Rangely RE 4 Curriculum Development 5 th Grade Mathematics
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1 Unit Title Dctr We Still Need t Operate... Length f Unit 12 weeks Fcusing Lens(es) Inquiry Questins (Engaging Debatable): Structure Systems Standards and Grade Level Expectatins Addressed in this Unit Hw are mathematical peratins related? (MA10 GR.5 S.1 GLE.2 IQ.1) Why is zer imprtant in ur place value system? (MA10 GR.5 S.1 GLE.1 IQ.4) MA10 GR.5 S.1 GLE.1, MA10 GR.5 S.1 GLE.2 Unit Strands Cncepts Number and Operatins in Base Ten, Operatins and Algebraic Thinking, Measurement and Data Measurements, equivalence, rati, cnversin, unit, measurement systems, multiplicatin, divisin, cnstant rate (factr), place value, decimal system, decimals, pwers f ten, digits, magnitude, standard algrithm, partial prducts, prperties f peratins, distributive prperty, relatinship, runding, additin, subtractin, denminatr, numeratr, prduct, dividend, divisr, qutient, fractins, rder f peratins, slutins, cmpare Generalizatins My students will Understand that Factual Guiding Questins Cnceptual A cnstant applicatin f multiplicatin by 10 t btain the next higher unit, r divisin by 10 t btain the next lwer unit, demnstrates 10 as the cnstant rate/factr f cmpsing and decmpsing place value units in ur decimal system (MA10 GR.5 S.1 GLE.1 EO.a.i, a.ii, b.i, b.ii) Multiplicatin r divisin by a pwer f 10 increases r decreases their place value t a magnitude equivalent t the pwer f 10 (MA10 GR.5 S.1 GLE.1 EO.a.i, a.ii) In the standard algrithm fr multiplicatin f whle numbers, the pwer f 10 represented by the place value f the digit multiplier determines the crrespnding amunt t shift the partial prducts t the left (MA10 GR.5 S.1 GLE.2 EO.a) What is the relatinship between 654 and 65.4? What wuld it mean if we did nt have a place value system? (MA10 GR.5 S.1 GLE.1 IQ.2) What is the purpse f the decimal pint? What is the purpse f ur place value system? (MA10 GR.5 S.1 GLE.1 IQ.3) What makes ne strategy r algrithm better than anther? (MA10 GR.5 S.1 GLE.2 IQ.2) Hw many place values des the partial prduct shift when multiplying by the digit in the hundreds place? Why is dividing by 10 the equivalent t multiplicatin by 1/10? Hw des understanding ur place value system help t read, write and cmpare decimals? Why is a place value system beneficial? (MA10 GR.5 S.1 GLE.1 IQ.1) Why d yu mve the decimal pint tw places t the right when multiply 100 and tw places t the left when dividing by 100? Why d yu shift partial prducts ver ne place value when multiplying by the digit in the tens place? December 13, 2013 Page 16 f 21
2 Place value, prperties f peratins and the relatinship between multiplicatin and divisin supprt the divisin f multi digit numbers. (MA10 GR.5 S.1 GLE.2 EO.b) As with the runding f whle numbers, the accurate runding f decimals depends upn place value cncepts and an attentin t cntext (MA10 GR.5 S.1 GLE.1 EO.c) The algrithm fr the additin and subtractin f decimals, a simple extensin f the algrithm fr whle numbers, requires precise attentin t place value such that digits with crrespnding place values are aligned prir t jining r separating (MA10 GR.5 S.1 GLE.2 EO.c) The algrithm fr multiplicatin f decimals relies n the equivalence f a decimal t a crrespnding fractin with a denminatr that is a pwer f ten (MA10 GR.5 S.1 GLE.2 EO.c) The algrithm fr the divisin f decimals dictates that the decimal pint in the dividend crrespnd t the lcatin f the decimal pint in the qutient and when a decimal appears in the divisr bth divisr and dividend bth must be multiplied by the same pwer f ten t eliminate it (MA10 GR.5 S.1 GLE.2 EO.c) Universal rder f peratin ensures unifrmity and accuracy f slutins. (MA10 GR.5 S.1 GLE.2 EO.d) Hw is multiplicatin used when dividing multi digit numbers? What is the rle f place value in the divisin algrithm? Hw d yu rund a decimal number t the nearest hundredth? Hw many tenths make ne whle? Hw d yu determine the lcatin f the decimal pint in the prduct f tw decimal numbers? When using the standard algrithm fr divisin, what strategy prvides a methd fr handling divisin f decimals? What is the rder f peratins? Hw des the relatinship between multiplicatin and divisin supprt divisin when using the standard algrithm? (MA10 GR.5 S.1 GLE.2 IQ.1) Hw is runding f decimal numbers similar and different frm runding whle numbers? Why is it imprtant that digits with the same place value are aligned when adding r subtracting using the standard algrithm? Hw des multiplicatin f fractins justify the standard algrithm fr multiplicatin f decimals? Why des the multiplicatin f the divisr and dividend by the same pwer f ten create an equivalent divisin prblem? (hint: a/b is the same as a divided by b) Why des rder f peratins matter? December 13, 2013 Page 17 f 21
