District Adopted Materials: Every Day Math (2007)

Transcription

1 Grade: Fifth Curse: athematics District Adpted aterials: Every Day ath (2007) Standard 1: Number and Cmputatin The student uses numerical and cmputatinal cncepts and prcedures in a variety f situatins. Benchmark 1: Number Sense The student demnstrates number sense fr integers, fractins, decimals, and mney in a variety f situatins. Benchmark 2: Number Systems and Their Prperties The student demnstrates an understanding f the whle number system; recgnizes, uses, and explains the cncepts f prperties as they relate t the whle number system; and extends these prperties t integers, fractins (including mixed numbers), and decimals. Benchmark 3: Estimatin The student uses cmputatinal estimatin with whle numbers, fractins, decimals, and mney in a variety f situatins. Benchmark 4: Cmputatin The student mdels, perfrms, and explains cmputatin with whle numbers, fractins including mixed numbers, and decimals including the use f cncrete bjects in a variety f situatins. Standard 2: Algebra The student uses algebraic cncepts and prcedures in a variety f situatins. Benchmark 1: Patterns The student recgnizes, describes, extends, develps, and explains relatinships in patterns in a variety f situatins. Benchmark 2: Variables, Equatins, and Inequalities The student uses variables, symbls, whle numbers, and algebraic expressins in ne variable t slve linear equatins in a variety f situatins. Benchmark 3: Functins The student recgnizes, describes, and examines whle number relatinships 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 1: Gemetric Figures and Their Prperties The student recgnizes gemetric shapes and cmpares their prperties in a variety f situatins. Benchmark 2: easurement and Estimatin The student estimates, measures, and uses measurement frmulas in a variety f situatins. Benchmark 3: Transfrmatinal Gemetry The student recgnizes and perfrms transfrmatins n gemetric shapes including the use f 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 1: 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 2: Statistics The student cllects, rganizes, displays, explains, and interprets numerical (ratinal numbers) and nn-numerical data sets in a variety f situatins with a special emphasis n measures f central tendency.

2 Indicatrs The student Blm s Strand Sequence Teaching Time.1.1.K1 N knws, explains, and uses equivalent representatins fr ($): whle numbers frm 0 thrugh 1,000,000 (2.4.K1a-b); fractins greater than r equal t zer (including mixed numbers) (2.4.K1c); decimals greater than r equal t zer thrugh hundredths place and when used as mnetary amunts (2.4.K1c).1.1.A1 slves real-wrld prblems using equivalent representatins and cncrete bjects t ($): cmpare and rder (2.4.A1a-d) whle numbers frm 0 thrugh 1,000,000; 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; fractins greater than r equal t zer (including mixed numbers), e.g., Frank ate 2 ½ pizzas, Tara ate 9/4 f the pizza. Frank says he ate mre. Is he crrect? Use a mdel t explain. With drawings and shadings, student shws amunt f pizza eaten by Frank and the amunt eaten by Tara. decimals greater than r equal t zer t hundredths place e.g., uses decimal squares, mney (dimes as tenths, pennies as hundredths), the crrect amunt f hundred chart filled in, r a number line t shw that.42 is less than.9. integers, e.g., plt winter temperature fr a very cld regin fr a week (use Internet data); represent n a thermmeter,number line, and with integers; add and subtract whle numbers frm 0 thrugh 0,000 and decimals when used as mnetary amunts (2.4.A1a,c), e.g.,use real mney t shw at least 2 ways t represent $ then subtract the cst f a new cmputer setup: multiply thrugh a tw-digit whle number by a tw-digit whle number (2.4.A1a-b), e.g., Gerge charges $23 fr mwing a lawn. Hw much will he make after he mws 3 lawns? epresent the $23 with mney mdels - 2 $ bills and 3 $1 bills and repeat that 3 times r represent the $23 using base ten blcks r 23 x 3 r ; divide thrugh a fur-digit whle number by a tw-digit whle Equivalent epresentatins Equivalent epresentatins 1

