MATHEMATICS CURRICULUM Grade 4

MIDDLETOWN PUBLIC SCHOOLS MATHEMATICS CURRICULUM Grade 4 Middle Schl Curriculum Writers: Erica Bulk, Hlly Cusens, Meghan Frd, Jennifer Hlubesk, Deb O Bryan, and Deanne Reilly January 2012

2/20/2012 Middletwn Public Schls 1

T he Middletwn Public Schls Mathematics Curriculum fr grades K-12 was cmpleted in January 2012 by a K-12 team f teachers. The team, identified as the Mathematics Task Frce and Mathematics Curriculum Writers referenced extensive resurces t design the dcument that included: Cmmn Cre State Standards fr Mathematics Cmmn Cre State Standards fr Mathematics, Appendix A Understanding Cmmn Cre State Standards, Kendall PARCC Mdel Cntent Framewrks Numerus state curriculum Cmmn Cre framewrks, e.g. Ohi Department f Educatin High Schl Traditinal Plus Mdel Curse Sequence, Achieve, Inc. Grade Level and Grade Span Expectatins (GLEs/GSEs) fr Mathematics Third Internatinal Mathematics and Science Test (TIMSS) Best Practice, New Standards fr Teaching and Learning in America s Schls; Differentiated Instructinal Strategies Instructinal Strategies That Wrk, Marzan Gals fr the district Missin Statement Our missin is t prvide a sequential and cmprehensive K-12 mathematics curriculum in a cllabrative student centered learning envirnment that develps critical thinkers, skillful prblem slvers, and effective cmmunicatrs f mathematics. The Middletwn Public Schls Mathematics Curriculum identifies what students shuld knw and be able t d in mathematics. Each grade r curse includes Cmmn Cre State Standards (CCSS), Grade Level Expectatins (GLEs), Grade Span Expectatins (GSEs), grade level supprtive tasks, teacher ntes, best practice instructinal strategies, resurces, a map (r suggested timeline), rubrics, checklists, and cmmn frmative and summative assessments. COMMON CORE STATE STANDARDS The Cmmn Cre State Standards (CCSS): Are fewer, higher, deeper, and clearer. Are aligned with cllege and wrkfrce expectatins. Include rigrus cntent and applicatins f knwledge thrugh high-rder skills. Build upn strengths and lessns f current state standards (GLEs and GSEs). Are internatinally benchmarked, s that all students are prepared fr succeeding in ur glbal ecnmy and sciety. Are research and evidence-based. Cmmn Cre State Standards cmpnents include: Standards fr Mathematical Practice (K-12) Standards fr Mathematical Cntent: Categries (high schl nly): e.g. numbers, algebra, functins, data Dmains: larger grups f related standards Clusters: grups f related standards Standards: define what students shuld understand and are able t d The Middletwn Public Schls Cmmn Cre Mathematics Curriculum prvides all students with a sequential cmprehensive educatin in mathematics thrugh the study f: Standards fr Mathematical Practice (K-12) Make sense f prblems and persevere in slving them Reasn abstractly and Cnstruct viable arguments and critique the reasning f thers Mdel with mathematics* Use apprpriate tls Attend t precisin Lk fr and make use f Lk fr and express reasning 2/20/2012 Middletwn Public Schls 2

Standards fr Mathematical Cntent: K 5 Grade Level Dmains f Cunting and Cardinality Operatins and Algebraic Thinking Number and Operatins in Base Ten Number and Operatins Fractins Measurement and Data Gemetry 6-8 Grade Level Dmains f Ratis and Prprtinal Relatinships The Number System Expressins and Equatins Functins Gemetry 9-12 Grade Level Cnceptual Categries f Number and Quantity Algebra Functins Mdeling Gemetry Statistics and Prbability RESEARCH-BASED The Middletwn Public Schls Cmmn Cre Mathematics Curriculum prvides a list f research-based best practice instructinal strategies that the teacher may mdel and/r facilitate. It is suggested the teacher: Use frmative assessment t guide instructin Prvide pprtunities fr independent, partner and cllabrative grup wrk Differentiate instructin by varying the cntent, prcess, and prduct and prviding pprtunities fr: anchring cubing jig-sawing pre/pst assessments tiered assignments Address multiple intelligences instructinal strategies, e.g. visual, bdily kinesthetic, interpersnal Prvide pprtunities fr higher level thinking: Webb s Depth f Knwledge, 2,3,4, skill/cnceptual understanding, strategic reasning, extended reasning Facilitate the integratin f Mathematical Practices in all cntent areas f mathematics Facilitate integratin f the Applied Learning Standards (SCANS): cmmunicatin critical thinking prblem slving reflectin/evaluatin research Emply strategies f best practice (student-centered, experiential, hlistic, authentic, expressive, reflective, scial, cllabrative, demcratic, cgnitive, develpmental, cnstructivist/heuristic, and challenging) Prvide rubrics and mdels 2/20/2012 Middletwn Public Schls 3

