MapsThe Shelby County Schools curriculum maps are intended to guide planning, pacing, and sequencing, reinforcing the major work of the grade/subject. Curriculum maps are NOT meant to replace teacher preparation or judgment; however, it does serve as a resource for good first teaching and making instructional decisions based on best practices, and student learning needs and progress. Teachers should consistently use student data differentiate and scaffold instruction to meet the needs of students. The curriculum maps should be referenced each week as you plan your daily lessons, as well as daily when instructional support and resources are needed to adjust instruction based on the needs of your students. How to Use the Mathematics Curriculum MapsTennessee 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 the 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 teachers' responsibility to examine the standards and skills needed in order to ensure student mastery of the indicated standard. ContentWeekly and daily objectives/learning targets should be included in your plans. These can be found under the column titled content. The enduring understandings will help clarify the “big picture” of the standard. The essential questions break that picture down into smaller questions and the learning targets/objectives provide specific outcomes for that standard(s). Best practices tell us that making objectives measureable increases student mastery.Instructional Support and ResourcesDistrict and web-based resources have been provided in the Instructional Support and Resources column. The additional resources provided are supplementary and should be used as needed for content support and ics Addressed in QuarterDecimal Expansions & Irrational NumbersCompare Irrational NumbersInteger ExponentsSquare Roots and Cube RootsVery Small & Very Large QuantitiesScientific NotationSolve Linear Equations in One VariableOverview 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)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 StandardType of RigorFoundational StandardsSample Assessment Items8.NS.1 Conceptual Understanding Learnzillion Assessment: 8.NS.1-28.NS.2 Conceptual Understanding8.EE.1Conceptual Understanding6.EE.1Learnzillion Assessment: 8.EE.1-38.EE.2Procedural Skill & Fluency6.EE.5, 7.NS.38.EE.3Procedural Skill & Fluency4.OA.2, 5.NBT.2, 8.EE.18.EE.4Procedural Skill & Fluency7.EE.3, 8.EE.1Math Shell Assessment Task: 100 People8.EE.7Procedural Skill & Fluency7.EE.1TNCore Assessment Task: School FairFluency NCTM PositionProcedural 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. 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 7References: STATE STANDARDSCONTENTINSTRUCTIONAL SUPPORT & RESOURCESRational and Irrational Numbers(Allow 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 rational 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 irrational 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). 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 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: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 distinguish between rational and irrational numbers.Students will convert a decimal expansion which repeats eventually into a rational number.Students will convert a fraction into a repeating decimal. Students will find rational approximations of irrational numbers.Students will use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions.Additional Information: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. Example(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 will be in front of the decimal. In this example, one digit repeats so both sides are multiplied by 10, giving 10x = 4.4444444….Additionally, students can investigate repeating patterns that occur when fractions have denominators of 9, 99, or 11.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 the 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 values, plotting them on a number line, and making comparative statements. Solution: Statements for the comparison could include: √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.Glencoe1-1A Rational Numbers p. 282-3D Compare Real Numbers p. 135Holt2-1 Rational Numbers p. 682-2 Comparing and Ordering Rational Numbers (This lesson only references comparing rational numbers to other rational numbers) p. 724-7 The Real Numbers p.195Choose from the following resources and use them to ensure that the intended outcome and level of rigor of the standards are met.Additional Lessons:Engage NY: Lesson 8 The Long Division AlgorithmEngage NY: Lesson 9 Decimal Expansions of FractionsEngage NY: Lesson 10 Converting Repeating Decimals to Engage NY: Lesson 11 Decimal Expansion of Some Irrational NumbersEngage NY: Lesson 13 Comparing Irrational NumbersTasks:Illustrative Math: Identifying Rational 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 Numbers 8.NS.A.1Illustrative Math: Approximating PiAdditional Resources:Station Activities for 8.NS.1 & 2 Refer to p. 1TNCORE Non-Summative Assessment Itemsp. 35 #3-5; p. 46 #6-7Correlated iReady Lesson(s)Rational and Irrational NumbersApproximating Rational NumbersVocabulary: rational number, irrational number, truncated decimal.Writing in Math:Your best friend was absent today. Write a letter to him or her to summarize what you learned in mathematics class. Have students explain the process of writing a fraction as a repeated decimal and vice versa.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. 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.Have students create a foldable for vocabulary terms and give examples of each. Rational/Irrational Number Foldables p. 49Additional Foldable IdeasPowers, Exponents and Roots( Allow 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 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 perfect cubes. Know that √2 is irrational.Enduring Understandings:Algebraic expressions and equations are used to model real-life problems and represent quantitative relationships.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:Students will evaluate square roots of small perfect squares and cube roots of small perfect cubes.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:Integer (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.Example(s):(23)/(52) = 8/25(22)/(26) = 22-6 = 2-4 = 1/1670 = 1Students understand this relationship from examples such as 62/62. This 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 = 46Students recognize perfect squares and cubes, understanding that non-perfect squares and cubes are irrational. 