3 number (2.4.A1a-b), e.g., the By Scut trp cllected cans and held bake sales fr a year and earned $ The mney will be divided evenly amng the 12 trp members t buy new unifrms. epresent each by s share f the mney at least 2 ways - traditinal divisin; use 4 hundreds, 9 tens, 2 nes, and 6 dimes.1.1.k2 cmpares and rders (2.4.K1a-c) ($) : integers, fractins greater than r equal t zer (including mixed numbers), decimals greater than r equal t zer thrugh hundredths place.1.1.a2 determines whether r nt slutins t real-wrld prblems that invlve the fllwing are reasnable ($): whle numbers frm 0 thrugh 0,000 (2.4.A1a-b), e.g., the ftball is placed n yur wn -yard line with 90 yards t g fr a tuchdwn. After the first dwn, yur team gains 7 yards. On the secnd dwn, yur team lses 4 yards. Is it reasnable fr the ftball t be placed n the 3-yard line fr the beginning f the third dwn? fractins greater than r equal t zer (including mixed numbers) (2.4.A1c), e.g., explain if it is reasnable t say that a dg is ½ bxer, ¼ bulldg, ¼ cllie, and ¼ rtweiler; decimals greater than r equal t zer thrugh hundredths place (2.4.A1c), e.g., five peple a ate pizza. Is it reasnable t say that each persn ate.3 f the pizza?.1.1.k3 explains the numerical relatinships (relative magnitude) between whle numbers, fractins greater than r equal t zer (including mixed numbers), and decimals greater than r equal t zer thrugh hundredths place (2.4.K1a-c).1.1.K4 knws equivalent percents and decimals fr ne whle, nehalf, ne-furth, three-furths, and ne tenth thrugh nine tenths (2.4.K1c), e.g., 1 = 0% = 1.0, 3/4 = 7% =.7, 3/ = 30% = K identifies integers and gives real-wrld prblems where integers are used (2.4.K1a), e.g., making a T-table f the temperature each hur ver a twelve hur perid in which the temperature at the beginning is degrees and then decreases 2 degrees per hur.1.2.k1 classifies subsets f numbers as integers, whle number, fractins (including mixed numbers), r decimals (2.4.K1a-c, 2.4.K1k) Synthesis Cmprehensin Knwledge Cmpare & Order Cmpare & Order Cmpare & Order Equivalent epresentatin Numerical ecgnitin Number Systems & their Prperties.1.2.K2 identifies prime and cmpsite numbers frm 0 thrugh 0 Number Systems & their

4 .1.2.K3 uses the cncepts f these prperties with whle numbers, integers, fractins greater than r equal t zer (including mixed numbers), and decimals greater than r equal t zer and demnstrates their meaning including the use f cncrete bjects (2.4.K1a) ($): cmmutative prperties f additin and multiplicatin, e.g., = and 12 x 1 = 1 x 12; assciative prperties f additin and multiplicatin, e.g., 4 + (3 + ) = (4 + 3) + ; zer prperty f additin (additive identity) and prperty f ne fr multiplicatin (multiplicative identity), e.g., = 342 and 76 x 1 = 76; symmetric prperty f equality, e.g., 3 = is the same as = 3; zer prperty f multiplicatin, e.g., 438,223 x 0 = 0; distributive prperty, e.g., 7(3 + ) = 7(3) + 7(); substitutin prperty, e.g., if a = 3 and a = b, then b = 3 Prperties Number Systems & their Prperties.1.2.A1 slves real-wrld prblems with whle numbers frm 0 thrugh 0,000 and decimals thrugh hundredths using place value mdels; mney; and the cncepts f these prperties t explain reasning (2.4.A1a-c,e) ($): cmmutative and assciative prperties f additin and multiplicatin, e.g., lay ut a $, $ and $20 bills. Ask fr the ttal f the mney. The student says: Because yu can add in any rder (cmmutative) I can rearrange the mney and cunt $20, $ and $ fr $20 + $ + $ r Lay ut 4 $ bills. The student is asked the amunt. The student says: I dn t knw what 4 x is, but I knw x 4 is $20 and since multiplicatin can be dne in any rder, then it is $20. zer prperty f additin, e.g., have students lay ut 6 dimes. Tell them t add zer. Hw many dimes? = 6 prperty f ne fr multiplicatin, e.g., there are 24 students in ur class. I want ne math bk per student, s I cmpute 24 x1= 24. ultiplying times 1 des nt change the prduct because it is ne grup f 24. symmetric prperty f equality, e.g., Pat knws he has $6. He has 2 twenty-dllar bills in his wallet. Hw much des he have at hme in his bank? This can be represented as 6 = (2 x 20) + _, s ( 2 x 20) + _ =6 6 = 40 + _, s 40 + _ = 6 6 = , s = 6.

5 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. distributive prperty, e.g., Juan has 7 quarters and 7 dimes. What is the ttal amunt f mney he has? 7($.2 + $.) = 7($.2) + 7($.)..1.2.A2 perfrms varius cmputatinal prcedures with whle numbers frm 0 thrugh 0,000 using the cncepts f these prperties; extends these prperties t fractins greater than r equal t zer (including mixed numbers) and decimals greater than r equal t zer thrugh hundredths place; and explains hw the prperties were used (2.4.A1a-c,e): cmmutative and assciative prperties f additin and multiplicatin, e.g., given 4.2 x, the student says: I knw that it is 42 because I knw that x 4.2 = 42, since yu can multiply in any rder and get the same answer. r The student says I dn t knw what is, but I knw my dubles f 8 + 8, s I make the 9 int and after adding 8 and 8, I add 1 mre; zer prperty f additin, e.g., given , the student says: I knw that the answer is 964 because adding 0 des nt change the answer (sum); prperty f ne fr multiplicatin, e.g., $9.62 x 1. The student says: I knw the prduct is still $9.62 because multiplicatin by ne never changes the prduct. It is like if I had $9.62 in ne pile, I wuld just have $9.62; symmetric prperty f equality, e.g., given _ = ½ + ¼, the student says: That is the same as ½ + ¼ because I must make bth sides equal; zer prperty f multiplicatin e.g., given.7 x 0, the student says: I knw the answer (prduct) is zer because n matter hw many factrs yu have, multiplying by 0, the prduct is 0; distributive prperty, e.g., given 4 x 614, the student can explain that yu can slve it (in yur head?) by cmputing 4(600) + 4() + 4(4), which is 2, = 2, K4 recgnizes man Numerals that are used fr dates, n clck faces, and in utlines.1.2.k recgnizes the need fr integers, e.g., with temperature, belw zer is negative and abve zer is psitive; in finances, mney in yur pcket is psitive and mney wed smene is negative.1.2.a3 states the reasn fr using integers, whle numbers, fractins (including mixed numbers), r decimals when slving a given Knwledge Number Systems & their Prperties Number Systems & their Prperties I 4