Address multiple intelligences and brain dminance (spatial, bdily kinesthetic, musical, linguistic, intrapersnal, interpersnal, mathematical/lgical, and naturalist) Emply mathematics best practice strategies e.g. using manipulatives facilitating cperative grup wrk discussing mathematics questining and making cnjectures justifying f thinking writing abut mathematics facilitating prblem slving apprach t instructin integrating cntent using calculatrs and cmputers facilitating learning using assessment t mdify instructin COMMON The Middletwn Public Schls Cmmn Cre Mathematics Curriculum includes cmmn assessments. Required (red ink) indicates the assessment is required f all students e.g. cmmn tasks/perfrmance-based tasks, standardized mid-term exam, standardized final exam. Required Assessments Benchmark Prblems Cmmn Unit Assessment Cmmn Tasks NWEA Test Cmmn Instructinal Assessments (I) - used by teachers and students during the instructin f CCSS. Cmmn Frmative Assessments (F) - used t measure hw well students are mastering the cntent standards befre taking state assessments teacher and student use t make decisins abut what actins t take t prmte further learning n-ging, dynamic prcess that invlves far mre frequent testing serves as a practice fr students Cmmn Summative Assessment (S)- used t measure the level f student, schl, r prgram success make sme srt f judgment, e.g. what grade prgram effectiveness e.g. state assessments (AYP), mid-year and final exams Additinal assessments include: Anecdtal recrds Oral presentatins Cnferencing Prblem/Perfrmance based/cmmn tasks Exhibits Rubrics/checklists (mathematical practice, mdeling) Interviews Tests and quizzes Graphic rganizers Technlgy Jurnals Think-aluds Mathematical Practices Writing genres Mdeling Opinin Multiple Intelligences assessments, e.g. Infrmative Rle playing - bdily kinesthetic Narrative Graphic rganizing - visual Cllabratin - interpersnal 2/20/2012 Middletwn Public Schls 4

FOR MATHEMATICS CURRICULUM Grade 4 Textbks Everyday Mathematics Everyday Mathematics Resurce Kit Everyday Mathematics Student Reference Bk and Jurnals Supplementary Classrm Instructin That Wrks, Marzan Exemplars (grade 6) NECAP, MCAS, NAEP Released Tasks NWEA MAP Assessments Prblem Slver Technlgy Calculatr Cmputers ELMO Graphing Calculatr Interactive bards LCD prjectrs MIMIO Overhead calculatr Smart bard TI Navigatr Websites http://illuminatins.nctm.rg/ http://ww.center.k12.m.us/edtech/everydaymath.htm http://www.achieve.rg/http://my.hrw.cm http://www.discveryeducatin.cm/ http://www.de.state.h.us/gd/templates/pages/ode/odedefaultpage.aspx?page=1 http://www.parccnline.rg/parcc-cntent-framewrks http://www.parccnline.rg/sites/parcc/files/parcc_draft_mdelcntentframewrksfrmathematics0.pdf www.cmmncre.rg/maps www.crestandards.rg www.csme.cm www.explrelearning.cm (Gizm ) www.fasttmath.cm www.glence.cm www.khanacademy.cm www.mathfrum.rg www.phschl.cm www.ride.ri.gv www.studyisland www.successnet.cm Materials Clred chips Cmpasses Dice EDM Templates Everyday Mathematics Games Exp markers Fractin sticks Number line Pattern blcks Prtractrs Rulers Student white bards 2/20/2012 Middletwn Public Schls 5

Middletwn Public Schls OPERATIONS AND Students use the fur peratins with whle numbers t slve prblems. ALGEBRAIC THINKING (4.OA) Practices t Make sense f prblems and persevere in slving them Reasn abstractly and Cnstruct viable arguments and critique the reasning f thers Mdel with mathematics Use apprpriate tls Attend t precisin Lk fr and make use f Lk fr and express reasning 2,3, 4,5, 6,7 PARCC Testing first pririty 4.OA.1 Interpret a multiplicatin equatin as a cmparisn, e.g., interpret 35 = 5 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements f multiplicative cmparisns as multiplicatin equatins. Accurately slve prblems invlving multiple peratins ( +, -,*,/) n whle numbers (multiplicatin limited t 2 digits by 2 digits, and divisin limited t 1 digit divisrs (fr assessment nly) ) the use f the prperties f factrs and multiples; additin and subtractin decimals psitive prper fractins with like/unlike denminatrs. M(N&O) 4 4 (state assessment) (1.4.1) 4.OA.2 Multiply r divide t slve wrd prblems invlving multiplicative cmparisn, e.g., by using drawings and equatins with a symbl fr the unknwn number t represent the prblem, distinguishing multiplicative cmparisn frm additive cmparisn. (see belw) GLE same as abve M(N&O) 4 4 (state assessment) (1.4.1) Students represent an unknwn number in a wrd prblem with a symbl. Wrd prblems which require multiplicatin r divisin are slved by using drawings and equatins. Present multistep wrd prblems with whle numbers and whle-number answers using the fur peratins. Students shuld knw which peratins are needed t slve the prblem. Drawing pictures r using mdels will help students understand what the prblem is asking. They shuld check the reasnableness f their answer using mental cmputatin and estimatin strategies. ODE 4.OA.3 Slve multistep wrd prblems psed with whle numbers and having whle-number answers using the fur peratins, including prblems in which remainders must be interpreted. Represent these prblems using equatins with a letter standing fr the unknwn quantity. Assess the reasnableness f answers using mental cmputatin and estimatin strategies including runding. GLE same as abve M(N&O) 4 4 (state assessment) (1.4.1) BENCHMARK PROBLEMS remved fr public viewing 2/20/2012 Middletwn Public Schls 6

