Utah Core State Standards Mathematics Curriculum Map .

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6th GradeUtah Core State StandardsMathematics Curriculum MapGranite School DistrictStriving toward greater focus and coherence throughContent Standards and Practice StandardsDee RigdonK-6 Mathematics Specialistdprigdon@graniteschools.org

How to Read the Grade Level Content StandardsStandards define what students should understand and be able to do.StrandStrands are larger groups of related standards. Standards from different strands may sometimes be closely related.Standard1

Standards for Mathematical PracticeThe Standards for Mathematical Practice in Sixth Grade describe mathematical habits of mind that teachers should seek to developin their students. Students become mathematically proficient in engaging with mathematical content and concepts as they learn,experience, and apply these skills and attitudes (Standards 6.MP.1–8).Standard 6.MP.1 Make sense of problems and persevere in solving them.Explain the meaning of a problem and look for entry points to its solution. Analyze givens, constraints, relationships, and goals. Makeconjectures about the form and meaning of the solution, plan a solution pathway, and continually monitor progress asking, “Does thismake sense?” Consider analogous problems, make connections between multiple representations, identify the correspondencebetween different approaches, look for trends, and transform algebraic expressions to highlight meaningful mathematics. Checkanswers to problems using a different method.Standard 6.MP.2 Reason abstractly and quantitatively.Make sense of the quantities and their relationships in problem situations. Translate between context and algebraic representationsby contextualizing and decontextualizing quantitative relationships. This includes the ability to decontextualize a given situation,representing it algebraically and manipulating symbols fluently as well as the ability to contextualize algebraic representations tomake sense of the problem.Standard 6.MP.3 Construct viable arguments and critique the reasoning of others.Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Make conjecturesand build a logical progression of statements to explore the truth of their conjectures. Justify conclusions and communicate them toothers. Respond to the arguments of others by listening, asking clarifying questions,and critiquing the reasoning of others.Standard 6.MP.4 Model with mathematics.Apply mathematics to solve problems arising in everyday life, society, and the workplace. Make assumptions and approximations,identifying important quantities to construct a mathematical model. Routinely interpret mathematical results in the context of thesituation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.Standard 6.MP.5 Use appropriate tools strategically.Consider the available tools and be sufficiently familiar with them to make sound decisions about when each tool might be helpful,recognizing both the insight to be gained as well as the limitations. Identify relevant external mathematical resources and use themto pose or solve problems. Use tools to explore and deepen their understanding of concepts.2

Standard 6.MP.6 Attend to precision.Communicate precisely to others. Use explicit definitions in discussion with others and in their own reasoning. They state themeaning of the symbols they choose. Specify units of measure and label axes to clarify the correspondence with quantities ina problem. Calculate accurately and efficiently, and express numerical answers with a degree of precision appropriate for theproblem context.AH CORE STATE STANDARDS for MATHEMATICSStandard 6.MP.7 Look for and make use of structure.Look closely at mathematical relationships to identify the underlying structure by recognizing a simple structure within a morecomplicated structure. See complicated things, such as some algebraic expressions, as single objects or as being composedof several objects. For example, see 5 – 3(x – y)2 as 5 minus a positive number times a square and use that to realize that itsvalue cannot be more than 5 for any real numbers x and y.Standard 6.MP.8 Look for and express regularity in repeated reasoning.Notice if reasoning is repeated, and look for both generalizations and shortcuts. Evaluate the reasonableness of intermediateresults by maintaining oversight of the process while attending to the details.GSD Instructional Resources Helping Students Master the Basic FactsHow Can I Use the Problem of the Day as a Self-Start?How Can I Build Ongoing Math Review and Practice?How Can I Implement Tasks Using a Go Math Lesson?Mathematical Practice Standards 1-8Math RoutinesProblem TypesBar Model DrawingWriting in MathDepth of Knowledge (DOK)Math HomeworkLevels of Geometric ThinkingRubricsAdditional ResourcesUtah Core State Standards for Mathematics K-5Learning Progressions for CCSSMSecondary Mathematics Core GuidesMath Vocabulary CardsGeneral Website ResourcesCurriculum Maps AppendixGSD Additional Instructional Resources Website Navigating Go Math User Guide Proficiency Scales Math Investigation Centers Newsletters3