6 real wrld prblem (2.4.A1a-c) ($)..1.3.K1 estimates whle numbers quantities frm 0 thrugh 0,000; fractins greater than r equal t zer (including mixed numbers); decimals greater than r equal t zer thrugh hundredths place; and mnetary amunts t $,000 using varius cmputatinal methds including mental math, paper and pencil, cncrete materials, and apprpriate technlgy (2.4.K1a-c) ($).1.3.A1 adjusts riginal estimate using whle numbers frm 0 thrugh 0,000 f a real-wrld prblem based n additinal infrmatin (a frame f reference) (2.4.A1a) ($), e.g., given a large cntainer f marbles, estimate the quantity f marbles. Then, using a smaller cntainer filled with marbles, cunt the number f marbles in the smaller cntainer and adjust yur riginal estimate..1.3.k2 N uses varius estimatin strategies t estimate whle number quantities frm 0 thrugh 0,000; fractins greater than r equal t zer (including mixed numbers); decimals greater than r equal t zer thrugh hundredths place; and mnetary amunts t $,000 and explains hw varius strategies are used (2.4.K1a-c) ($).1.3.A2 estimates t check whether r nt the result f a real-wrld prblem using whle numbers frm 0 thrugh 0,000; fractins greater than r equal t zer (including mixed numbers); decimals greater than r equal t zer t tenths place; and mnetary amunts t $,000 is reasnable and makes predictins based n the infrmatin (2.4.A1a-c) ($), e.g., at yur birthday party, yu ate 4 ½ pepperni pizzas, 3 ¼ cheese pizzas, and 2 ¾ sausage pizzas. On the bill they charged yu fr pizzas. Is that reasnable? If pizzas cst $6.99 each, abut hw much shuld yu save fr yur next birthday party?.1.3.k3 recgnizes and explains the difference between an exact and an apprximate answer (2.4.K1a-c).1.3.A3 selects a reasnable magnitude frm given quantities based n a real-wrld prblem using whle numbers frm 0 thrugh 0,000 and explains the reasnableness f selectin (2.4.A1a), e.g., abut hw many tulips can fit in the flwer vase, 2,, r 2? The student chses ten and explains that the vase at hme is a jelly jar and either tw r ten will fit, but ten lks prettier..1.3.k4 explains the apprpriateness f an estimatin strategy used and whether the estimate is greater than (verestimate) r less than (underestimate) the exact answer (2.4.K1a).1.3.A4 determines if a real-wrld prblem calls fr an exact r apprximate answer using whle numbers frm 0 thrugh 0,000 and perfrms the apprpriate cmputatin using varius Estimatin 8 Estimatin S- Estimatin Estimatin Estimatin 9 12

7 cmputatinal methds including mental math, paper and pencil, cncrete materials, and apprpriate technlgy (2.4.A1a) ($)..1.4.K1 cmputes with efficiency and accuracy using varius cmputatinal methds including mental math, paper and pencil, cncrete materials, and apprpriate technlgy (2.4.K1a).1.4.K2 perfrms and explains these cmputatinal prcedures: N divides whle numbers thrugh a 2-digit divisr and a 4- digit dividend with the remainder as a whle number r a fractin using paper and pencil (2.4.K1a-b), e.g., = 3 r 12 r 3 ½; divides whle numbers beynd a 2-digit divisr and a 4- digit dividend using apprpriate technlgy (2.4.K1a-b), e.g., 73, = 2,038; N adds and subtracts decimals frm thusands place thrugh hundredths place (2.4.K1c); N multiplies decimals up t three digits by tw digits frm hundreds place thrugh hundredths place (2.4.K1c); N adds and subtracts fractins (like and unlike denminatrs) greater than r equal t zer (including mixed numbers) withut regruping and withut expressing answers in simplest frm with special emphasis n manipulatives, drawings, and mdels; (2.4.K1c); N multiplies and divides by ; 0; 1,000; r single-digit multiples f each (2.4.K1a-b), e.g., r 4, A1 N slves ne- and tw-step real-wrld prblems using these cmputatinal prcedures ($) (Fr the purpse f assessment, tw-step culd include any cmbinatin f a, b, c, d, e, r f.): adds and subtracts whle numbers frm 0 thrugh 0,000 (2.4.A1a-b); e.g., Lee buys a bike fr $139, a helmet fr $29 and a reflectr fr $6. Hw much f his $200 check frm his grandparents will he have left? multiplies thrugh a fur-digit whle number by a tw-digit whle number (2.4.A1a-b), e.g., at the amusement park, nday s attendance was 4,414 peple. Tuesday s attendance was 3,042 peple. If the cst per persn is $23, hw much mney was cllected n thse days? multiplies mnetary amunts up t $1,000 by a ne- r tw-digit whle number (2.4.A1c), e.g., what is the cst f 4 items each priced at $3.49? divides whle numbers thrugh a 2-digit divisr and a 4- digit dividend with the remainder as a whle number r a fractin (2.4.A1a-c); Cmputatin 14 Cmputatin I Synthesis Cmputatin I 2 2