Middletwn Public Schls OPERATIONS AND Students gain familiarity with factrs and multiples. ALGEBRAIC THINKING (4.OA) Practices t Make sense f prblems and persevere in slving them Reasn abstractly and Cnstruct viable arguments and critique the reasning f thers Mdel with mathematics Use apprpriate tls Attend t precisin Lk fr and make use f Lk fr and express reasning PARCC Testing secnd pririty 4. OA.4 Find all factr pairs fr a whle number in the range 1 100. Recgnize that a whle number is a multiple f each f its factrs. Determine whether a given whle number in the range 1 100 is a multiple f a given ne-digit number. Determine whether a given whle number in the range 1 100 is prime r cmpsite. GLE same as abve M(N&O) 4 4 (state assessment) (1.4.1) BENCHMARK PROBLEMS remved fr public viewing Students need t develp an understanding f the cncepts f number thery such as prime numbers and cmpsite numbers. This includes the relatinship f factrs and multiples. Multiplicatin and divisin are used t develp cncepts f factrs and multiples. Divisin prblems resulting in remainders are used as cunter-examples f factrs. Review vcabulary s that students have an understanding f terms such as factr, prduct, multiples, and dd and even numbers. OPERATIONS AND ALGEBRAIC THINKING (4.OA) Students generate and analyze patterns. Students need t develp strategies fr determining if a number is prime r cmpsite, in ther wrds, if a number has a whle number factr that is nt ne r itself. ODE Practices t Make sense f prblems and persevere in slving them Reasn abstractly and Cnstruct viable arguments and critique the reasning f thers Mdel with mathematics Use apprpriate tls Attend t precisin Lk fr and make use f Lk fr and express 3, 5 PARCC Testing third pririty 4. OA.5 Generate a number r shape pattern that fllws a given rule. Identify apparent features f the pattern that were nt explicit in the rule itself. Fr example, given the rule Add 3 and the starting number 1, generate terms in the resulting sequence and bserve that the terms appear t alternate between dd and even numbers. Explain infrmally why the numbers will cntinue t alternate in this way. Identify and extend t specific cases a variety f patterns linear cnsistent r repeating number pattern nnlinear incnsistent number pattern represented in mdels Students shuld generate numerical r gemetric patterns that fllw a given rule. They shuld lk fr relatinships in the patterns and be able t describe and make generalizatins. ODE 2/20/2012 Middletwn Public Schls 7

Middletwn Public Schls tables sequences M(F&A) 4 1 (state assessment) (3.1.1 reasning Write a rule in wrds r symbls t find the next case (t cntinue the pattern) (state assessment) M(F&A) 4 1 (3.1.2) BENCHMARK PROBLEMS remved fr public viewing NUMBER AND OPERATIONS IN BASE TEN (4.NBT) Practices t Make sense f prblems and persevere in slving them Reasn abstractly and Cnstruct viable arguments and critique the reasning f thers Mdel with mathematics Use apprpriate tls Attend t precisin Lk fr and make use f Lk fr and express reasning 2, lessn 2.3 Students generalize place value under-standing fr multi-digit whle numbers. PARCC Testing first pririty 4.NBT.1 Recgnize that in a multi-digit whle number, a digit in ne place represents ten times what it represents in the place t its right. Fr example, recgnize that 700 70 = 10 by applying cncepts f place value and divisin. Grade 4 expectatins in this dmain are limited t whle numbers less than r equal t 1,000,000. In Grade 4, runding is nt 7 Demnstrate cnceptual understanding f ratinal numbers using new, and students need t mdels, explanatins, r ther representatins with respect t: build n the Grade 3 skill f whle numbers frm 0 t 999,999 M(N&O) 4 1 (1.1.1) runding t the nearest 10 r (0 t 9, 999,999 (D) M(N&O) 5 1thrugh 100 t include larger numbers equivalency, e.g. 601,458 (>, <, =)300,297 and place value. What is new cmpsitin, e.g. 40+50+5=95 fr Grade 4 is runding t decmpsitin e.g. 95=50+40+5 digits ther than the leading place value, e.g. seven thusand, nine hundred, thirtynine digit, e.g., rund 23,960 t the and frty-five hundredths (use and nly when nearest hundred. This requires reading numbers with decimals) greater sphisticatin than psitive fractinal numbers r benchmark fractins (halves, thirds, runding t the nearest ten 4 furths, fifths, sixths, eighths, tenths) M(N&O) 4 1 (1.1.1) thusand because the digit in twelfths (D) M(N&O) 5 1 the hundreds place represents as a part t whle relatinship in area, set r linear 900 and when runded it mdels e.g. number line, scales (temperature), and becmes 1000, nt just zer. linear measurements ODE where the number f parts in the whle are equal t, and a multiple r factr f the denminatr (equivalent fractins; simplifying fractins prper M(N&O) 4 1 (1.1.1) mixed number (D) M(N&O) 5-1 2 imprper (D) M(N&O) 5 1 decimals using mdels, explanatins, r ther representatins. as hundredths within the cntext f mney, r tenths within the cntext f metric measurements (e.g., 2.3 cm) M(N&O) 4 1 (1.1.1) state assessment) benchmark percents (10%, 25%, 50%, 75% r 100%) as a part t whle relatinship in area, set, r linear mdels using mdels, explanatins, r ther representatins. (D) M(N&O) 5 1 2/20/2012 Middletwn Public Schls 8

