District Adopted Materials: Every Day Math (2007)

Transcription

1 Grade: Furth Curse: athematics District Adpted aterials: Every Day ath (007) Standard : Number and Cmputatin The student uses numerical and cmputatinal cncepts and prcedures in a variety f situatins. Benchmark : Number Sense The student demnstrates number sense fr whle numbers, fractins (including mixed numbers), decimals, and mney including the use f cncrete bjects in a variety f situatins. Benchmark : Number Systems and Their Prperties The student demnstrates an understanding f whle numbers with a special emphasis n place value; recgnizes, uses, and explains the cncepts f prperties as they relate t whle numbers; and extends these prperties t fractins (including mixed numbers), decimals, and mney. Benchmark 3: Estimatin The student uses cmputatinal estimatin with whle numbers, fractins (including mixed numbers) and mney in a variety f situatins. Benchmark 4: Cmputatin The student mdels, perfrms, and explains cmputatin with whle numbers, fractins, and mney including the use f cncrete bjects in a variety f situatins. Standard : Algebra The student uses algebraic cncepts and prcedures in a variety f situatins. Benchmark : Patterns The student recgnizes, describes, extends, develps, and explains relatinships in patterns using cncrete bjects in a variety f situatins. Benchmark : Variables, Equatins, and nequalities The student uses variables, symbls, and whle numbers t slve equatins including the use f cncrete bjects in a variety f situatins. Benchmark 3: Functins The student recgnizes and describes whle number relatinships including the use f cncrete bjects in a variety f situatins. Benchmark 4: dels The student develps and uses mathematical mdels including the use f cncrete bjects t represent and explain mathematical relatinships in a variety f situatins. Standard 3: Gemetry The student uses gemetric cncepts and prcedures in a variety f situatins. Benchmark : Gemetric Figures and Their Prperties The student recgnizes gemetric shapes and investigates their prperties including the use f cncrete bjects in a variety f situatins. Benchmark : easurement and Estimatin The student estimates and measures using standard and nnstandard units f measure including the use f cncrete bjects in a variety f situatins. Benchmark 3: Transfrmatinal Gemetry The student recgnizes and perfrms ne transfrmatin n simple shapes r cncrete bjects in a variety f situatins. Benchmark 4: Gemetry Frm An Algebraic Perspective The student relates gemetric cncepts t a number line and the first quadrant f a crdinate plane in a variety f situatins. Standard 4: Data The student uses cncepts and prcedures f data analysis in a variety f situatins. Benchmark : Prbability The student applies the cncepts f prbability t draw cnclusins and t make predictins and decisins including the use f cncrete bjects in a variety f situatins. Benchmark : Statistics The student cllects, rganizes, displays, explains, and interprets numerical (whle numbers) and nn-numerical data sets including the use f cncrete bjects in a variety f situatins.

2 ndicatrs The student Blm s Strand Sequence Teaching Time 4...K knws, explains, and uses equivalent representatins fr ($): whle numbers frm 0 thrugh 00,000 (.4.Ka-b); fractins greater than r equal t zer (halves, furths, thirds, eighths, tenths, twelfths, sixteenths, hundredths) including mixed numbers (.4.Kc); decimals greater than r equal t zer thrugh hundredths place and when used as mnetary amunts (.4.Kc-d) ($), e.g., 7 = $.07 = 7/00 f a dllar r a hundreds grid with 7 sectins clred r. = /0 = 4...A slves real-wrld prblems using equivalent representatins and cncrete bjects t ($): cmpare and rder whle numbers frm 0 thrugh 00,000 (.4.Aa-b); e.g., using base ten blcks, represent the attendance at the circus ver a three day stay; then represent the numbers using digits and cmpare and rder in different ways; add and subtract whle numbers frm 0 thrugh 0,000 and decimals when used as mnetary amunts (.4.Aa-d), e.g., use real mney t shw at least ways t represent $4.78, then subtract the cst f a pair f tennis shes; multiply a ne-digit whle number by a tw-digit whle number (.4.Aa-b), e.g., use base ten blcks t represent 4 x 5 t find the ttal number f hurs in 5 days, r use repeated additin t slve, r use the algrithm. 4...K cmpares and rders: whle numbers frm 0 thrugh 00,000 (.4.Ka-b) ($); fractins greater than r equal t zer (halves, furths, thirds, eighths, tenths, twelfths, sixteenths, hundredths) including mixed numbers with a special emphasis n cncrete bjects (.4.Kc); decimals greater than r equal t zer thrugh hundredths place and when used as mnetary amunts (.4.Kc-d) ($) Applicatin Analysis Equivalent epresentatins Equivalent epresentatins Analysis Cmpare & Order 8 7