6th Grade Mathematics Curriculum MapGranite School District Scope and Sequence OverviewUnit of Go Math!Study AlignmentGo Math! Chapter Title1Chapter 1Whole Numbers and Decimals2Chapter 2Fractions3Chapter 3Rational Numbers4Chapter 4Ratios and Rates5Chapter 5Percents6Chapter 6Units of Measure7Chapter 7Algebra: Expressions8Chapter 8Algebra: Equations and Inequalities9Chapter 9Algebra: Relationships Between Variables10Chapter 10Area11Chapter 11Surface Area and Volume12Chapter 12Data Displays and Measures of Center13Chapter 13Variability and Data DistributionsStrand and StandardsStrand: The Number SystemStandards: 2, 3, 4Strand: The Number SystemStandards: 1, 4, 6cStrand: The Number SystemStandards: 5, 6a, 6b, 6c, 7a, 7b, 7c, 7d, 8Strand: Ratios and Proportional RelationshipsStandards: 1, 2, 3a, 3bStrand: Ratios and Proportional RelationshipsStandard: 3cStrand: Ratios and Proportional RelationshipsStandard: 3dStrand: Expressions and EquationsStandards: 1, 2a, 2b, 2c, 3, 4, 6Strand: Expressions and EquationsStandards: 5, 7, 8Strand: Expressions and EquationsStandard: 9Strand: GeometryStandards: 1, 3Strand: GeometryStandards: 2, 4Strand: Statistics and ProbabilityStandards: 1, 4, 5a, 5b, 5c, 5dStrand: Statistics and ProbabilityStandards: 2, 3, 4, 5c, 5d4

6th GradeInstruction and Assessment Semester Schedule2019-2020Math Standards1818151191010865Unit ofStudy1Unit ofStudy2Unit ofStudy3Unit ofStudy4Unit ofStudy5Unit S.7*6.NS.8*6.RP.1*6.RP.2*6.RP.3*Indicates emphasized standards.1719101078891059788Unit ofStudy7Unit ofStudy8Unit ofStudy9Unit ofStudy10Unit ofStudy11Unit ofStudy12Unit 26.SP.3*6.SP.4*6.SP.5End ofYearRISE (Summative) 3/24 – 5/1516Semester 2 Posttest 3/2 – 5/22 (supplemental)InstructionalContent11Semester 2 Pretest 12/2 – 3/2 (required)Number ofLessonsSemester 1 Pretest 8/19 – 1/30 (required)Approx. Number ofDays of InstructionSemester 1Posttest 12/2 – 1/30 (required)It is expected that the units will be taught consecutively. The table below reflects which units and standards are assessedon each semester test. Semester Benchmark Tests are required by GSD except for the Semester 2 Posttest which issupplemental. Additional assessment options are on each Unit of Study in the GSD maps.GettingReady forGr. 7 UnitBeginning and Ending of Semesters1st Semester Aug 19, 2019 – Jan 9, 20202nd Semester Jan 13, 2020 – May 22, 20205

6th GradeInstruction and Assessment Quarterly Schedule2018-2019It is expected that the units will be taught consecutively. The table below reflects which units and standards are taught andassessed each quarter. Assessment options are on each Unit of Study in the GSD maps.151117191010788Number of Lesson9101086591059788InstructionalContentMath StandardsUnit ofStudy1Unit ofStudy2Unit S.7*6.NS.8*Indicates emphasized standards.Unit ofStudy4Unit ofStudy5*6.RP.1*6.RP.2*6.RP.3Unit ofStudy6Unit ofStudy7Unit ofStudy8Unit ofStudy9Unit EE.76.EE.8*6.EE.9Unit ofStudy11Unit 6.SP.4*6.SP.5Unit ofStudy13End ofYearRISE (Summative) 3/24 – 5/15 (required)18Quarter 418Quarter 316Quarter 211Quarter 1Approx. Number ofDays of InstructionGettingReadyfor Gr. 7UnitBeginning and Ending of Quarters1st2nd3rd4thQuarter Aug 19, 2019 – Oct 24, 2019Quarter Oct 28, 2019 – Jan 9, 2020Quarter Jan 13, 2020 – Mar 18, 2020Quarter Mar 24, 2020 – May 22, 20206