Middletwn Public Schls 4 7 9 4.NBT.2 Read and write multi-digit whle numbers using base-ten numerals, number names, and expanded frm. Cmpare tw multi-digit numbers based n meanings f the digits in each place, using >, =, and < symbls t recrd the results f cmparisns. Demnstrate understanding f the relative magnitude f numbers frm 0 t 999,999 using mdels, number lines, r explanatins by rdering, cmparing, r identifying within number frmats (fractins t fractins, decimals t decimals, r percents t percents) whle numbers equivalent prper psitive fractinal numbers (halves, thirds, furths, fifths, sixths, eighths, tenths, M(N&O) 4 2 (state assessment) (1.2.1) twelfths (D) M(N&O) 5 2 decimals t hundredths M(N&O) 4 2 (state assessment), thusandths (D) M(N&O) 5 2 benchmark percents 10%, 25%, 50%, 75% r 100% (D) M(N&O) 5 2 2 4.NBT.3 Use place value understanding t rund multi-digit whle numbers t any place GLE same as abve M(N&O) 4 1 (state assessment) (1.1.1) BENCHMARK PROBLEMS remved fr public viewing NUMBER AND OPERATIONS IN BASE TEN (4.NBT) Students use place value understanding and prperties f peratins t perfrm multi-digit arithmetic. PARCC Testing first pririty Practices t 4.NBT.4 Fluently add and subtract multi-digit whle numbers using the Grade 4 expectatins in this Make sense f prblems and standard algrithm. dmain are limited t whle persevere in slving them 6 Demnstrate cnceptual understanding f mathematical peratins numbers less than r Reasn abstractly and using mdels, number lines, r explanatins by describing r illustrating equal t 1,000,000. Cnstruct viable arguments the relatinship between repeated subtractin and divisin (n and critique the reasning f remainders) Fr multi-digit additin and thers e.g. 12-4-4-4=0; 12/4=3 subtractin in Grade 4, the Mdel with mathematics 3 the inverse relatinship between multiplicatin and divisin f gal is fluency, which means 2/20/2012 Middletwn Public Schls 9

Middletwn Public Schls Use apprpriate tls whle numbers e.g. 4x4=16; 16/4=4 Attend t precisin 7 the additin r subtractin f psitive fractinal numbers with like Lk fr and make use f denminatrs (state assessment) M(N&O) 4 3 (1.3.1) Lk fr and express 4 & adding and subtracting decimals t hundredths and psitive prper 7 fractins with unlike denminatrs. (D) M(N&O) 5 3 reasning 2,3, 4,5, 6,7 2,3, 4,5, 6,7 4.NBT.5 Multiply a whle number f up t fur digits by a ne-digit whle number, and multiply tw tw-digit numbers, using strategies based n place value and the prperties f peratins. Illustrate and explain the calculatin by using equatins, rectangular arrays, and/r area mdels. Accurately slve prblems invlving multiple peratins ( +, -,*,/) n whle numbers (multiplicatin limited t 2 digits by 2 digits, and divisin limited t 1 digit divisrs (fr assessment nly) ) the use f the prperties f factrs and multiples; additin and subtractin decimals psitive prper fractins with like/unlike denminatrs. M(N&O) 4 4 (state assessment) (1.4.1) 4.NBT.6 Find whle-number qutients and remainders with up t fur-digit dividends and ne-digit divisrs, using strategies based n place value, the prperties f peratins, and/r the relatinship between multiplicatin and divisin. students must be able t carry ut the calculatins efficiently and accurately. ODE Start with a student s understanding f a certain strategy, and then make intentinal, clear-cut cnnectins fr the student t the standard algrithm. This allws the student t gain understanding f the algrithm rather than just memrize certain steps t fllw. It is very imprtant fr sme students t talk thrugh their understanding f cnnectins between different strategies and standard additin and subtractins algrithms. Give students many pprtunities t talk with classmates abut hw they culd explain standard algrithms. Think- Pair-Share is a gd prtcl fr all students. ODE Illustrate and explain the calculatin by using equatins, rectangular arrays, and/r area mdels. GLE same as abve M(N&O) 4 4 (state assessment) (1.4.1) BENCHMARK PROBLEMS remved fr public viewing NUMBER AND OPERATIONS FRACTIONS (4.NF) Practices t Make sense f prblems and persevere in slving them Reasn abstractly and 2,4, 7,9 Students extend understanding f fractin equivalence and rdering. PARCC Testing first pririty 4.NF.1 Explain why a fractin a/b is equivalent t a fractin (n a)/(n b) by using visual fractin mdels, with attentin t hw the number and size f the parts differ even thugh the tw fractins themselves are the same size. Grade 4 expectatins in this dmain are limited t fractins with denminatrs 2, 3, 4, 5, 6, 8, 10, 12, and 100. 2/20/2012 Middletwn Public Schls 10

