Math Grade 5 - Burlington-nj

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CITY OF BURLINGTON PUBLIC SCHOOL DISTRICT CURRICULUMMath – Grade 5Revision Date: July 2017Submitted by: Antoinette Margaretta1

Table of Contents:Page #Course OverviewPacing ChartUnit #1 Understanding the Place Value System - Overview At-a-Glance34Unit #1 Understanding the Place Value System Targeted Instructional Planning to Address Central Unit Standards10Unit #2 Understanding Volume and Operations on Fractions - Overview At-a-Glance13Unit #2 Understanding Volume and Operation on Fractions Targeted Instructional Planning to Address Central Unit StandardsUnit #3 More Operations and Fractions - Overview At-a-Glance1823Unit #3 More Operations and Fractions - Targeted Instructional Planning to Address Central Unit Standards27Unit #4 Coordinate Geometry and Classifying Figures - Overview At-a-Glance31Unit #4 Coordinate Geometry and Classifying Figures - Targeted Instructional Planning to Address Central Unit Standards3625

Course OverviewIn this course, students will focus on four units that that develop skills involving place value, fractions, mixed numbers, volume, andcoordinate geometry. These units are based on the NJ Student Learning Standards (NJSLS) and the Curricular Framework for fifthgrade mathematics. The course will incorporate many activities that promote critical thinking, problem solving, and math practicesendorsed by the NJSLS. PARCC preparation is an essential component of the activities and students will utilize the many resourcesprovided by the NJ Department of Education, PARCC practice assessments and released items, and the performance tasks provided bythe curricular framework.Primary Resource(s)TextbooksTitle: Envision Math 2.0Publisher: Pearson Education, Inc.Copyright: 2016Supplemental Materials and ResourcesTitle: Mathematics Common Core Performance CoachPublisher: Triumph LearningCopyright: 2015Dept. of Education Curricular Frameworks: ath/NJ Center for Teaching and Learning: C Online: http://parcc-assessment.org/NJ Common Core Standards for Mathematics, 5th Grade: uction/Teacher Generated materials3

Pacing ChartUnit # & TitlePacing(must equal 165 days for full-year or83 days forhalf-year course)Unit 1: Understanding the Place Value System40 daysUnit 2: Understanding Volume and Operations on Fractions60 daysUnit 3: More Operations on Fractions30 daysUnit 4: Coordinate Geometry and Classifying Figures35 days4

Unit 1 Overview At-a-GlanceUnit #1 – Understanding the Place Value SystemUnit Description:In this unit, students will write and interpret numerical expressions; understand the place value system; and perform operations withmulti-digit whole numbers and with decimals to hundredths. This unit will cover topics 1 through 6 from Envision Math 2.0, whichinclude:Topic 1: Understand Place ValueTopic 2: Add and Subtract Decimals to HundredthsTopic 3: Fluently Multiply Multi-Digit Whole NumbersTopic 4: Use Models and Strategies to Multiply DecimalsTopic 5: Use Models and Strategies to Divide Whole NumbersTopic 6: Use Models and Strategies to Divide Decimals.Essential Skills: Explain that a digit in one place represents 1/10 of what I would represent in the place to its left and ten times what it wouldrepresent in the place to its right Explain patterns in the number of zeros in the product when a whole number is multiplied by a power of 10; represent powers of10 using whole-number exponents Use the standard algorithm to multiply a whole number of up to four digits by a whole number of up to two digits Calculate whole number quotients of whole numbers with 4-digit dividends and 2-digit divisors; explain and representcalculations with equations, rectangular arrays, and area modules Compare two decimals to thousandths using , , and for numbers presented as base ten numerals, number names, and/ or inexpanded form Round decimals to any place valueStandards Addressed within Unit 1 – Understanding the Place Value SystemCentral Unit Standards- This unit will focus primarily onSupporting Unit Standards- This unit will also include activitieslearning goals aligned with the following standards:aligned with the following standards:NJSLS 5.NBT.A.1NJSLS 5.OA.A.1NJSLS 5.NBT.A.2NJSLS 5.OA.A.2NJSLS 5.NBT.A.3NJSLS SA.R1NJSLS 5.NBT.A.4NJSLS RI.5.15