6th Grade Mathematics Curriculum Map - OverviewLesson Plan Format:Lesson Plan Format with Go Math! References:Lesson Plan Format for TasksUnit of StudyGo Math! AlignmentMath Content andLanguageObjectivesKey Concepts AdditionalResourcesAssessmentThe mathematical content is sequenced in Units of Study that will take approximately 2-3 weeks each to teach. The sequenceof Units of Study provides a coherent flow to mathematics instruction throughout the year. It is expected that the units will betaught consecutively.The primary textbook adopted in Granite School District for Grades K-6 is Houghton Mifflin Harcourt’s Go Math!, 2015 Edition.The Math Content Objectives and Language Objectives are to be posted for each lesson, restated to students during the lesson,and revisited at the end of each lesson. These are written as “I Can” statements. Suggested Math Language Objectives can belocated on the next page.In an effort to assist teachers in the process of differentiation in Tier I teaching, key concepts have been identified in thecurriculum maps as those specific objectives a teacher would focus on during small group instruction with struggling students.Key concepts cover minimum, basic skills and knowledge every student must master. Key concepts are NOT an alternative toteaching the entire Utah State Core Standards, rather they emphasize which concepts to prioritize for differentiation.Vocabulary cards for instruction and word walls can be found e Learning Progressions Documents are anchor documents to the Math Core Standards. These research-based documentsdescribe the progression of each math core strand across various grade levels. They were written by the authors of the CCSSMto offer more in-depth explanation and details regarding the Math Core Standards. Click here to access these documents.The websites are a resource for lesson plans, teacher tutorials, content videos, student applets, and games. GSD AdditionalTeacher Resources are available to Granite School District teachers only. These resources are NOT intended to be all-inclusive.It is the teacher’s responsibility to teach the Utah Core State Standards for Mathematics content, not the resources.There are many formative and summative assessment options: Go Math! Options: Prerequisite Skills Inventory; Beginning-of-Year, Middle-of-Year, and End-of-Year Benchmark Tests;Show What You Know Diagnostic Assessments; Diagnostic Interview Assessments; Portfolio Assessment; Mid-ChapterCheckpoints; Chapter Review/Tests; Chapter Tests; Performance Assessments; Quick Checks; and, Personal MathTrainer. The assessments provide immediate feedback that can be used for Tier 2 and/or Tier 3 interventions forindividual students. The results may also be used to identify concepts for reteaching the whole class if needed. Semester Benchmark Assessments – These are cumulative tests for multiple Units of Study. These are to be given as apretest and a posttest. Students not mastering content will need Tier 2 and/or Tier 3 interventions. Exit slips, teacher observations, daily class work, homework, and basal assessments are to be used at the teacher’sdiscretion to help guide and direct instruction.7

Math Language Objectives[Note: The following language objectives must be written in student-friendly terms, adapted to specific lessons, and aligned with the language needs of students.]Reading Standards for Informational Text Cite textual evidence to support analysis of a math text. Determine the meaning of specific math words or phrases in a text. Integrate information presented in visual, quantitative, and text formats to understand a math topic. Read and comprehend math texts.Writing Standards Write arguments to support math claims with clear reasons and evidence. Write explanatory math text to convey ideas, concepts, and information, including graphics and multimedia when useful to aiding comprehension. Produce clear, coherent math writing appropriate to the task. Use technology to produce math writing and collaborate with others. Draw evidence from informational math texts to support analysis and reflection. Write routinely for a range of math tasks.Speaking and Listening Standards Engage in collaborative math discussions. Interpret math information presented in visual, quantitative, and oral formats. Delineate a speaker’s argument, distinguishing math claims that are supported by reasons and evidence from claims that are not. Present math claims and findings, sequencing ideas logically and using pertinent facts and details. Add visual displays in math presentations8

Unit of Study 16th GradeQuarter 1Approx. 11 daysGSD Revised 5/1/19Strand: The Number System6.NSCompute (add, subtract, multiply and divide) fluently with multi-digit numbers and decimals and find common factors andmultiples.2. Fluently divide multi-digit numbers using the standard algorithm.3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.a. Fluently divide multi-digit decimals using the standard algorithm, limited to a whole number dividend with a decimal divisor or a decimal dividend with a wholenumber divisor.b. Solve division problems in which both the dividend and the divisor are multi-digit decimals; develop the standard algorithm by using models, the meaning ofdivision, and place value understanding.4. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Usethe distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.For example, express 36 8 as 4 (9 2).Math Content ObjectivesI can:6.NS.2 Fluently divide multi-digit numbers using thestandard algorithm.6.NS.3G Fluently add multi-digit decimals using thestandard algorithm.G Fluently subtract multi-digit decimals using thestandard algorithm. Fluently multiply multi-digit decimals using thestandard algorithm. Fluently divide multi-digit decimals using thestandard algorithm.6.NS.4 Find the greatest common factor (GCF) of twowhole numbers less than or equal to 100. Find the least common multiple of two wholenumbers less than or equal to 12. Use the distributive property to express a sum oftwo numbers with a common factor as a multipleof a sum of two whole numbers with no commonfactor.GVocabulary addendalgorithmarraycommon factorcommon multiplecompatible numbersdecimaldifferenceDistributive factorgreatest common factor (GCF)least common multiple (LCM)minuendmultipleVocabulary (cont.) prime factorizationprime numberproductquotientsubtrahendsumwhole numbersKey Concepts for Differentiation - See p. 7.9