8 adds and subtracts decimals frm thusands place thrugh hundredths place when used as mnetary amunts (2.4.A1a-c) (The set f decimal numbers includes whle numbers.), e.g., at the track meet, Peter ran the 0 meter dash in 12.3 secnds. Tanner ran the same race in secnds. Hw much faster was Tanner? multiplies and divides by ; 0; and 1,000 and single digit multiples f each (, 20, 30, etc.; 0, 200, 300, etc.; 1,000; 2,000; 3,000) (2.4.A1a-b), e.g., atti has 1,90 stamps t place in her stamp album. 30 stamps fit n a page. What is the minimum number f pages she needs in her album? finds percent f ratinal numbers (80% f 0= x).1.4.k3 reads and writes hrizntally, vertically, and with different peratinal symbls the same additin, subtractin, multiplicatin, r divisin expressin.1.4.k4 N identifies, explains, and finds the greatest cmmn factr and least cmmn multiple f tw r mre whle numbers thrugh the basic multiplicatin facts frm 1 x 1 thrugh 12 x 12 (2.4.K1d).2.1.K1 uses cncrete bjects, drawings, and ther representatins t wrk with these types f patterns(2.4.k1a): repeating patterns, e.g., 9,, 11, 9,, 11, ; grwing patterns, e.g., 20, 30, 28, 38, 36, where the rule is add, then subtract 2; r 2,, 8, as an example f an arithmetic sequence each term after the first is fund by adding the same number t the preceding term.2.1.a1 generalizes these patterns using a written descriptin: numerical patterns (2.4.K1a) ($), patterns using gemetric shapes thrugh tw attribute changes(2.4.a1a,g), measurement patterns (2.4.A1a), patterns related t daily life (2.4.A1a).2.1.K2 uses these attributes t generate patterns: cunting numbers related t number thery (2.4.K1a), e.g., multiples r perfect squares; whle numbers (2.4.K1a) ($), e.g., ; 0; 1,000;,000; 0,000; (pwers f ten); gemetric shapes thrugh tw attribute changes (2.4.K1g), e.g., when the next shape has ne mre Cmputatin I Cmputatin I S- Patterns Patterns

9 side; r when bth the clr and the shape change at the same time; measurements (2.4.K1a), e.g., 3 m, 6 m, 9 m, ; things related t daily life (2.4.K1a), e.g., sprts scres, lngitude and latitude, electins, eras, r apprpriate tpics acrss the curriculum; things related t size, shape, clr, texture, r mvement (2.4.K1a), e.g., square dancing mves (kinesthetic patterns).2.1.a2 recgnizes multiple representatins f the same pattern (2.4.A1a)($), e.g., ; 0; 1,000; represented as ; x ; x x ; ; represented as a rd, a flat, a cube, using base ten blcks; r represented by a $ bill; a $0 bill; a $1,000 bill;..2.1.k3 identifies the rule, states, and cntinues a pattern presented in varius frmats including numeric (list r table), visual (picture, table, r graph), verbal (ral descriptin), kinesthetic (actin), and written (2.4.K1a) ($).2.1.K4 generates: a pattern (repeating, grwing) (2.4.K1a). a pattern using a functin table (input/utput machines, T- tables) (2.4.K1g) Patterns Synthesis Patterns K1 explains and uses variables and symbls t represent unknwn whle number quantities frm 0 thrugh 1,000 and variable relatinships (2.4.K1a) Variable, Equatins & Inequalities.2.2.A1 represents real-wrld prblems using variables, symbls, and ne-step equatins with unknwn whle number quantities frm 0 thrugh 1,000 (2.4.A1a,e) ($); e.g., Yur parents say yu must read minutes each and every day f the next year. Hw many minutes will yu read? This is represented by 36 x =..2.2.K2 N slves ne-step linear equatins with ne variable and a whle number slutin using additin and subtractin with whle numbers frm 0 thrugh 0 and multiplicatin with the basic facts (2.4.K1a,e) ($), e.g., 3y = 12, 4 = 17 + q, r r 42 = A2 generates ne-step linear equatins t slve real-wrld prblems with whle numbers frm 0 thrugh 1,000 with ne unknwn and a whle number slutin using additin, subtractin, multiplicatin, and divisin (2.4.A1a,e) ($), e.g., Ninety-six items are being shared with fur peple. Hw much des each persn receive? becmes 96 4 = n Variable, Equatins & Inequalities Variable, Equatins & Inequalities Variable, Equatins & Inequalities S-