3 Key Knwledge and Skills: My students will What students will knw and be able t d are s clsely linked in the cncept based discipline f mathematics. Therefre, in the mathematics samples what students shuld knw and d are cmbined. Recgnize that in a multi digit number, a digit in ne place represents 10 times as much as it represents in the place t its right and 1/10 f what it represents in the place t its left (MA10 GR.5 S.1 GLE.1 EO.a) (5.CC.NBT.1) Recgnize that in a multi digit number, a digit in ne place represents 10 times as much as it represents in the place t its right and 1/10 f what it represents in the place t its left. PARCC i) Tasks have thin cntext r n cntext. ii) Tasks invlve the decimal pint in a substantial way (e.g., by invlving a cmparisn f a tenths digit t a thusandths digit r a tenths digit t a tens digit). Explain patterns in the number f zers f the prduct when multiplying a number by pwers f 10, and explain patterns in the placement f the decimal pint when a decimal is multiplied r divided by a pwer f 10 (MA10 GR.5 S.1 GLE.1 EO.a.i, a.ii) (5.CC.NBT.2) Use whle number expnents t dente pwer f 10 (MA10 GR.5 S.1 GLE.1 EO.a.iii) (5.CC.NBT.2) Use whle number expnents t dente pwers f 10. PARCC i) The explanatin aspect f 5.NBT.2 is nt assessed here. Read and write decimals t thusandths using base ten numerals, number names, and expanded frm (MA10 GR.5 S.1 GLE.1 EO.b.i) (5.CC.NBT.3a) Read, write, and cmpare decimals t thusandths. a. Read and write decimals t thusandths using base ten numerals, number names, and expanded frm, e.g = 3 x x x x (1/10) + 9 x (1/100) + 2 x (1/1000). PARCC i) Tasks assess cnceptual understanding, e.g. by including a mixture (bth within and between items) f expanded frm, number names, and base ten numerals. ii) Tasks have thin cntext r n cntext. Cmpare tw decimal s t thusandths based n meanings f the digits in each place, using >, =, < symbls t recrd the cmparisns (MA10 GR.5 S.1 GLE.1 EO.b.ii) (5.CC.NBT.3b) Read, write and cmpare decimals t thusandths. b. Cmpare tw decimals t thusandths based n meanings f the digits in each place, using >, =, and < symbls t recrd the results f cmparisns. PARCC i) Tasks assess cnceptual understanding, e.g. by including a mixture (bth within and between items) f expanded frm, number names, and base ten numerals. ii) Tasks have thin cntext r n cntext. Use place value understanding t rund decimals t any place (MA10 GR.5 S.1 GLE.1 EO.c) (5.CC.NBT.4) Use place value understanding t rund decimals t any place. PARCC i) Tasks have thin cntext r n cntext. Demnstrate understanding f the place value system by cmbining r synthesizing knwledge and skills articulated in 5.NBT.A. Prmpts d nt prvide visual fractin mdels; students may at their discretin draw visual fractin mdels as a strategy. PARCC 5.NBT.A Int. 1. Fluently multiply multi digit whle numbers using the standard algrithm (MA10 GR.5 S.1 GLE.2 EO.a) (5.CC.NBT.5) December 13, 2013 Page 18 f 21
4 Fluently multiply multi digit whle numbers using the standard algrithm. PARCC i) Tasks assess fluency implicitly, simply in virtue f the fact that there are tw substantial cmputatins n the EOY. Tasks need nt be timed. ii) The given factrs are such as t require an efficient/standard algrithm (e.g ). Factrs in the task d nt suggest any bvius ad hc r mental strategy (as wuld be present fr example in a case such as ). iii) Tasks d nt have a cntext. iv) Fr purpses f assessment, the pssibilities are 3 digit 4 digit. Find whle number qutients f whle numbers with up t fur digit dividends and tw digit divisrs, using strategies based n place value, the prperties f peratins, and the relatinship between multiplicatin and divisin; illustrate and explain the calculatin by using equatins, rectangular arrays, and/r area mdels. (MA10 GR.5 S.1 GLE.2 EO.b.i, b.ii) (5.CC.NBT.6) Find whle number qutients f whle numbers with up t fur digit dividends and tw digit divisrs, using strategies based n place value, the prperties f peratins, and/r the relatinship between multiplicatin and divisin. Illustrate and explain the calculatin by using equatins, rectangular arrays, and/r area mdels. PARCC i) Tasks d nt require students t illustrate r explain. ii) Tasks invlve 3 r 4 digit dividends and ne r tw digit divisrs. Add, subtract, multiply, and divide decimals t hundredths, using cncrete mdels r drawings and strategies based n place value, prperties f peratins, and