3 4...A determines whether r nt slutins t real-wrld prblems that invlve the fllwing are reasnable ($): whle numbers frm 0 thrugh 0,000 (.4.Aa-b), e.g., a student says that there are,000 students in grade 4 at her schl, is this reasnable? fractins greater than r equal t zer (halves, furths, thirds, eighths, tenths, sixteenths) (.4.Ac), e.g., yu ate ½ f a sandwich and a friend ate ¾ f the same sandwich; is this reasnable? decimals greater than r equal t zer when used as mnetary amunts (.4.Ac-d), e.g., a pack f chewing gum csts what amunt - $6 $ ? s this reasnable? 4...K identifies, mdels, reads, and writes numbers using numerals, wrds, and expanded ntatin frm hundredths place thrugh ne-hundred thusands place (.4.Ka-b) ($), e.g., fur hundred sixty-tw thusand, tw hundred eighty-fur and fifty hundredths = 46,84.50 r 46,84.50 = (4 x 00,000) + (6 x 0,000) + ( x,000) + ( x 00) + (8 x 0) + (4 x ) + (5 x.) + (0 x.0) = 400, ,000 +, Analysis Cmpare & Order S-6 Analysis Place Value

4 4...Aa-e slves real-wrld prblems with whle numbers frm 0 thrugh 0,000 using place value mdels; mney; and the cncepts f these prperties t explain reasning (.4.Aa-b,d) ($): cmmutative prperties f additin and multiplicatin, e.g., a student has a $5, a $0, and a $0 bill; a student ttals the amunt t see hw much can be spent shpping fr schl supplies. The student says: Because yu can add in any rder, can rearrange the mney and cunt $0, $0, and $5 fr $0 + $0 + $5. Anther student has 4 $5 bills. The student is asked the amunt. The student says: dn t knw 4 x 5 but knw 5 x4 is $0, since multiplicatin can be dne in any rder. zer prperty f additin, e.g., a student has 6 marbles in ne pcket and nne in the ther pcket. Hw many marbles altgether? prperty f ne fr multiplicatin, e.g., there are 4 students in ur class, each student shuld have ne math bk; s cmpute 4 x = 4. ultiplying times des nt change the prduct because it is ne grup f 4. assciative prperties f additin and multiplicatin, e.g., a student has tw dimes and a quarter. Using cins r mney mdels, there are at least ways t grup the cins t find the ttal. One way is 0 (dime) + 0 (dime) = 0, then add the quarter, s (quarter) = 45. Anther way 0 (dime) + 5 (quarter) = 35, then add the ther dime t 35 s = 45 This mdels that (D + D) + Q = D + (D + Q). zer prperty f multiplicatin, e.g., in science, yu are bserving a snail. The snail des nt mve ver a 4-hur perid. T figure its ttal mvement, yu say 4 x 0 = 0. Applicatin Place Value 4...K classifies varius subsets f numbers as whle numbers, fractins (including mixed numbers), r decimals (.4.Kb-c,.4.Ki) Analysis Number Systems & their Prperties

5 4...Aa-c perfrms varius cmputatinal prcedures with whle numbers frm 0 thrugh 0,000 using the cncepts f the fllwing prperties; extends the prperties t fractins (halves, furths, thirds, eighths, tenths, sixteenths) including mixed numbers, and decimals thrugh hundredths place; and explains hw the prperties were used (.4.Aa-c): cmmutative prperty f additin and multiplicatin, e.g., = 6 + 5, the student says: knw that = and adding in any rder still gets the answer, s is the same as x 6 = 6 x 4, the student says: knw that 4 x 6 = 4 and multiplying in any rder still gets the answer, s 4 x 6 is the same as 6 x 4. zer prperty f multiplicatin withut cmputing, e.g., 58 x 0 = 0; the student says: knw the answer (prduct) is zer because n matter hw many factrs yu have, when yu multiply with a 0, the prduct is zer. assciative prperty f additin, e.g., culd be slved as + (8 + 8) r ( + 8) + 8, the student says: dn t knw 9 + 8, but knw my dubles f 8 + 8, s made the 9 int + 8 and then added mre t make K3 identifies the place value f varius digits frm hundredths place thrugh ne hundred thusands place (.4.Kb) ($) 4...A3 states the reasn fr using whle numbers, fractins, mixed numbers, r decimals when slving a given real-wrld prblem (.4.Aa-d). Applicatin Number Systems & their Prperties Knwledge Place Value Applicatin Number Systems & their Prperties K4 identifies any whle number as even r dd (.4.Ka) Knwledge Number Systems & their Prperties