NJSLS 5.NBT.B.5NJSLS 5.NBT.B.6NJSLS 5.NBT.B.7NJSLS A.SL4Unit 1 Details - Understanding the Place Value SystemModifications for Special Education Students, Integration of 21st century skills through NJSLS 9 and Career Education:English Language Learners, Students at Risk The 5th grade math curriculum emphasizes collaboration, communication,of Failure, and Gifted Students- Modifyproblem solving, and critical thinking. We have supported and stressed theinstructional approach and/or assignments and21st century skills by incorporating the following activities into our lessons:evaluations as needed based for students witho Group Relay RacesIEPs, 504s, ELLs and gifted and talentedo Scavenger Huntsstudents including but not limited to:o Menu Matho GRAPHiti Envision 2.0 online personalized practiceo Study Island PARCC like questions Envision 2.0 Visual Learning Bridge Lessons, where appropriate, incorporate multiple perspectives to infuseactivitiescultural and global awareness. Envision ELL Toolkit Supporting Learning incorporates skills focusing on financial, economic, business, andEnglish Language Learnersentrepreneurial literacy. Alternate responses (drawings with Lessons integrate a focus on civic literacy so that students can bettercaptions, spoken responses, etc.)understand the rights and obligations of citizenship. Advance/guided notes Learning advocates for health literacy as a critical component of a healthy Extended timelifestyle and the ability to make good health-related decisions. Teacher modeling (non-verbal teacher Students explore areas that support environmental literacy, includingcommunication in addition to spokensociety’s impact on the environment and what can be done to supportinstructions)environmental solutions. Simplified written and verbal instructions Lessons, activities, and assessments require creativity and innovation on the ELL support materials (eDictionaries,part of the students. They are required to create projects and products asnative language prompts, etc.)examples of mastery in each unit.6

Differentiated instruction to meet variedneeds and levels of all students (taskcards, centers, labs)Multi-sensory instructionHeterogeneous and homogeneousgroupingOne-on-one instruction in small groupsfor remediationIncreased integration of higher orderthinking processes, creative and criticalthinking activities, problem-solving, andopen-ended tasksSelf-regulated group interactionAdvanced pacing levelsGreater opportunities for freedom ofchoice and independent study thatencourage independent and intrinsiclearningInquiry-based projects and assignmentsAssessments- including benchmarks,formative, summative, and alternativeassessments Fall NWEA Curricular Framework Illustrated Mathresources Mid-topic assessments Topic performance tasks Critical thinking and problem solving skills are a core component of learningand assessment throughout this curriculum. Students are required, in eachunit, to advance their learning through all levels of Bloom’s Taxonomy toaddress the evaluation, synthesis, and creation of products using learning atthe highest levels. Problem-solving is a recurring theme in the curriculum asstudents must seek ways to creatively apply the concepts to solve problemsrather than simply remember the material.Communication and collaboration is crucial for student success as learners.Throughout this curriculum, students must be able to communicate deepunderstanding through open ended responses (both orally and in writing). Inaddition, students are often required to work collaboratively with their peerswhich promotes the ability to succeed in the area of social cooperative work,increases communication skills, and promotes leadership and responsibility.Students must be information literate, i.e. they must be able to find and useinformation effectively, in order to succeed in class as learning activitiesrequire independent research of relevant information outside of the providedtextbook and/or resources.In order to succeed in this course, students must be able to use technology asa tool in order to research, organize, evaluate, and communicate information.Activities in the curriculum help develop life and career skills in all studentsby promoting flexibility and adaptability, requiring initiative and selfdirection in the learning process, supporting social and cross-cultural skills inboth content and teamwork efforts, and measuring productivity andaccountability through independent and group assignment completion.Suggested Interdisciplinary Activities for this UnitCareer Education: Research a math career and make a poster that illustrates thecareer responsibilities and skills.Health/PE: Have students calculate the cost of materials used to engage in variousPE activities. Have students estimate the cost of materials, and eventually have themcalculate to find an exact answer.7

Exit ticketsLesson quizzesWeekly math journalPARCC released questionsPearson cumulative topic assessmentsUnit 1 testUnit 1 performance tasksEnglish Language Arts/Literacy: Using “Problem Solving Reading Mat” beforeeach new topic, read about: Oceans of the Past; Nature’s Survivors; Company ofWolves; Bats; Migrants and Residents; and Clouds of All Kinds. In math journal, listany terms that are unfamiliar; write a questions you may have about the real-worldmath topic; write a word problem based on the information provided in the “ProblemSolving Reading Mat”; or work with a partner to add an additional fact about thetopic as it relates to your community.Science: Research Envision topics in the math and science projects pages regardingproducers and consumers. Write and solve decimal addition and subtraction problemsfor the amounts of food the consumers need; estimate weekly water usage for varioushousehold activities and organize data in a table.Social Studies: Research populations in various towns in NJ or in different states.Write these population numbers in expanded form.Technical Subjects: Use a “Data Grapher” to illustrate data gather in the classroomor school – number of students who buy lunch over a period of a week; number ofstudents who 1, 2, 3, etc. siblings; populations in different states. Make a visualdisplay for the aspx?id 4098World Languages: Count to 10 (or more) in a different language (Spanish). Makevisual vocabulary cards to illustrate the word and its meaning.Arts: Have students work in teams to put on short skits. Student will be digits, androles will be based on their place value. The higher their place values, the “older”their character should act. The smallest place value should be the baby of the numberfamily. (Assign the “older” place values small digits, and the “younger” place values,larger digits. This could spark the conversation that says a digit is only as valuable asthe place he resides!)8