10 .2.2.K3 explains and uses equality and inequality symbls (=,, <,, >, ) and crrespnding meanings (is equal t, is nt equal t, is less than, is less than r equal t, is greater than, is greater than r equal t) with whle numbers frm 0 t 0,000 (2.4.K1a-b) ($).2.2.A3 generates (2.4.A1a,e) ($): a real-wrld prblem with ne peratin t match a given additin, subtractin, multiplicatin, r divisin equatin using whle numbers frm 0 thrugh 1,000 (2.4.A1a), e.g., given 9 = x students write: There are 9 kids at camp wh need t be divided int teams f. Hw many teams will there be? generates number cmparisn statements using equality and inequality symbls (=, <, >) with whle numbers, measurement, and mney e.g., 1 ft < 1 in r quarters > $ K4 recgnizes rati as a cmparisn f part-t-part and part-twhle relatinships (2.4.K1a), e.g., the relatinship between the number f bys and the number f girls (part-t-part) r the relatinship between the number f girls t the ttal number f students in the classrm (part-t-whle).2.3.k1 states mathematical relatinships between whle numbers frm 0 thrugh,000 using varius methds including mental math, paper and pencil, cncrete bjects, and apprpriate technlgy (2.4.K1a) ($).2.3.A1 represents and describes mathematical relatinships between whle numbers frm 0 thrugh,000 using written and ral descriptins, tables, graphs, and symblic ntatin (2.4.A1a).2.3.K2 finds the values, determines the rule, and states the rule using symblic ntatin with ne peratin f whle numbers frm 0 thrugh,000 using a vertical r hrizntal functin table (input/utput machine, T-table) (2.4.K1f), e.g., using the functin table, fill in the values and find the rule, the rule is N 80 Knwledge Cmprehensin Variable, Equatins & Inequalities Variable, Equatins & Inequalities elatins & Functins elatins & Functins elatins & Functins I I I N ? 2 7?? ?? A2 finds the rule, states the rule, and extends numerical patterns using real-wrld prblems with whle numbers frm 0 thrugh,000 (2.4.A1a,f) ($), e.g., the class sells ckies at lunch recess t raise mney fr a field trip. The gal is t sell 3,000 ckies at 2 each. A student ntices that every 4th day, a new case f

11 ckies has t be pened. Each case hlds 40ckies. If the class keeps selling ckies at the same rate, hw many days will it take t sell 3,000 ckies? A student s answer might be: 28 days because that will be ver the gal r n day 27 until 3,000 ckies are sld. Day # f ckies sld K3 generalizes numerical patterns using whle numbers frm 0 thrugh,000 up t tw peratins by stating the rule using wrds, e.g., If the sequence is 2400, 1200, 600, 300,, ; in wrds, the rule culd be split the number in half r divide the previus number by 2 r if the sequence is 4, 11, 2, 3, 9, ; in wrds, the rule culd be duble the number and add 3 t get the next number r multiply the number by 2 and add 3).2.3.K4 uses a functin table (input/utput machine, T-table) t identify, plt, and label whle number rdered pairs in the first quadrant f a crdinate plane (2.4.K1a,f).2.3.K plts and lcates pints fr integers (psitive and negative whle numbers) n a hrizntal number line and vertical number line (2.4.K1a).2.3.K6 describes whle number relatinships using letters and symbls.2.4.k1 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 and mathematical relatinships and t slve equatins (1.1.K1a, 1.1K1c, 1.1.K2, 1.1.K3, 1.1.K, 1.2.K1, 1.2.K3, 1.3.K1-4, 1.4.K1, 1.4.K2a-b, 1.4.K.2f, 2.1.K1, 2.1.K2a-b, 2.1.K2d-h, 2.1.K2, 2.2.K1-4, 2.3.K1, 2.3.K4-, 3.1.K1-6, elatins & Functins I Pints I S- Cmprehensin elatins & Functins I dels

12 3.2.K1-4, 3.3.K1-2, 3.4.K1-4, 4.2.K3) ($); place value mdels (place value mats, hundred charts, base ten blcks, r unifix cubes) t cmpare, rder, and represent numerical quantities and t mdel cmputatinal prcedures (1.1.K1a, 1.1.K2, 1.1.K4, 1.2.K1, 1.3.K1-3, 1.4.K2a-b, 1.4.K2f, 2.2.K3) ($); fractin and mixed number mdels (fractin strips r pattern blcks) and decimal and mney mdels (base ten blcks r cins) t cmpare, rder and represent numerical quantities (1.1.K1b, 1.1.K2-4, 1.2.K1, 1.3.K1-3, 1.4.K2c-e, 4.1.K4) ($); factr trees t find least cmmn multiple and greatest cmmn factr (1.2.K2, 1.4.K4); equatins and inequalities t mdel numerical relatinships (2.2.K2) ($) functin tables (input/utput machines, T-tables) t mdel numerical and algebraic relatinships (2.1.K1c, 2.1.K1j, 3.1.K1-8, 3.2.K7-8, 3.3.K1-3) ($) tw-dimensinal gemetric mdels (gebards r dt paper) t mdel perimeter, area, and prperties f gemetric shapes and three-dimensinal mdels (nets r slids) and real-wrld bjects t cmpare size and t mdel vlume and prperties f gemetric shapes (2.1.K2c, 2.1.K4b, 3.2.K, 3.3.K3, 4.1.K2); tree diagrams t rganize attributes thrugh three different sets and determine the number f pssible cmbinatins (4.1.K2, 4.2.K1a-d, 4.2.K1f-I; 4.2.K2, 4.2); tw- and three-dimensinal gemetric mdels (spinners r number cubes) and prcess mdels (cncrete bjects, pictures, diagrams, r cins) t mdel prbability (4.1.K1-3, 4.2.K1e, 4.2.K2) ($) ; graphs using cncrete bjects, pictgraphs, frequency tables, bar graphs, line graphs, circle graphs, Venn diagrams, line plts, charts, tables, and single stem-andleaf plts t rganize and display data (4.1.K2, 4.2.K1-2) ($) ; Venn diagrams t srt data and shw relatinships.2.4.a1 The student 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, hundred charts, measurement tls,