6 4...(a-d)K5 uses the cncepts f these prperties with the whle number system and demnstrates their meaning including the use f cncrete bjects (.4.Ka) ($): cmmutative prperties f additin and multiplicatin, e.g., + 8 = 8 + and 8 x 9 = 9 x 8; zer prperty f additin (additive identity) and prperty f ne fr multiplicatin (multiplicative identity), e.g., = 4 and 75 x = 75; assciative prperties f additin and multiplicatin, e.g., 4 + ( + 3) = (4 + ) + 3 and x (3 x 4) = ( x 3) x 4; symmetric prperty f equality applied t additin and multiplicatin, e.g., 00 = is the same as = 00 and = 7 x 3 is the same as 3 x 7 = ; zer prperty f multiplicatin, e.g., 9 x 0 = 0 r 0 x = 0; distributive prperty, e.g., 6(7 + 3) = (6 7) + (6 3) 4..3.K estimates whle number quantities frm 0 thrugh 0,000; fractins (halves, furths, thirds); and mnetary amunts thrugh $,000 using varius cmputatinal methds including mental math, paper and pencil, cncrete materials, and apprpriate technlgy (.4.Ka-d) ($) 4..3.A adjusts riginal whle number estimates f a real-wrld prblem using numbers frm 0 thrugh 0,000 based n additinal infrmatin (a frame f reference) (.4.Aa) ($), e.g., if given a small jar and tld the number f pieces f candy it has in it, the student wuld adjust his/her riginal estimate f the number f pieces f candy in a larger jar K uses varius estimatin strategies and explains hw they are used when estimating whle numbers quantities frm 0 thrugh 0,000; fractins [(halves, furths, thirds) including mixed numbers)]; and mnetary amunts thrugh $,000 (.4.Ka-d) ($) 4..3.A estimates t check whether r nt the result f a real-wrld prblem using whle numbers frm 0 thrugh 0,000, fractins (including mixed numbers), and mnetary amunts is reasnable and makes predictins based n the infrmatin (.4.Aa-d) ($), e.g., at the mvies, yu bught ppcrn fr $.35, a sda fr $.50, and paid $4.50 fr the ticket. s it reasnable t say yu spent $0? Hw much will yu need t save t g t the mvies nce a week fr the next mnth? 4..3.K3 recgnizes and explains the difference between an exact and an apprximate answer (.4.Ka), e.g., when asked hw many desks are in the rm, the student gives an estimate f abut 30 and then cunts the desks and indicates an exact answer is 8 desks Applicatin Number Systems & their Prperties Cmprehensin Estimatin Applicatin Estimatin Applicatin Estimatin Cmprehensin Estimatin S-6 Cmprehensin Estimatin 8 0

7 4..3.A3 selects a reasnable magnitude frm three given quantities based n a familiar prblem situatin and explains the reasnableness f selectin (.4.Aa), e.g., abut hw many new pencils will fit in yur pencil bx? s it abut 5, abut 50, r abut 00? The answer will depend n the size f yur pencil bx K4 selects frm an apprpriate range f estimatin strategies and determines if the estimate is an verestimate r underestimate, (.4.Ka) Knwledge Estimatin Cmprehensin Estimatin 4..3.A4 determines if a real-wrld prblem calls fr an exact r apprximate answer and perfrms the apprpriate cmputatin using varius cmputatinal methds including mental math, paper and pencil, cncrete bjects, and apprpriate technlgy (.4.Aa) ($) K cmputes with efficiency and accuracy using varius cmputatinal methds including mental math, paper and pencil, cncrete materials, and apprpriate technlgy (.4.Ka) ($) Applicatin Estimatin Applicatin Cmputatin 8

8 4..4.A a-e N slves ne- and tw-step real-wrld prblems with ne r tw peratins using these cmputatinal prcedures ($): adds and subtracts whle numbers frm 0 thrugh 0,000 and when used as mnetary amunts (.4.Aa-b,d), e.g., Lee buys a bicycle fr $39, a helmet fr $9, and a reflectr fr $6. He paid fr it with a $00 check frm his grandparents. Hw much will he have left frm the $00 check? multiplies thrugh a tw-digit whle number by a tw-digit whle number (.4.Aa-b), e.g., at schl, there are students in each classrm. f there are 4 classes, hw many students are in the classrms? multiplies whle dllar mnetary amunts (up thrugh three-digit) by a ne- r tw-digit whle number (.4.Aa-b,d), e.g., third and furth graders are planning a field trip. The cst per student is $9.00. Hw much will the trip cst? multiplies mnetary amunts less than $00 by whle numbers less than ten (.4.Aa-d), e.g., at the bk fair, a student buys 8 bks n animals fr $.69 each. Hw much did the student pay fr the bks? figures crrect change thrugh $0.00 (.4.Aa-d), e.g., buying a 65 drink, paying fr it with a $ bill, and then figuring the amunt f change K N states and uses with efficiency and accuracy multiplicatin facts frm x thrugh x and crrespnding divisin facts (.4.Ka) ($) Applicatin Cmputatin,6 Knwledge Cmputatin A generates a family f multiplicatin and divisin facts given ne equatin/fact (.4.Ab), e.g., given 8 x 9 = 7, the ther facts are 9 x 8 = 7, 7 8 = 9, and 7 9 = 8. Applicatin Cmputatin 3