Go Math!Utah CoreAlignmentLesson 1.16.NS.2Lesson 1.26.NS.4Unit of Study 1 – Additional ResourcesDivision of Whole NumbersLearnAlberta - “Division of Whole Numbers” - Video TutorialDivision by a 2-Digit Number - Algorithm AppletLesson 1.46.NS.4Addition/Subtraction of DecimalsNLVM - Base Block Decimals - Interactive AppletNLVM - Circle 3 - Adding Decimals - Interactive AppletLearnAlberta - “Solving Problems with Decimals” Video LessonLearnAlberta - “Addition and Subtraction of Decimals” Video LessonMath Play - Jeopardy - Computation Gameeduplace – Decimal and Fraction Converter – Interactive AppletLesson 1.56.NS.4Multiplication/Division of DecimalsLearnAlberta - Multiplication and Division of Decimals - Video TutorialLesson 1.66.NS.3Greatest Common Factor and Least Common MultipleIlluminations - “The Venn Factor” LessonIlluminations - “Factor Findings” LessonIlluminations - “Factor Trail Game” LessonNLVM - Factor Tree - Interactive AppletLearnAlberta Spy Guys - “Factors, Multiples, and Prime Factorization” Video LessonAmby - Teacher TutorialIXL - GCF and LCM Word Problems - AssessmentFun 4 The Brain - Snowball Fight - GameUEN – Factor Capture - GameIlluminations – The Factor GameLesson 1.36.NS.4Lesson 1.76.NS.3Lesson 1.86.NS.3Lesson 1.96.NS.310

Unit of Study 1 - Additional Resources - ContinuedDistributive PropertyIlluminations - “Distributing and Factoring Using Area” LessonGSD Additional Teacher ResourcesMath Investigation Center – Unit 1Math Tasks – Unit 1GCF GameLiteratureThe Monster Who Did My Math by Danny SchnitzleinMultiplying Menace Divides by Pam CalvertThe Phantom Tollbooth by Norton JusterAssessmentOptions Go Math! Assessment Options: Show What You Know Diagnostic Assessment; Mid-ChapterCheckpoint; Quick Checks; Portfolio Assessment; Chapter 1 Review/Test; Chapter 1 Test; DiagnosticInterview Assessment; Personal Math Trainer.Daily/Weekly Formative Assessment Options: Exit Slips, Observation, Daily Work, Homework.11

Unit of Study 26th GradeQuarter 1Approx. 12 – 16 daysGSD Revised 5/1/19Strand: The Number System6.NSApply and extend previous understandings of multiplication and division of whole numbers to divide fractions by fractions.1. Interpret and compute quotients of fractions.a. Compute quotients of fractions by fractions, for example, by applying strategies such as visual fraction models, equations, and the relationship betweenmultiplication and division, to represent problems.b. Solve real-world problems involving division of fractions by fractions. For example, how much chocolate will each person get if three people share 1/2 pound ofchocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mile and area 1/2 square mile?c. Explain the meaning of quotients in fraction division problems. For example, create a story context for (2/3) (3/4) and use a visual fraction model to show the quotient.Use the relationship between multiplication and division to explain that (2/3) (3/4) 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) (c/d) ad/bc )Compute (add, subtract, multiply and divide) fluently with multi-digit numbers and decimals and find common factors andmultiples.4. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Usethe distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.For example, express 36 8 as 4 (9 2).Apply and extend previous understandings of numbers to the system of rational numbers.6. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points onthe line and in the plane with negative number coordinates.c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rationalnumbers on a coordinate plane.Math Content ObjectivesI can:6.NS.1 Use a model to show division of fractions. Use my understanding of multiplication offractions to explain division of f

6th Grade Mathematics Curriculum Map - Overview Lesson Plan Format: Lesson Plan Format with Go Math! References: Lesson Plan Format for Tasks Unit of Study The mathematical content is sequenced in Units of Study that will take approximately 2-3 weeks each to teach. The sequence

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