13 multiplicatin arrays, divisin sets, r crdinate planes/grids) t mdel cmputatinal prcedures, mathematical relatinships, and prblem situatins and t slve equatins (1.1.A1, 1.1.A2a, 1.2.A1-3, 1.3.A1-4,1.4.A1a-b, 1.4.A1d-f, 2.1.A1a, 2.1.A1c-d, 2.1.A2, 2.2.A1-3, 2.3.A1-3, 3.2.A1a-f, 3.2.A2-4, 3.3.A1, 3.4.A A2) ($); place value mdels (place value mats, hundred charts, base ten blcks, r unifix cubes) t mdel prblem situatins (1.1.A1,1.1.A2a, 1.2.A1-3, 1.3.A2, 1.4.A1a-b, 1.4.A1f, 1.4.A3a-e, 2.2.K3) ($); fractin and mixed number mdels (fractin strips r pattern blcks) and decimal and mney mdels (base ten blcks r cins) t cmpare, rder, and represent numerical quantities (1.1.A1a-b, 1.1.A2b-c, 1.2.A1-3, 1.3.A2, 1.4.A1c-e) ($); factr trees t find least cmmn multiple and greatest cmmn factr; equatins and inequalities t mdel numerical relatinships (2.1.A1-2, 2.2.A1-3) ($); functin tables (input/utput machines, T-tables) t mdel numerical and algebraic relatinships (2.3.A2, 3.2.A1g-h, 3.3.A3) ($); tw-dimensinal gemetric mdels (gebards r dt paper) t mdel perimeter, area, and prperties f gemetric shapes and three-dimensinal mdels (nets r slids) and real-wrld bjects t cmpare size and t mdel vlume and prperties f gemetric shapes (2.1.A1b, 3.1.A1-2, 3.2.A4, 4.1.A1-3); scale drawings t mdel large and small real-wrld bjects (3.3.A2); tree diagrams t rganize attributes thrugh three different sets and determine the number f pssible cmbinatins; tw- and three-dimensinal gemetric mdels (spinners r number cubes) and prcess mdels (cncrete bjects, pictures, diagrams, r cins) t mdel prbability (4.1.A1-3, 4.2.A1) ($); graphs using cncrete bjects, pictgraphs, frequency tables, bar graphs, line graphs, circle graphs, Venn diagrams, line plts, charts, and tables t rganize, display, explain, and interpret data (2.3.A3; 4.1.A1-2, 4.2.A1, 4.2.A3-4) ($);

14 Venn diagrams t srt data and shw relatinships..2.4.k2 selects and determines r creates mathematical mdels t shw the relatinship between tw r mre things, e.g., using trapezids t represent numerical quantities. r 1/2 Synthesis dels S r r 1 1/2 2 r A2 selects a mathematical mdel and explains why sme mathematical mdels are mre useful than ther mathematical mdels in certain situatins..3.1.a1 the student slves real-wrld prblems by applying the prperties f plane figures (circles, squares, rectangles, triangles, ellipses, rhmbi, parallelgrams, hexagns, pentagns) and the line(s) f symmetry; e.g., twins are having a birthday party. The rectangular birthday cake is t be cut int tw pieces f equal size and with the same shape. Hw wuld the cake be cut? Wuld the cut be a line f symmetry? Hw wuld yu knw? slids (cubes, rectangular prisms, cylinders, cnes, spheres, triangular prisms) emphasizing faces, edges, vertices, and bases; e.g., ribbn is t be glued n all f the edges f a cube. If ne edge measures inches, hw much ribbn is needed? If a letter was placed n each face, hw many letters wuld be needed? intersecting, parallel, and perpendicular lines; e.g., relate these terms t maps f city streets, bus rutes, r walking paths. Which street is parallel t the street where the schl is lcated? Shapes & their Attributes.3.1.K1 recgnizes and investigates prperties f plane figures and Shapes & their S-8