9 4..4.K3 N perfrms and explains these cmputatinal prcedures ($): Applicatin Cmputatin adds and subtracts whle numbers frm 0 thrugh 00,000 and when used as mnetary amunts (.4.Ka-b,d); multiplies thrugh a three-digit whle number by a tw-digit whle number (.4.Ka-b); multiplies whle dllar mnetary amunts (thrugh three-digits) by a ne- r tw-digit whle number (.4.Kd), e.g., $45 x 6; multiplies mnetary amunts ten (.4.Kd), e.g., $4. x 7;less than $00.00 by whle numbers less than divides thrugh a tw-digit whle number by a ne-digit whle number with a ne-digit whle number qutient with r withut a remainder (.4.Ka-b), e.g., 47 5 = 9 r ; adds and subtracts fractins greater than r equal t zer with like denminatrs (.4.Kc); figures crrect change thrugh $0.00 (.4.Kd) 4..4.K4 identifies multiplicatin and divisin fact families (.4.Ka) Knwledge Cmputatin 4..4.K5 reads and writes hrizntally, vertically, and with different peratinal symbls the same additin, subtractin, multiplicatin, r divisin expressin, e.g., 6 4 is the same as 6 x 4 is the same as 4 and 6(4) r X6; 0 divided by is the same as 0 r K6 N shws the relatinship between these peratins with the basic fact families (additin facts with sums frm 0 thrugh 0 and crrespnding subtractin facts, multiplicatin facts frm x thrugh x and crrespnding divisin facts) including the use f mathematical mdels (.4.Ka) ($): additin and subtractin, additin and multiplicatin, multiplicatin and divisin, subtractin and divisin 4..4.K7 finds factrs and multiples f whle numbers frm thrugh 00 (.4.Ka) Knwledge Cmputatin Applicatin Cmputatin Analysis Cmputatin 5 3 4

10 4...K uses cncrete bjects, drawings, and ther representatins t wrk with types f patterns(.4.ka): repeating patterns, e.g., an AB pattern is like -, -, ; an ABC pattern is like dg-hrse-pig, dg-hrse-pig, ; an AAB pattern is like,, ; grwing patterns e.g.,, 5,, 0, 4...A a-f generalizes these patterns using a written descriptin: cunting numbers related t number thery (.4.Aa), whle number patterns (.4.Aa) ($), patterns using gemetric shapes (.4.Af), measurement patterns (.4.Aa), mney and time patterns (.4.Aa,d) ($), patterns using size, shape, clr, texture, r mvement (.4.Aa). 4...K uses these attributes t generate patterns: cunting numbers related t number thery (.4.Ka), e.g., multiples and factrs thrugh r multiplying by 0, 00, r,000; whle numbers that increase r decrease (.4.Ka) ($), e.g., 0, 5, 0, ; gemetric shapes including ne r tw attributes changes (.4.Kf), e.g., Synthesis Patterns Synthesis Patterns Synthesis Patterns when the next shape has ne mre side; r when bth clr and shape change at the same time such as measurements (.4.Ka), e.g., 3 ft., 6 ft., 9 ft., ; mney and time (.4.Ka,d) ($), e.g., $.5, $.50, $.75, r :05 p.m., :0 p.m., :5 p.m., ; things related t daily life (.4.Ka), e.g., water cycle, fd cycle, r life cycle; things related t size, shape, clr, texture, r mvement (.4.Ka), e.g., rugh, smth, rugh, smth, rugh, smth, r clapping hands (kinesthetic patterns)

11 4...A recgnizes multiple representatins f the same pattern (.4.Aa), e.g., skip cunting by 5s t 60; whle number multiples f 5 thrugh 60; the multiplicatin table f 5 given the numerical pattern f 5, 0, 5,, 60; relating the cncept f five minute time intervals t each f the numerals n a clck giving the pattern f 5, 0, 5,, 60; ne nickel, tw nickels, three nickels, ; the number f fingers n twelve hands; recgnizing that all f these representatins are the same general pattern. 4...K3 identifies, states and cntinues a pattern presented in visual varius frmats including numeric (list r table), visual (picture, table, r graph), verbal (ral descriptin), kinesthetic (actin), and written (.4.Ka) ($) Knwledge Patterns Synthesis Patterns 4...K4 generates: a pattern (repeating, grwing) (.4.Ka); a pattern using a functin table (input/utput machines, T-tables) (.4.Ke) 4...K explains and uses variables and symbls t represent unknwn whle number quantities frm 0 thrugh,000 (.4.Ka) 4...A represents real-wrld prblems using variables and symbls with unknwn whle number quantities frm 0 thrugh,000 (.4.Aa) ($), e.g., Hw many weeks in twenty-eight days? can be represented by n x 7 = 8 r n = K slves ne-step equatins using whle numbers with ne variable and a whle number slutin that: find the unknwn in a multiplicatin r divisin equatin based n the multiplicatin facts frm x thrugh x and crrespnding divisin facts (.4.Ka), e.g., 60 = 0 x n; find the unknwn in a mney equatin using multiplicatin and divisin based upn the facts and additin and subtractin with values thrugh $0 (.4.Kd) ($), e.g., 8 quarters + 0 dimes = y dllars; find the unknwn in a time equatin invlving whle minutes, hurs, days, and weeks with values thrugh 00 (.4.Ka), e.g., 80 minutes = y hurs Synthesis Patterns Applicatin Knwledge Applicatin Variables, Equatins & nequalities Variables, Equatins & nequalities Variables, Equatins & nequalities 6 4