Unit ResourcesTeachers should utilize school resources available in our Media Center to infuse alternate sources, perspectives, and approaches.Resources should include textual support but also span multimedia options to engage multiple modalities. In addition, to supportstruggling readers and increase rigor for advanced readers, the coursework may also draw on additional developmentally appropriateresources to facilitate challenging levels of work for all students.Leveled Supplemental Materials andIntegration of the Technology StandardMedia/School Library ResourcesNJSLS 8.1.8.A.4, NJSLS 8.1.8.A.5Including but not limited to:Presentations, posters, and visual vocabulary definitions generated on Microsoft softwareprograms, such as Word and Publisher.Scholastic Math magazinePics for Learning for a free gallery of photos and clipart for visual vocabularyDan Meyer’s 3-Act problems(http://www.pics4learning.com/)Online Resources:Books created on the Cloud on various topics to publish and share using ttp://www.ixl.comUtilize various websites, including but not limited to:http://www.brainpop.com Pearson Realize: m Front Row Edhttp://www.studyisland.com Pearson Realize Math Gameshttp://www.kahnacademy.com PBS Math Clubhttp://thinkmath.edc.org/resources-5th Illustrative Mathematicsgrade Math Anticshttps://whenmathhappens.com/3-act-math/ National Library of Virtual Manipulatives Study Island Khan Academy Brain Pop AAA Study Mathisfun.com https://whenmathhappens.com/3-act-math/ Coolmath.com www.nctm.org Smartech.com9

Unit #1 Targeted Instructional Planning to Address Central Unit Standards:Central Unit Standardand Student LearningObjectiveNJSLS 5.NBT.A.1NJSLS 5.NBT.A.2NJSLS 5.NBT.A.3NJSLS 5.NBT.A.4Number and Operation inBase Ten – Understandthe place value systemNJSLS 5.NBT.B.5NJSLS 5.NBT.B.6NJSLS 5.NBT.B.7Number and Operationsin Base Ten – Performoperations with multidigit whole numbers andwith decimals tohundredths.Suggested Instructional ActivitiesFacilitate guided, group, and independentpractice using tasks from the NJ DOECurricular Framework for Mathematics:5.NBT.A.1 Which number is it?The purpose of this task is to help studentsunderstand the fact that the value of a digitin one place is ten times the value of thesame digit in the place to the right.5.NBT.A.1 Millions and Billions of PeopleThe purpose of this task is to help studentsunderstand the multiplicative relationshipbetween commonly used large numbers(millions and billions) by using theirunderstanding of place value.5.NBT.A.3 Placing Thousandths on theNumber LineThough this task primarily deals withcomparing decimal numbers on a numberline, it also requires students to draw uponwhat they know about the base ten system.They must recognize that the distance from0 to 0.1 is partitioned into ten equal piecesand that one tenth of one tenth is 0.01.5.NBT.A.4 Rounding to Tenths andHundredths10Suggested StudentOutputJournals using pertinentmath vocabulary such astenths, hundredths, tens,hundreds, base ten, andplace valueConstructed arguments oftopics to explain correctreasoning in performingmulti-digit operationsModeling of place valueand multi-digit operationsusing pictures, equations,or manipulativesFormative Assessments(Portfolios, Projects, Tasks,Evaluations, & Rubrics)Performance Assessment Fall NWEA Curricular FrameworkIllustrated Mathresources performancetasks Mid Topic AssessmentsTopic Performance Tasks Topic Tests Exit Tickets Lesson Quizzes Weekly Math Journalbased on mathvocabulary; erroranalysis; real-worldconnection; lessonreflections PARCC ReleasedQuestions Pearson CumulativeTopic Assessments Unit 1TestSolutions to variouspractice problemsExplain that a digit’svalue based on its place ina numberExplain patterns in thenumber of zeros whenmultiplied by powers often