15 slids using cncrete bjects, drawings, and apprpriate technlgy (2.4.K1g)..3.1.K2 recgnizes and describes (2.4.K1g): regular plygns having up t and including ten sides; similar and cngruent figures..3.1.k3 recgnizes and describes the slids (cubes, rectangular prisms, cylinders, cnes, spheres, triangular prisms, rectangular pyramids, triangular pyramids) using the terms faces, edges, and vertices (crners) (2.4.K1g).3.1.K4 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) (2.4.K1g).3.1.A2 identifies the plane figures (circles, squares, rectangles, triangles, ellipses, rhmbi, ctagns, pentagns, hexagns, trapezids, parallelgrams) used t frm a cmpsite figure (2.4.A1g)..3.1.K recgnizes, draws, describes and cmpares (2.4.K1g): pints, lines, line segments, and rays; angles as right, btuse, r acute and triangles by side and angle (right, acute, btuse, scalene, equilateral and issceles).3.1.k6 recgnizes and describes the difference between intersecting, parallel, and perpendicular lines.3.1.k7 identifies circumference, radius, and diameter f a circle (2.4.K1g).3.2.K1 determines and uses whle number apprximatins (estimatins) fr length, width, weight, vlume, temperature, time, perimeter, and area using standard and nnstandard units f measure (2.4.K1a) ($).3.2.A1 slves real-wrld prblems by applying apprpriate measurements and measurement frmulas ($): length t the nearest eighth f an inch r t the nearest centimeter (2.4.A1a), e.g., in science, we are studying butterflies. What is the wingspan f each f the butterflies studied t the nearest eighth f an inch? temperature t the nearest degree (2.4.A1a), e.g., what wuld the temperature be if it was a gd day fr swimming? weight t the nearest whle unit (punds, grams, nnstandard units) (2.4.A1a), e.g., if yu bught 200 bricks (each ne weighed punds), hw much wuld the whle lad f bricks weigh? Synthesis Attributes; Special Quadrilaterals Shapes & their Attributes Shapes & their Attributes Cmpse & Decmpse Pints, Lines, ays & Angles S-8 S- Pints, Lines, ays & Angles Knwledge Circles I Estimates

16 time including elapsed time (2.4.A1a), e.g., Bb left Wichita at :4 a.m. He arrived in Kansas city at 1:30. Hw lng did it take Bb t travel t Kansas City? hurs in a day, days in a week, and days and weeks in a year (2.4.A1a), e.g., Jhn spent 9 days in New Yrk City. Hw many weeks did he stay in New Yrk City? mnths in a year and minutes in an hur (2.4.A1a), e.g., it tk Susan 180 minutes t cmplete her hmewrk assignment. Hw many hurs did she spend ding hmewrk? perimeter f squares, rectangles, and triangles (2.4.A1g), e.g., ark wants t put up a fence up in his rectangle-shaped back yard. If his yard measures 18 feet by 36 feet, hw many feet f fence will he need t g arund his yard? area f squares and rectangles (2.4.A1g), e.g., a farmer's square-shaped field is 3 feet n each side. Hw many square feet des he have t plw?.3.2.k2 selects, explains the selectin f, and uses measurement tls, units f measure, and degree f accuracy apprpriate fr a given situatin t measure length, width, weight, vlume, temperature, time, perimeter, and area using (2.4.K1a) ($): custmary units f measure t the nearest furth and eighth inch, metric units f measure t the nearest centimeter, nnstandard units f measure t the nearest whle unit, time including elapsed time..3.2.a2 slves real-wrld prblems that invlve cnversins within the same measurement system: inches and feet, feet and yards, inches and yards, cups and pints, pints and quarts, quarts and gallns, centimeters and meters (2.4.A1a), e.g., yu estimate that each persn will chew 6 inches f bubblegum tape. If each package has 9 feet f bubblegum tape, hw many peple will get gum frm that package?.3.2.k3 states the number f feet and yards in a mile (2.4.K1a)..3.2.A3 estimates t check whether r nt measurements r calculatins fr length, weight, temperature, time, perimeter, and area in real-wrld prblems are reasnable (2.4.A1a) ($), e.g. is it reasnable t say yu need 30 ml f water t fill a fish tank r wuld yu need 30 L f water t fill the fish tank?.3.2.k4 cnverts (2.4.K1a): within the custmary system: inches and feet, feet and yards, inches and yards, cups and pints, pints and quarts, quarts and gallns, punds and unces; easurement Cnversin 20