12 4..A generates ne-step equatins t slve real-wrld prblems with ne unknwn (represented by a variable r symbl) and a whle number slutin that (.4.Aa) ($): add r subtract whle numbers frm 0 thrugh,000; e.g., Hmer, Kansas has 83 nnfictin bks in its library. Hmer, dah has 65 nnfictin bks in its library. Hw many fewer bks nnfictin bks are in Hmer, dah s library? = B; multiply r divide using the basic facts, e.g., Tm has a sticker bk and each page hlds 5 stickers. f the same number f stickers is placed n each page, the bk will hld 30 stickers. Hw many pages are in his bk? This is represented by 5 x S = 30 r 30 5 = S. 4...K3 cmpares tw whle numbers frm 0 thrugh 0,000 using the equality and inequality symbls (=,, <, >) and their crrespnding meanings (is equal t, is nt equal t, is less than, is greater than) (.4.Kb) ($) Synthesis Analysis Variables, Equatins & nequalities Variables, Equatins & nequalities A3 generates (.4.Aa) ($): real-wrld prblems with ne peratin t match a given additin, subtractin, multiplicatin, r divisin equatin using whle numbers thrugh 99, e.g., given x 3 = Y, the student writes: was sick fr 3 days, when gt back had 3 pages f hmewrk. There are prblems n each page. Hw many ttal prblems must wrk? number cmparisn statements using equality and inequality symbls (=, <, >) with whle numbers, measurement, and mney, e.g., ft < 5 in r 0 quarters > $. 4...K4 reads and writes whle number equatins and inequalities using mathematical vcabulary and ntatin, e.g., 5 = 3 x 5 is the same as fifteen equals three times five r 4,564 >,000 is the same as fur thusand, five hundred sixty-fur is greater than ne thusand Synthesis Knwledge Variables, Equatins & nequalities Variables, Equatins & nequalities S K states mathematical relatinships between whle numbers frm 0 thrugh,000 using varius methds including mental math, paper and pencil, cncrete materials, and apprpriate technlgy (.4.Ka) ($) Knwledge elatins & Functins 4..3.A represents and describes mathematical relatinships between whle numbers frm 0 thrugh,000 using cncrete bjects, pictures, written descriptins, symbls, equatins, tables, and graphs (.4.Aa) ($). Cmprehensin elatin & Functins

13 4..3.K finds the values, determines the rule, and states the rule using symblic ntatin with ne peratin f whle numbers frm 0 thrugh 00 using a hrizntal r vertical functin table (input/utput machine, T-table) (.4.Ke), e.g., using the functin table, find the rule, the rule is N 4 N? ? 4?? A finds the rule, states the rule, and extends numerical patterns using real-wrld applicatins using whle numbers frm 0 thrugh 00 (.4.Aa,e), e.g., the teacher must rder supplies fr field day. Fr every students, ne red rubber ball is needed. f 6 balls are rdered, hw many students will be able t play? A slutin using a functin table might be: Analysis Analysis elatins & Functins elatins & Functins 3 Number f Students Number f Balls N N The rule is divide the number f students by r fr each grup f students, anther ball is added. Other slutins might be using a pattern t cunt by six times, 4, 36, 48, 60, 7 r t skip cunt by fr each ball rdered K3 generalizes numerical patterns using whle numbers frm 0 thrugh 00 with ne peratin by stating the rule using wrds, e.g., if the pattern is 46, 68,90,, 34, ; in wrds, the rule is add t the number befre 4..3.K4 uses a functin table (input/utput machine, T-table) t identify, plt, and label the rdered pairs in the first quadrant f a crdinate plane (.4.Ka,e) Analysis elatins & Functins Applicatin Pints

14 4..4.K knws, explains, and uses mathematical mdels t represent mathematical cncepts, prcedures, and relatinships. athematical mdels include: prcess mdels (cncrete bjects, pictures, diagrams, number lines, hundred charts, measurement tls, multiplicatin arrays, divisin sets, r crdinate planes/grids) t mdel cmputatinal prcedures, mathematical relatinships, and equatins (..Ka,..Ka,..K,..K4-5,.3.K-4,.4.K-,.4.K3a-b,.4.K3e,.4.K4,.4.K6-7,..K,..K.a-b,..Kd-g,..K3,..K4a,..K,..Ka,..K3-4,.3.K,.3.K4, 3..K-4, 3.3.K-, 3.4.K-4, 4..K3) ($); place value mdels (place value mats, hundred charts, base ten blcks, r unifix cubes) t cmpare, rder, and represent numerical quantities and t mdel cmputatinal prcedures (..Ka,..Ka,..K-3,.3.K-,.4.K3a-b,.4.K3e,..K4) ($); fractin and mixed number mdels (fractin strips r pattern blcks) and decimal mdels (base ten blcks r cins) t cmpare, rder, and represent numerical quantities (..Kb-c,..Kb-c,..K,.3.K-,.4.Kf) ($); mney mdels (base ten blcks r cins) t cmpare, rder, and represent numerical quantities (..Kc,..Kc,.3.K-,.4.K3a,.4.K3a,.4.K3c-d,.4.K3g,..Ke,..Kb) ($); functin tables (input/utput machines, T-tables) t mdel numerical and algebraic relatinships (..K4b,.3.K,.3.K4, 3.4.K4) ($); tw-dimensinal gemetric mdels (gebards, dt paper, pattern blcks, r tangrams) t mdel perimeter, area, and prperties f gemetric shapes and three-dimensinal gemetric mdels (slids) and real-wrld bjects t cmpare size and t mdel prperties f gemetric shapes (..Kc,..Ke, 3..K-6, 3..K5, 3.3.K3); tw-dimensinal gemetric mdels (spinners), three-dimensinal mdels (number cubes), and prcess mdels (cncrete bjects) t mdel prbability (4..K-3) ($); graphs using cncrete bjects, pictgraphs, frequency tables, hrizntal and vertical bar graphs, line graphs, circle graphs, Venn diagrams, line plts, charts, and tables t rganize and display data (4..K, 4..K-) ($); Venn diagrams t srt data and shw relatinships (..K) Applicatin dels 6