Middletwn Public Schls Cnstruct viable arguments and critique the reasning f thers Mdel with mathematics Use apprpriate tls Attend t precisin Lk fr and make use f Lk fr and express reasning 2,4, 7,9 Use this principle t recgnize and generate equivalent fractins. Demnstrate understanding f the relative magnitude f numbers frm 0 t 999,999 using mdels, number lines, r explanatins by rdering, cmparing, r identifying within number frmats (fractins t fractins, decimals t decimals, r percents t percents) whle numbers equivalent prper psitive fractinal numbers (halves, thirds, furths, fifths, sixths, eighths, tenths, M(N&O) 4 2 (state assessment) (1.2.1) twelfths (D) M(N&O) 5 2 decimals t hundredths M(N&O) 4 2 (state assessment) benchmark percents 10%, 25%, 50%, 75% r 100% (D) M(N&O) 5 2 4.NF.2 Cmpare tw fractins with different numeratrs and different denminatrs, e.g., by creating cmmn denminatrs r numeratrs, r by cmparing t a benchmark fractin such as 1/2. Students shuld use mdels t cmpare tw fractins with different denminatrs by creating cmmn denminatrs r numeratrs. The mdels shuld be the same (bth fractins shwn using fractin bars r bth fractins using circular mdels) s that the mdels represent the same whle. The mdels shuld be represented in drawings. Students shuld als use benchmark fractins such as t cmpare tw fractins. The result f the cmparisns shuld be recrded using, and = symbls. ODE Recgnize that cmparisns are valid nly when the tw fractins refer t the same whle. Recrd the results f cmparisns with symbls >, =, r <, and justify the cnclusins, e.g., by using a visual fractin mdel. GLE same as abve M(N&O) 4 2 (state assessment) (1.2.1) BENCHMARK PROBLEMS remved fr public viewing NUMBER AND OPERATIONS FRACTIONS (4.NF) Practices t Make sense f prblems and persevere in slving them Reasn abstractly and Cnstruct viable arguments and critique the reasning f thers 3,4, 6,7 Students build fractins frm unit fractins by applying and extending previus understandings f peratins n whle numbers. PARCC Testing first pririty 4.NF.3 Understand a fractin a/b with a > 1 as a sum f fractins 1/b. a. Understand additin and subtractin f fractins as jining and separating parts referring t the same whle. 4.NF.3a Decmpse a fractin int a sum f fractins with the same denminatr in mre than ne way, recrding each decmpsitin by an equatin. Grade 4 expectatins in this dmain are limited t fractins with denminatrs 2, 3, 4, 5, 6, 8, 10, 12, and 100. ODE Nw, they begin t represent a 2/20/2012 Middletwn Public Schls 11

Middletwn Public Schls Mdel with mathematics Use apprpriate tls Attend t precisin Lk fr and make use f Lk fr and express reasning b. Justify decmpsitins, e.g., by using a visual fractin mdel. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. 4.NF.3b c. Add and subtract mixed numbers with like denminatrs, e.g., by replacing each mixed number with an equivalent fractin, and/r by using prperties f peratins and the relatinship between additin and subtractin. 4.NF.3c d. Slve wrd prblems invlving additin and subtractin f fractins referring t the same whle and having like denminatrs, e.g., by using visual fractin mdels and equatins t represent the prblem. 4.NF.3d Demnstrate cnceptual understanding f mathematical peratins using mdels, number lines, r explanatins by describing r illustrating the relatinship between repeated subtractin and divisin (n remainders) e.g. 12-4-4-4=0; 12/4=3 the inverse relatinship between multiplicatin and divisin f whle numbers e.g. 4x4=16; 16/4=4 the additin r subtractin f psitive fractinal numbers with like denminatrs (state assessment) M(N&O) 4 3 (1.3.1) fractin by decmpsing the fractin as the sum f unit fractin and justify with a fractin mdel. Fr example, = + +. Students als represented whle numbers as fractins. They use this knwledge t add and subtract mixed numbers with like denminatrs using prperties f number and apprpriate fractin mdels. It is imprtant t stress that whichever mdel is used, it shuld be the same fr the same whle. Fr example, a circular mdel and a rectangular mdel shuld nt be used in the same prblem. ODE adding and subtracting decimals t hundredths and psitive prper fractins with unlike denminatrs. (D) M(N&O) 5 3 2,3, 4,5 6,7 4.NF.4 Apply and extend previus understandings f multiplicatin t multiply a fractin by a whle number. a. Understand a fractin a/b as a multiple f 1/b. Fr example, use a visual fractin mdel t represent 5/4 as the prduct 5 (1/4), recrding the cnclusin by the equatin 5/4 = 5 (1/4). 4.NF.4a b. Understand a multiple f a/b as a multiple f 1/b, and use this understanding t multiply a fractin by a whle number. Fr example, use a visual fractin mdel t express 3 (2/5) as 6 (1/5), recgnizing this prduct as 6/5. (In general, n (a/b) = (n a)/b.) 4.NF.4b c. Slve wrd prblems invlving multiplicatin f a fractin by a whle number, e.g., by using visual fractin mdels and equatins t represent the prblem. 5.NF.4c Fr example, if each persn at a party will 2/20/2012 Middletwn Public Schls 12