17 within the metric system: centimeters and meters, meters and kilmeters, milliliters and liters, grams and kilgrams (prefixes: kil, hectr, deca, deci, centi, milli and the relatinship between them.3.2.a4 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) (2.4.A1a,g) ($), e.g., after estimating the utside temperature t be 7º F, yu find ut that yesterday s high temperature at 3 p.m. was 62º. Shuld yu adjust yur estimate? Why r why nt?.3.2.k knws and uses perimeter (circumference) and area frmulas fr squares, rectangles, triangles, parallelgrams and circles.(2.4.k1g).3.3.k1 recgnizes and perfrms thrugh tw transfrmatins Perimeter, Area & Vlume Transfrmatins & Tessellatins (reflectin, rtatin, translatin) n a tw-dimensinal figure (2.4.K1a).3.3.A1 describes and draws a tw-dimensinal figure after perfrming ne transfrmatin (reflectin, rtatin, translatin) (2.4.A1a)..3.3.K2 recgnizes when an bject is reduced r enlarged (2.4.K1a) Cmprehensin Transfrmatins & Tessellatins.3.3.K3 recgnizes three-dimensinal figures (rectangular prisms, cylinders, cnes, spheres, triangular prisms, rectangular pyramids) frm varius perspectives (tp, bttm, side, crners) (2.4.K1g).3.3.A2 makes scale drawings f tw-dimensinal figures using a simple scale and grid paper (2.4.A1h), e.g., using the scale 1 cm = 3 m, the student makes a scale drawing f the classrm..3.4.k1 lcates and plts pints n a number line (vertical/hrizntal) using integers (psitive and negative whle numbers) (2.4.K1a).3.4.K2 explains mathematical relatinships between whle numbers, fractins, and decimals and where they appear n a number line (2.4.K1a).3.4.A1 slves real-wrld prblems that invlve distance and lcatin using crdinate planes (crdinate grids) and map grids with psitive whle number and letter crdinates (2.4.A1a), e.g., identifying lcatins and giving and fllwing directins t mve frm ne lcatin t anther..3.4.k3 identifies and plts pints as rdered pairs in the first quadrant f a crdinate plane, the ther three quadrants and in real wrld prblems (crdinate grid) (2.4.K1a).3.4.A2 slves real-wrld prblems by pltting rdered pairs in the first quadrant f a crdinate plane and the ther three quadrants f Perspective & Scale Perspective & Scale Number Lines & Crdinate Planes Number Lines & Crdinate Planes Number Lines & Crdinate Planes Number Lines & Crdinate Planes S- I

18 the crdinate plane (crdinate grid) (2.4.A1a) ($), e.g., graph daily the cumulative number f recess minutes in a -day schl week..3.4.k4 rganizes whle number data using a T-table and plts the rdered pairs in the first quadrant f a crdinate plane (crdinate grid) (2.4.K1a,f).4.1.K1 recgnizes that all prbabilities range frm zer (impssible) thrugh ne (certain) (2.4.K1i) ($).4.1.K2 lists all pssible utcmes f a simple event in an experiment r simulatin in an rganized manner including the use f cncrete bjects (2.4.K1g-j) vcab: cmpund event Number Lines & Crdinate Planes Prbability Knwledge Prbability K3 recgnizes a simple event in an experiment r simulatin where the prbabilities f all utcmes are equal (2.4.K1i).4.1.K4 represents the prbability f a simple event in an experiment r simulatin using fractins, decimals and percents (2.4.K1c).4.1.A1 cnducts an experiment r simulatin with a simple event including the use f cncrete materials; recrds the results in a chart, table, r graph; uses the results t draw cnclusins abut the event; and makes predictins abut future events (2.4.A1j-k)..4.1.A2 uses the results frm a cmpleted experiment r simulatin f a simple event t make predictins in a variety f real-wrld situatins (2.4.A1j-k), e.g., the manufacturer f Crunchy Flakes puts a prize in 20 ut f every 0 bxes. What is the prbability that a shpper will find a prize in a bx f Crunchy Flakes, if they purchase bxes? Prbability Synthesis Prbability Synthesis Prbability.4.1.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 (2.4.A1j)..4.2.K1 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 and decimal intervals using these data displays (2.4.K1j) ($): graphs using cncrete bjects, pictgraphs, frequency tables, bar and line graphs, Venn diagrams and ther pictrial displays, e.g., glyphs, line plts, Synthesis epresenting Data 1

19 charts and tables, circle graphs, single stem-and-leaf plts.4.2.a1 interprets and uses data t make reasnable inferences, predictins, and decisins, and t develp cnvincing arguments frm these data displays (2.4.A1k) ($): graphs using cncrete materials, pictgraphs, frequency tables, bar and line graphs, Venn diagrams and ther pictrial displays, line plts, charts and tables, circle graphs..4.2.k2 cllects data using different techniques (bservatins, plls, tallying, interviews, surveys, r randm sampling) and explains the results(2.4.k1j) ($).4.2.K3 identifies, explains, and calculates r finds these statistical measures f a whle number data set f up t twenty whle number data pints frm 0 thrugh 1,000 (2.4.K1a) ($): minimum and maximum values, range, mde (n-, uni-, bi-), median (including answers expressed as a decimal r a fractin withut reducing t simplest frm), mean (including answers expressed as a decimal r a fractin withut reducing t simplest frm).4.2.a2 uses these statistical measures f a whle number data set t make reasnable inferences and predictins, answer questins, and make decisins (2.4.A1a) ($): minimum and maximum values, range, mde, median, mean when the data set has a whle number mean..4.2.a3 recgnizes that the same data set can be displayed in varius frmats and discusses why a particular frmat may be mre apprpriate than anther (2.4.A1k) ($)..4.2.A4 recgnizes and explains the effects f scale and interval changes n graphs f whle number data sets (2.4.A1k). Synthesis Synthesis epresenting Data epresenting Data Statistics S-8 Statistics S-8 Statistics 20