15 4..4.A recgnizes that varius mathematical mdels can be used t represent the same prblem situatin. athematical mdels include: prcess mdels (cncrete bjects, pictures, diagrams, number lines, crdinate planes/grids, hundred charts, measurement tls, multiplicatin arrays, r divisin sets) t mdel cmputatinal prcedures, mathematical relatinships, and prblem situatins (..A,..Aa,..A-3,.3.A-4,.4.A,..Aa-b,..Ad-f,..A,..A-3,.3.A-, 3..Aa-g, 3..A-3, 3.3.A-, 3.4.A-, 4..A) ($); place value mdels (place value mats, hundred charts, base ten blcks, r unfix cubes) t mdel prblem situatins (.A,..Aa,..A-3,.3.A,.4.A) ($); fractin and mixed number mdels (fractin strips r pattern blcks) and decimal mdels (base ten blcks r cins) t cmpare, rder, and represent numerical quantities (..Ab,..Ab-c,..A-3,.3.A,.4.Ad-e) ($); mney mdels (base ten blcks r cins) t cmpare, rder, and represent numerical quantities (..Ab,..Ac,..A,..A3,.3.A,.4.Aa,.4.Ac-e,..Ae) ($); functin tables (input/utput machines, T-tables) t mdel numerical and algebraic relatinships (.3.A) ($); tw-dimensinal gemetric mdels (gebards, dt paper, pattern blcks, r tangrams) t mdel perimeter, area, and prperties f gemetric shapes and three-dimensinal gemetric mdels (slids) and real-wrld bjects t cmpare size and t mdel prperties f gemetric shapes (..Ac, 3..A-, 3..Ah, 3.3.A3); tw-dimensinal gemetric mdels (spinners), three-dimensinal gemetric mdels (number cubes), and prcess mdels (cncrete bjects) t mdel prbability (4..A-3) ($); graphs using cncrete bjects, pictgraphs, frequency tables, hrizntal and vertical bar graphs, line graphs, Venn diagrams, line plts, charts, and tables t rganize, display, explain, and interpret data (4..A, 4..A, 4..A3-4) ($); Venn diagrams t srt data and shw relatinships. Applicatin dels 4

16 4..4.K creates a mathematical mdel t shw the relatinship between tw r mre things, e.g., using pattern blcks, a whle () can be represented as Synthesis dels a (/) r tw (/) r three (3/3) r six (6/6) 4..4.A selects a mathematical mdel and explains why sme mathematical mdels are mre useful than ther mathematical mdels in certain situatins. Evaluatin dels 4.3..K recgnizes and investigates prperties f plane figures (circles, squares, rectangles, triangles, ellipses, rhmbi, ctagns, hexagns, pentagns) using cncrete bjects, drawings, and apprpriate technlgy (.4.Kf) 4.3..K recgnizes, draws, and describes plane figures (circles, squares, rectangles, triangles, ellipses, rhmbi, ctagns, hexagns, pentagns) (.4.Kf) Knwledge Shapes and their Attributes A slves real-wrld prblems by applying the prperties f (.4.Af): plane figures (circles, squares, rectangles, triangles, ellipses, rhmbi, parallelgrams, hexagns) and lines f symmetry, e.g., print yur name r the schl s name in all capital letters. dentify the lines f symmetry in each letter. slids (cubes, rectangular prisms, cylinders, cnes, spheres), e.g., yu want t design smething t stre schl supplies. Which f the slids culd yu use fr strage? Why did yu select that slid? Applicatin Shapes and their Attributes 3

17 4.3..A identifies the plane figures (circles, squares, rectangles, triangles, ellipses, rhmbi, ctagns, hexagns, pentagns, trapezids) used t frm a cmpsite figure (.4.Af) Knwledge Shapes and their Attributes 4.3..K3 describes the slids (cubes, rectangular prisms, cylinders, cnes, spheres, triangular prisms) using the terms faces, edges, and vertices (crners) (.4.Kf) 4.3..K4 recgnizes and describes the square, triangle, rhmbus, hexagn, parallelgram, and trapezid frm a pattern blck set (.4.Kf) 4.3..K5 recgnizes (.4.kf): squares, rectangles, rhmbi, parallelgrams, trapezids as special quadrilaterals; similar and cngruent figures; pints, lines (intersecting, parallel, perpendicular), line segments, and rays 4.3..K6 determines if gemetric shapes and real-wrld bjects cntain line(s) f symmetry and draws the line(s) f symmetry if the line(s) exist(s) (.4.Kf) 4.3..K uses whle number apprximatins (estimatins) fr length, width, weight, vlume, temperature, time, perimeter, and area using standard and nnstandard units f measure (.4.Ka) ($) Analysis Cmprehensin Applicatin Applicatin Shapes and their Attributes Shapes and their Attributes Shapes and their Attributes Shapes and their Attributes Knwledge Estimates 3 5