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. Glencoe2-1A Powers and Exponents p. 912-1B Multiply and Divide Monomials p.972-1C Powers of Monomials p. 1022-2A Negative Exponents 9.1082-3A Roots p. 124Holt4-1 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. 192Additional Topic: Square Roots and Cube Roots p. AT5Choose from the following resources and use them to ensure that the intended outcome and level of rigor of the standards are met.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 RootsEngage NY: Lesson Use Factors to Simplify Square RootsLearnzillion Lesson: 8.EE.2CMP CCSS Investigations: Investigation 1 ExponentsMath Shell Lesson: Applying Properties of ExponentsCMP Lesson: Investigation 5- Patterns with Exponents SummaryThe following links support CMP Investigation 5 CMP: Inv 5 Lesson PlanCMP: Inv 5 Problem 1 Lab SheetCMP: Inv 5 Problem 1 Student PagesCMP: Problem 5.2 Operating with 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 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 HotelAdditional Resources:Station Activities Refer to p.9 & 24Correlated iReady LessonsProperties of Integer ExponentsSquare Roots and Cube RootsVocabulary: power, base, exponent, monomial, laws of exponents, root, square root, cube root, perfect square, perfect cube, radical sign 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 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 FoldableAdditional Graphic Organizer IdeasScientific Notation( Allow 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 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 quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.Enduring Understandings:Real world situations involving exponential relationships can be solved using multiple representations. Essential Questions:Why would you want to use scientific notation to compare very large or very small numbers?Objectives:Students will estimate very large or very small quantities using a single digit times a power of ten.Students will express how much larger one number expressed as a single digit times a power of ten is than another in the context of the situation.Students will express numbers in scientific notation.Students will perform operations with numbers expressed in scientific notation and a mix of scientific notation and decimal notation.Students will choose appropriate units of measurements for a given number in scientific notation.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, recognizing 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.Example(s):Write 75,000,000,000 in scientific notation7.5 x 1010Write 0.000592 in scientific notation5.92 x 10-4Express 4.76 x 102 in standard form476Compare 7.5 x 1010 and 5.92 x 10-47.5x1010 is larger because it has the larger value exponentStudents will begin to see scientific expressed 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. 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. (6.45x1011)(3.2x104) = (6.45x3.2)(1011 x 104) = 20.64 x 1015 = 2.064 x 1016The 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.Glencoe2-2B Scientific Notation p. 1132-2C Compute with Scientific Notation p.118Holt4-4 Scientific Notation p. 174Additional Topic: Scientific Notation Operations p. AT2Scientific Notation Lab p. 179Choose from the following resources and use them to ensure that the intended outcome and level of rigor of the standards are met.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 notationMath Shell Lesson: Scientific NotationMath Shell: Generalizing Patterns 8.EE.3Tasks:Illustrative Math Tasks: 8.EE1- 4 Illustrative Math: Ants vs Humans 8.EE.4 & 8.EE.1Additional Resource(s):Station Activities Refer to p.24Correlated iReady Lessons:Scientific NotationOperations with Numbers Expressed in Scientific NotationVocabulary: scientific notation Writing in Math:Why are numbers expressed in scientific notation more efficient? Linear Equations( Allow 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.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.Enduring Understanding(s):Algebraic equations are used to model real-life problems and represent quantitative relationships.Essential Question(s):Why is it important to know whether a linear equation has one solution, infinitely many solutions, or no solution?Objectives:Students will simplify a linear equation by using properties and combining like terms.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 numbers 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. When 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, the equation is not true and therefore has no solution.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 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 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. 2414-2C Solve Multi-step Equations p. 246Holt1-8: Solving Equations by Adding or Subtracting p. 381-9: Solving Equations by Multiplying or Dividing2-7: Solving Equations with Rational Numbers2-8: 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: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(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 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 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 EquationsIllustrative Math: The Sign of SolutionsAdditional Resources:Correlated iReady Lessons:Solving Linear EquationsSolving Linear Equations with Rational CoefficientsVocabulary: linear equation, one solution, infinite solutions, no solution, coefficient, like terms, (inconsistent ), one –step and two –step equationWriting in Math:Explain why showing the steps used 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 work. Multi-step Equations Graphic OrganizerHave students create a flow chart, similar to the one below, for solving linear equations.RESOURCE TOOLBOXNWEA MAP Resources: - 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) - These Khan Academy lessons are aligned to RIT scores.Textbook Resourcesmy.connected.mcgraw-Holt, Course 3 Text ResourcesTN Core/CCSSTNReady Math StandardsTNCoreAchieve the CoreVideosKhan AcademyWatch Know LearnLearnZillionVirtual NerdMath PlaygroundStudyJamsCalculator ActivitiesGreatest Common Factor CalculatorTI-73 ActivitiesCASIO ActivitiesTI-Inspire for Middle GradesTI-Inspire Activity ExchangeInteractive ManipulativesNational Library of Interactive ManipulativesGlencoe Virtual ManipulativesRational vs Irrational ActivityRational vs Irrational GameIrrational Numbers on the Number LineAdditional SitesTeacher TubeThe Futures ChannelSTEM Resources HYPERLINK "" ................
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