The purpose of this task is for students touse the position of a number on the numberline to round the number without knowingits exact value.Multiply a whole numberof up to four digits by awhole number of up totwo digits 5.NBT.B.5 Elmer's Multiplication ErrorThis task has students explore a verycommon multiplication error that occurswhen using the standard algorithm.Pose the Solve-and- Share Problem fortopicsAsk guiding questions as neededCalculate whole numberquotients of wholenumbers with 4-digitdividends and 2-digitdivisorsUnit Journal Prompt:A centurion was an officer inthe Roman army. Eachcenturion led a unit of 100men. At the height of theRoman Empire, the armyconsisted of 175 legions. Thenumber of men in a legioncould vary from 4,000 to6,000 men. What is thehighest number of men in the175 legions? Research howthe U.S. governmentdetermines how many troopsare needed to build a military.5.OA.A.1 Using Operations andParentheses (supporting)The purpose of this task is to give students achance to work creatively with three of thefour fundamental arithmetic operations(addition, subtraction, and multiplication).5.OA.A.1 Watch out for Parentheses 1(supporting)This problem asks the student to evaluatesix numerical expressions that contain thesame integers and operations yet havediffering results due to placement ofparentheses.Share and discuss solutions of exampleproblemsProvide guided practice of concepts andskills using Envision 2.0 presentation tools11Explain and representcalculations withequations, rectangulararrays, and area modules.Compare two decimals tothousandths using , ,and for numberspresented as base tennumerals, number names,and/ or in expanded form.Round decimals to anyplace value.Use of Envision rubrics –Listen and Look forLesson Videos (teacherobservations)

Practice the use of math vocabulary intopics (My Word Cards) by completingdefinitions and recreating visualrepresentations for notes and classroomword wall.Write explanations for understandingconcepts and procedural execution of mathtopics using unit Envision 2.0 features, suchas Solve and Share, Convince Me!, andMath Practice and Problem SolvingUtilize online tools for instruction, practice,and remediation Content videos Practice Buddy for skills Gaming for reinforcing lesson content Thinking games and Fluency games toreinforce concepts, procedural skills,and fluency Adapted Assignments for differentiatedinstruction Envision Centers kit for independentlearning Another Look Homework Videos),Envision 2.0 Problem-Solving ReadingMats (real-world literacy activities)Discuss skills in Math Practice posters toexplain strategies in problem solving12

Unit 2 Overview At-a-GlanceUnit #2 – Understanding Volume and Operations on FractionsUnit Description:In this unit, students will use equivalent fractions as a strategy to add and subtract fractions, and apply and extend previousunderstandings of multiplication and division to multiply and divide fractions. They will use geometric measurement by understandingconcepts of volume and relate volume to multiplication and to addition. This unit will cover Envision topics 7, 8, and 10 which include:Topic 7: Equivalent fractions to add and subtract fractionsTopic 8: Apply understanding of multiplication and divisions to multiply and divide fractionsTopic 10: Understand volume conceptsEssential Skills: Add and subtract fractions (including mixed numbers) with unlike denominators by replacing the given fractions with equivalentfractions having like denominators Fluently multiply multi-digit whole numbers with accuracy and efficiency Solve word problems involving adding or subtracting fractions with unlike denominators, and determine if the answer to theword problem is reasonable, using estimations with benchmark fractions Interpret a fraction as a division of the numerator by the denominator; solve word problems in which division of whole numbersleads to fractions or mixed numbers as solutions For whole number or fraction q, interpret the product (a/b) x q as a parts of a whole partitioned into b equal parts added q times(e.g. using a visual fraction model) Tile a rectangle with unit fraction squares to find the area and multiply side lengths to find the area of the rectangle, showing thatthe areas are the same Measure volume by counting the total number cubic units required to fill a figure without gaps or overlaps Show that the volume of a right rectangular prism found by counting all the unit cubes is the same as the formulas V l w hor V B h Apply formulas to solve real world and mathematical problems involving volum

2 Table of Contents: Page # Course Overview 3 Pacing Chart 4 Unit #1 Understanding the Place Value System - Overview At-a-Glance 5 Unit #1 Understanding the Place Value System Targeted Instructional Planning to Address Central Unit Standards 10 Unit #2 Understanding Volume and Operations on Fractions - Overview At-a-Glance 13 Unit #2 Understanding Volume and Operation on Fractions Targeted .

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