18 4.3..A slves real-wrld prblems by applying apprpriate measurements; Length t the nearest furth f an inch (.4.Aa), e.g., hw much lnger is the math textbk than the science textbk? Length t the nearest centimeter (.4.Aa), e.g., a new pencil is abut hw many centimeters lng? Temperature t the nearest degree (.4.Aa). e.g., what wuld the temperature utside be if it was a gd day fr sledding? Weight t the nearest whle unit (punds, grams, nnstandard packages f hamburger fr a meatlaf. One f the hamburget packages weighed lb. and 9 zs. The ther packages weighed lb and 8 zs. What is the cmbined weight (t the nearest pund) f the tw packages f hamburger? Time including elapsed time (.4.Aa), e.g., Jy went t the mall at 0:00 a.m. She shpped until 4:5 p.m. Hw lng did she shp at the mall? nths in a year (.4.Aa) e.g., if it takes 08 weeks t get a cllege degree, and Susan has cmpleted ne year, hw many mre weeks des she have t cmplete t get her degree? inutes in an hur (.4.Aa), e.g., Bb spent 40 minutes wrking n a prject fr Science. Hw many hurs has he wrked n the prject? Perimeter f squares, rectangles, and triangles (.4.Af), e.g., a triangle has 3 equal sides f 3 inches. What is the perimeter f the triangle? 4.3..K selects, explains the selectin f, and uses measurement tls, units f measure, and degree f accuracy apprpriate fr a given situatin t measure (.4.Ka) ($): length, width, and height t the nearest furth f an inch r t the nearest centimeter; eighth nearest whle unit f nn-standard unit vlume t the nearest cup, pint, quart, r galln; t the nearest liter; r t the nearest whle unit f a nnstandard unit; weight t the nearest unce r pund r t the nearest whle unit f a nnstandard unit f measure; temperature t the nearest degree; time including elapsed time Applicatin easurement 5

19 4.3..A estimates t check whether r nt measurements and calculatins fr length, width, weight, vlume, temperature, time, and perimeter in real-wrld prblems are reasnable (.4.Aa) ($), e.g., which is the mst reasnable weight fr yur scissrs unces, punds, 0 unces, r 0 punds? A teacher measures ne side f a square desktp at feet. Which f the fllwing perimeters is reasnable fr the desktp feet, 4 square feet, 6 square feet, r 8 feet? Evaluatin easurement K3 states: the number f weeks in a year; the number f unces in a pund; the number f milliliters in a liter, grams in a kilgram, and meters in a kilmeter; the number f items in a dzen 4.3..A3 adjusts riginal measurement r estimatin fr length, width, weight, vlume, temperature, time, and perimeter in real-wrld prblems based n additinal infrmatin (a frame f reference) (.4.Aa) ($), e.g., yur class has a large jar and a small jar. Yu estimate it will take 5 small jars f liquid t fill the large jar. After yu pur the cntents f small jars in, the large jar is mre than half full. Shuld yu need t adjust yur estimate? 4.3..K4 cnverts (.4.Ka): within the custmary system: inches and feet, feet and yards, inches and yards, cups and pints, pints and quarts, quarts and gallns; within the metric system: centimeters and meters 4.3..K5 finds(.4.kf): the perimeter f tw-dimensinal figures given the measures f all the sides. the area f squares and rectangles using cncrete bjects K describes a transfrmatin using cardinal pints r psitinal directins (.4.Ka), e.g., g nrth three blcks and then west fur blcks r mve the triangle three units t the right and tw units up Knwledge easurement Analysis Cnversin Cmprehensin Perimeter, Area & Vlume Knwledge Cardinal Pints & Directins A recgnizes real-wrld transfrmatins (reflectin/flip, rtatin/turn, translatin/slide) (w.r.aa)