Middletwn Public Schls eat 3/8 f a pund f rast beef, and there will be 5 peple at the party, hw many punds f rast beef will be needed? Between what tw whle numbers des yur answer lie? Accurately slve prblems invlving multiple peratins ( +, -,*,/) n whle numbers (multiplicatin limited t 2 digits by 2 digits, and divisin limited t 1 digit divisrs (fr assessment nly) ) the use f the prperties f factrs and multiples; additin and subtractin decimals psitive prper fractins with like/unlike denminatrs. M(N&O) 4 4 (state assessment) (1.4.1) BENCHMARK PROBLEMS remved fr public viewing NUMBER AND OPERATIONS FRACTIONS (4.NF) Students understand decimal ntatin fr fractins, and cmpare decimal fractins. Practices t Make sense f prblems and persevere in slving them Reasn abstractly and Cnstruct viable arguments and critique the reasning f thers Mdel with mathematics Use apprpriate tls Attend t precisin Lk fr and make use f Lk fr and express reasning 2,4, 7,9 2,4, 7,9 PARCC Testing first pririty 4.NF.5 Express a fractin with denminatr 10 as an equivalent fractin with denminatr 100, and use this technique t add tw fractins with respective denminatrs 10 and 100.4 Fr example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. GLE same as abve M(N&O) 4 2 (state assessment) (1.2.1) 4.NF.6 Use decimal ntatin fr fractins with denminatrs 10 r 100. Fr example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; lcate 0.62 n a number line diagram. GLE same as abve M(N&O) 4 1 (state assessment) (1.1.1) Grade 4 expectatins in this dmain are limited t fractins with denminatrs 2, 3, 4, 5, 6, 8, 10, 12, and 100. Students wh can generate equivalent fractins can develp strategies fr adding fractins with unlike denminatrs in general. But additin and subtractin with unlike denminatrs in general is nt a requirement at this grade. Students need t make cnnectins between fractins and decimals. They shuld be able t write decimals fr 2,4, 4.NF.7 Cmpare tw decimals t hundredths by reasning abut their size. fractins with denminatrs f 7,9 10 r 100. Have students say Recgnize that cmparisns are valid nly when the tw decimals the fractin with denminatrs refer t the same whle. f 10 and 100 alud. Fr example 410 wuld fur Recrd the results f cmparisns with the symbls >, =, r <, and justify the cnclusins, e.g., by using a visual tenths r wuld be 2/20/2012 Middletwn Public Schls 13

Middletwn Public Schls mdel. twenty-seven hundredths. GLE same as abve M(N&O) 4 2 (state assessment) (1.2.1) BENCHMARK PROBLEMS remved fr public viewing Students shuld be able t express decimals t the hundredths as the sum f tw decimals r fractins. In decimal numbers, the value f each place is 10 times the value f the place t its immediate right. ODE MEASUREMENT AND DATA (4.MD) Students slve prblems invlving measurement and cnversin f measurements frm a larger unit t a smaller unit. Practices t Make sense f prblems and persevere in slving them Reasn abstractly and Cnstruct viable arguments and critique the reasning f thers Mdel with mathematics Use apprpriate tls Attend t precisin Lk fr and make use f Lk fr and express reasning 4,5 6,8, 11 PARCC Testing secnd pririty 4.MD.1 Knw relative sizes f measurement units within ne system f units including km, m, cm; kg, g; lb, z.; l, ml; hr, min, sec. Within a single system f measurement, express measurements in a larger unit in terms f a smaller unit. Recrd measurement equivalents in a tw clumn table. Fr example, knw that 1 ft is 12 times as lng as 1 in. Express the length f a 4 ft snake as 48 in. Generate a cnversin table fr feet and inches listing the number pairs (1, 12), (2, 24), (3, 36),... Measure and use units f measures apprpriately and cnsistently (state assessment ) M(G&M) 4 7 (2.6.1) Make cnversins within systems when slving prblems acrss the cntent strands. (state assessment ) M(G&M) 4 7 (2.6.2) Length Unit (accuracy): Inch (t 1/4 inch); Ft; Centimeter (t 0.5 centimeter); Meter (t 0.5 centimeter); Yard; Mile (use in scale questins); Kilmeter (use in scale questins) Equivalencies: 12 inches in 1 ft; 10 mm in 1 cm (D) M(G&M) 5 7 100; centimeters in 1 meter; 3 feet in 1 yard; 36 inches in 1 yard Time Unit (accuracy):hur (t 5 minute interval) (t 1 minute interval) (D) M (G&M) 5 7 ; Day; Year Equivalencies:24 hurs in 1 day; 7 days in 1 week; 365 days in 1 year; 60 secnds in 1 minute; 60 minutes in 1 hur 2/20/2012 Middletwn Public Schls 14