20 4.3.3.K recgnizes, perfrms, and describes ne transfrmatin (reflectin/flip, rtatin/turn, translatin/slide) n a tw-dimensinal figure r cncrete bject (.4.Ka) K.3.3.A gives and uses cardinal pints r psitinal directins t mve frm ne lcatin t anther n a map r grid (.4.Aa). Applicatin Applicatin Transfrmatins & Tessellatins Cardinal Pints & Directins S-6 S K3 recgnizes three-dimensinal figures (rectangular prisms, cylinders) and cncrete bjects frm varius perspectives (tp, bttm, sides, crners) (.4.Kf) A3 describes the prperties f gemetric shapes r cncrete bjects that stay the same and the prperties that change when a transfrmatin is perfrmed (.4.Af) K uses a number line (hrizntal/vertical) t mdel whle number multiplicatin facts frm x thrugh x and crrespnding divisin facts (.4.Ka) A slves real-wrld prblems that invlve distance and lcatin using crdinate planes (crdinate grids) and map grids with psitive whle number and letter crdinates (.4.Aa), e.g., identifying lcatins and giving and fllwing directins t mve frm ne lcatin t anther K uses pints in the first quadrant f a crdinate plane (crdinate grid) t identify lcatins (.4.Ka) Aslves real-wrld prblems by pltting whle number rdered pairs in the first quadrant f a crdinate plane (crdinate grid) (.4.Aa) ($), e.g., given that each mvie ticket cst $5, the student graphs the number f tickets bught and the ttal cst f tickets t attend a mvie. Knwledge Perspective & Scale S Analysis Applicatin Applicatin Applicatin Applicatin Number Lines & Crdinate Planes Number Lines & Crdinate Planes Number Lines & Crdinate Planes Number Lines & Crdinate Planes Number Lines & Crdinate Planes S K3 identifies and plts pints as whle number rdered pairs in the first quadrant f a crdinate plane (crdinate grid) (.4.Ka) K4 rganizes whle number data using a T-table and plts the rdered pairs in the first quadrant f a crdinate plane (crdinate grid) (.4.Ka,e) Analysis Analysis Number Lines & Crdinate Planes Number Lines & Crdinate Planes S-6

21 4.4..K recgnizes that the prbability f an impssible event is zer and that the prbability f a certain event is ne (.4.Kg) ($) 4.4..A makes predictins abut a simple event in an experiment r simulatin; cnducts an experiment r simulatin including the use f cncrete bjects; recrds the results in a chart, table, r graph; and uses the results t draw cnclusins abut the event (.4.Ag-h) K lists all pssible utcmes f a simple event in an experiment r simulatin including the use f cncrete bjects (.4.Kg-h) 4.4..A uses the results frm a cmpleted experiment r simulatin f a simple event t make predictins in a variety f real-wrld prblems (.4.Agh), e.g., the manufacturer f Crunchy Flakes puts a prize in 0 ut f every 00 bxes. What is the prbability that a shpper will find a prize in a bx f Crunchy Flakes, if they purchase 0 bxes? Knwledge Prbability Evaluatin Prbability Analysis Prbability S-6 Applicatin Prbability K3 recgnizes and states the prbability f a simple event in an experiment r simulatin (.4.Kg), e.g., when a cin is flipped, the prbability f landing heads up is ½ and the prbability f landing tails up is ½. This can be read as ne ut f tw r ne half 4.4..A3 cmpares what shuld happen (theretical prbability/expected results) with what did happen (empirical prbability/experimental results) in an experiment r simulatin with a simple event (.4.Ag). Cmprehensin Prbability S-6 Analysis Prbability

22 4.4.K rganizes, displays, and reads numerical (quantitative) and nn-numerical (qualitative) data in a clear, rganized, and accurate manner including a title, labels, categries, and whle number intervals using these data displays (.4.Kh) ($): graphs using cncrete bjects, (fr testing, des nt have t use cncrete bjects in items); pictgraphs with a symbl r picture representing ne, tw, five, ten, twenty-five, r ne-hundred including partial symbls when the symbl represents an even amunt; frequency tables (tally marks); hrizntal and vertical bar graphs; Venn diagrams r ther pictrial displays, e.g., glyphs; line plts; charts and tables; line graphs; circle graphs 4.4..A interprets and uses data t make reasnable inferences and predictins, answer questins, and make decisins frm these data displays (.4.Ah) ($): graphs using cncrete bjects; pictgraphs with a symbl r picture representing ne, tw, five, ten, twenty-five, r ne-hundred including partial symbls when the symbl represents an even amunt; frequency tables (tally marks); hrizntal and vertical bar graphs; Venn diagrams r ther pictrial displays; line plts; charts and tables; line graphs K cllects data using different techniques (bservatins, plls, surveys, interviews, r randm sampling) and explains the results (.4.Kh) ($) Synthesis epresenting Data Analysis epresenting Data Applicatin epresenting Data 3

23 4.4..A uses these statistical measures f a data set using whle numbers frm 0 thrugh,000 with less than ten whle number data pints t make reasnable inferences and predictins, answer questins, and make decisins (.4.Ka) ($): minimum and maximum values, range, mde, median when data set has an dd number f data pints, mean when data set has a whle number mean 4.4..K3 identifies, explains, and calculates r finds these statistical measures f a data set with less than ten whle number data pints using whle numbers frm 0 thrugh,000 (.4.Ka) ($): minimum and maximum values, range, mde, median when data set has an dd number f data pints, mean when data set has a whle number mean A3 recgnizes that the same data set can be displayed in varius frmats including the use f cncrete bjects (.4.Ah) ($). Analysis Statistics Analysis Statistics Applicatin Statistics A4 recgnizes and explains the effects f scale and interval changes n graphs f whle number data sets (.4.Ah). Analysis Statistics