Middletwn Public Schls Temperature Unit (accuracy): Cº and Fº (t 1 degree) Capacity Unit (accuracy): Quart (t whle quart) Mass Unit (accuracy): Kilgram (t whle kilgram); Gram (t whle gram) Weight Unit (accuracy): Pund (t whle pund) 4,5, 11 4.MD.2 Use the fur peratins t slve wrd prblems invlving distances, intervals f time, liquid vlumes, masses f bjects, and mney, including prblems invlving simple fractins r decimals, and prblems that require expressing measurements given in a larger unit in terms f a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. GLE same as abve (state assessment ) M(G&M) 4 7 (2.6.1) and (state assessment ) M(G&M) 4 7 (2.6.2) 8 4.MD.3 Apply the area and perimeter frmulas fr rectangles in real wrld and mathematical prblems. Fr example, find the width f a rectangular rm given the area f the flring and the length, by viewing the area frmula as a multiplicatin equatin with an unknwn factr. Demnstrate cnceptual understanding f: perimeter f plygns using a variety f mdels, manipulatives, r frmulas. the area f rectangles, plygns r irregular shapes n grids using a variety f mdels, manipulatives, r frmulas. Expresses all measures using apprpriate units. M(G&M) 4 6 (state Assessment) (2.5.1) BENCHMARK PROBLEMS remved fr public viewing 2/20/2012 Middletwn Public Schls 15

DOMAINS UNIT CLUSTERS AND STANDARDS Middletwn Public Schls MEASUREMENT AND DATA (4.MD) Students represent and interpret data. Practices t Make sense f prblems and persevere in slving them Reasn abstractly and Cnstruct viable arguments and critique the reasning f thers Mdel with mathematics Use apprpriate tls Attend t precisin Lk fr and make use f Lk fr and express reasning PARCC Testing third pririty 4.MD.4 Make a line plt t display a data set f measurements in fractins f a unit (1/2, 1/4, 1/8). Slve prblems invlving additin and subtractin f fractins by using infrmatin presented in line plts. Fr example, frm a line plt find and interpret the difference in length between the lngest and shrtest specimens in an insect cllectin. Interpret a given representatin line plts tables bar graphs pictgraphs circle graphs t answer questins related t the data t analyze the data t frmulate r justify cnclusins t make predictins t slve prblems (state assessment) M(DSP) 4 1 (4.1.1) Data has been measured and represented n line plts in units f whle numbers, halves r quarters. Students have als represented fractins n number lines. Nw students are using line plts t display measurement data in fractin units and using the data t slve prblems invlving additin r subtractin f fractins. Instructinal Strategies Have students create line plts with fractins f a unit (,, ) and plt data shwing multiple data pints fr each fractin. ODE 2 9 Organize and display data using tables line plts bar graphs pictgraphs t answer questins related t the data t analyze the data t frmulate r justify cnclusins t make predictins, r t slve prblems (Lcal) M(DSP) 4 3 (4.3.1) BENCHMARK PROBLEMS Pse questins that students may answer, such as Hw many ne-eighths are shwn n the line plt? Expect tw ne-eighths as the answer. Then ask, What is the ttal f these tw neeighths? Encurage students t cunt the fractinal numbers as they wuld with whle-number cunting, but using the fractin name. What is the ttal number f inches fr insects measuring 2/20/2012 Middletwn Public Schls 16

DOMAINS UNIT CLUSTERS AND STANDARDS Middletwn Public Schls inches? Students can use skip cunting with fractin names t find the ttal, such as, three-eighths, six-eighths, nine-eighths. The last fractin names the ttal. Students shuld ntice that the denminatr did nt change when they were saying the fractin name. have them make a statement abut the result f adding fractins with the same denminatr. What is the ttal number f insects measuring inch r inches? Have students write number sentences t represent the prblem and slutin such as, + + = inches. Use visual fractin strips and fractin bars t represent prblems t slve prblems invlving additin and subtractin f fractins. ODE MEASUREMENT AND DATA (4.MD) Students understand cncepts f angle and measure angles (gemetric measurement). Practices t Make sense f prblems and persevere in slving them Reasn abstractly and Cnstruct viable arguments and critique the reasning f thers Mdel with mathematics Use apprpriate tls Attend t precisin Lk fr and make use f Lk fr and express reasning 1 PARCC Testing secnd pririty 4.MD.5 Recgnize angles as gemetric shapes that are frmed wherever tw rays share a cmmn endpint, and understand cncepts f angle measurement: a. An angle is measured with reference t a circle with its center at the cmmn endpint f the rays, by cnsidering the fractin f the circular arc between the pints where the tw rays intersect the circle. An angle that turns thrugh 1/360 f a circle is called a ne-degree angle, and can be used t measure angles. 4.MD.5a b. An angle that turns thrugh n ne-degree angles is said t have an angle measure f n degrees. 4.MD.5b Use prperties r attributes f angles (number f angles) sides (number f sides, length f sides, parallelism, r perpendicularity) t identify, describe, r distinguish amng Students can als create an angle explrer (tw strips f cardbard attached with a brass fastener) t learn abut angles. They can use the angle explrer t get a feel f the relative size f angles as they rtate the cardbard strips arund. ODE 2/20/2012 Middletwn Public Schls 17

Middletwn Public Schls triangles squares rectangles rhmbi trapezids hexagns ctagns t classify angles relative t 90 as mre than, less than, r equal t (btuse, acute, and right). M(G&M) 4 1 (state assessment) (2.1.1) 1 4.MD.6 Measure angles in whle-number degrees using a prtractr. Sketch angles f specified measure. GLE same as abve M(G&M) 4 1 (state assessment) (2.1.1) 1 4.MD.7 Recgnize angle measure as additive. When an angle is decmpsed int nn-verlapping parts, the angle measure f the whle is the sum f the angle measures f the parts. Slve additin and subtractin prblems t find unknwn angles n a diagram in real wrld and mathematical prblems, e.g., by using an equatin with a symbl fr the unknwn angle measure. GLE same as abve M(G&M) 4 1 (state assessment) (2.1.1) BENCHMARK PROBLEMS remved fr public viewing GEOMETRY (4.G) Students draw and identify lines and angles, and classify shapes by prperties f their lines and angles. Practices t Make sense f prblems and persevere in slving them Reasn abstractly and Cnstruct viable arguments and critique the reasning f thers Mdel with mathematics Use apprpriate tls Attend t precisin Lk fr and make use f Lk fr and express 1 PARCC Testing secnd pririty 4.G.1 Draw pints, lines, line segments, rays, angles (right, acute, btuse), and perpendicular and parallel lines. Identify these in tw-dimensinal figures. GLE same as abve M(G&M) 4 1 (state assessment) (2.1.1) 4.G.2 Classify tw-dimensinal figures based n the presence r absence f parallel r perpendicular lines, r the presence r absence f angles f a specified size. Recgnize right triangles as a categry, and identify right triangles. GLE same as abve M(G&M) 4 1 (state assessment) (2.1.1) Tw-dimensinal shapes are classified based n relatinships by the angles and sides. Students can determine if the sides are parallel r perpendicular, and classify accrdingly. Characteristics f rectangles (including squares) are used t develp the cncept f parallel and perpendicular lines. The characteristics and understanding f parallel and 2/20/2012 Middletwn Public Schls 18

Middletwn Public Schls reasning 4.G.3 Recgnize a line f symmetry fr a tw-dimensinal figure as a line acrss the figure such that the figure can be flded alng the line int matching parts. Identify line-symmetric figures and draw lines f symmetry. GLE same as abve M(G&M) 4 1 (state assessment) (2.1.1) BENCHMARK PROBLEMS remved fr public viewing perpendicular lines are used t draw rectangles. Repeated experiences in cmparing and cntrasting shapes enable students t gain a deeper understanding abut shapes and their prperties. Infrmal understanding f the characteristics f triangles is develped thrugh angle measures and side length relatinships. Triangles are named accrding t their angle measures (right, acute r btuse) and side lengths (scalene, issceles r equilateral). These characteristics are used t draw triangles. ODE 11 1,6 GLEs NOT COVERED IN CCSS, STATE ASSESSED UNTIL 2013 Use prperties r attributes shape f bases number f lateral faces number f bases (D) M(G&M) 5 3 number f edges (B) M(G&M) 6 3 number f vertices (B) M(G&M) 6 3 t identify, cmpare, r describe three-dimensinal shapes : rectangular prisms triangular prisms cylinders spheres (state assessment) M(G&M) 4 3 (2.2.1) pyramids (D) M(G&M) 5 3 cnes (D) M(G&M) 5 3 Demnstrate cnceptual understanding f similarity by applying scales n maps by applying characteristics f similar figures (same shape but nt necessarily the same size) t identify similar figures r t slve prblems invlving similar figures. Describes relatinships using mdels r explanatins (student chice). M(G&M) 4 5 (state assessment) (2.4.1) 2/20/2012 Middletwn Public Schls 19

Middletwn Public Schls 3 2 Demnstrate cnceptual understanding f equality by shwing equivalence between tw expressins using mdels r different representatins f the expressins e.g. pan balances simplifying numerical expressins where left t right cmputatins may be mdified nly by the use f parentheses [e.g., 14 (2 5)] (expressins cnsistent with the parameters f M(F&A) 4 3) slving ne-step linear equatins f the frm ax = c; x ± b = c; where a, b, and c are whle numbers with a 0. M(F&A) 4 4 (state assessment) (3.3.1) e.g. ax=c (3x=24; x=8) x+b=c (x+5=20; x=15) x-b=c (x-5=20; x=25) Analyze patterns, trends, r distributins in data in a variety f cntexts by determining r using landmarks (Everyday Math) minimum maximum range M(DSP) 4 2 (state assessment) measures f central tendency median mde M(DSP) 4 2 M(DSP) 4 2 (state assessment) (4.2.1) mean (D) M(DSP)-5-2 t analyze situatins r t slve prblems (D) M(DSP) 5 2 2/20/2012 Middletwn Public Schls 20