the relatinship between additin and subtractin; relate the strategy t a written methd and explain the reasning used (MA10 GR.5 S.1 GLE.2 EO.c.i, c.ii) (5.CC.NBT.7) Add tw decimals t hundredths, using cncrete mdels r drawings and strategies based n place value, prperties f peratins, and/r the relatinship between additin and subtractin; relate the strategy t a written methd and explain the reasning used. PARCC i) Tasks d nt have a cntext. ii) Only the sum is required; explanatins are nt assessed here. iii) Prmpts may include visual mdels, but prmpts must als present the addends as numbers, and the answer sught is a number, nt a picture. iv) Each addend is greater than r equal t 0.01 and less than r equal t v) 20% f cases invlve a whle number either the sum is a whle number, r else ne f the addends is a whle number presented withut a decimal pint. (The addends cannt bth be whle numbers.) Subtract tw decimals t hundredths, using cncrete mdels r drawings and strategies based n place value, prperties f peratins, and/r the relatinship between additin and subtractin; relate the strategy t a written methd and explain the reasning used. PARCC i) Tasks d nt have a cntext. ii) Only the difference is required; explanatins are nt assessed here. iii) Prmpts may include visual mdels, but prmpts must als present the subtrahend and minuend as numbers, and the answer sught is a number, nt a picture. iv) The subtrahend and minuend are each greater than r equal t 0.01 and less than r equal t Psitive differences nly. (Every included subtractin prblem is an unknwn addend prblem included in 5.NBT.7 1.) v) 20% f cases invlve a whle number either the difference is a whle number, r the subtrahend is a whle number presented withut a decimal pint, r the minuend is a whle number presented withut a decimal pint. (The subtrahend and minuend cannt bth be whle numbers.) Multiply tenths with tenths r tenths with hundredths, using cncrete mdels r drawings and strategies based n place value, prperties f peratins, and/r the relatinship between additin and subtractin; relate the strategy t a written methd and explain the reasning used. PARCC i) Tasks d nt have a cntext. ii) Only the prduct is required; explanatins are nt assessed here. iii) Prmpts may include visual mdels, but prmpts must als present the factrs as numbers, and the answer sught is a number, nt a picture. December 13, 2013 Page 19 f 21
5 iv) Each factr is greater than r equal t 0.01 and less than r equal t v) The prduct must nt have any nn zer digits beynd the thusandths place. (Fr example, 1.67 x 0.34 = is excluded because the prduct has an 8 beynd the thusandths place; cf. 5.NBT.3 and see p. 17 f Prgressin fr Number and Operatins in Base Ten.) vi) Prblems are 2 digit 2 digit r 1 digit by 3 r 4 digit. (Fr example, 7.8 x 5.3 r 0.3 x 18.24) vii) 20% f cases invlve a whle number either the prduct is a whle number, r else ne factr is a whle number presented withut a decimal pint. (Bth factrs cannt bth be whle numbers.) Divide in prblems invlving tenths and/r hundredths, using cncrete mdels r drawings and strategies based n place value, prperties f peratins, and/r the relatinship between additin and subtractin; relate the strategy t a written methd and explain the reasning used. PARCC i) Tasks d nt have a cntext. ii) Only the qutient is required; explanatins are nt assessed here. iii) Prmpts may include visual mdels, but prmpts must als present the dividend and divisr as numbers, and the answer sught is a number, nt a picture. iv) Divisrs are f the frm XY, X0, X, X.Y, 0.XY, 0.X, r 0.0X (cf. 5.NBT.6) where X and Y represent nn zer digits. Dividends are f the frm XYZ.W, XY0.X, X00.Y, XY.Z, X0.Y, X.YZ, X.Y, X.0Y, 0.XY, r 0.0X, where X, Y, Z, and W represent nn zer digits. [(Als add XY, X0, and X.)] v) Qutients are either whle numbers r else decimals terminating at the tenths r hundredths place. (Every included divisin prblem is an unknwnfactr prblem included in 5.NBT.7 3.) vi) 20% f cases invlve a whle number either the qutient is a whle number, r the dividend is a whle number presented withut a decimal pint, r the divisr is a whle number presented withut a decimal pint. (If the qutient is a whle number, then neither the divisr nr the dividend can be a whle number. Perfrm exact r apprximate multiplicatins and/r divisins that are best dne mentally by applying cncepts f place value, rather than by applying multi digit algrithms r written strategies. PARCC 5.NBT.Int.1 i) Tasks have n cntext. ii) See ITN Appendix F, sectin A, Illustratins f Innvative Task Characteristics, subsectin 4, Integrative tasks with machine scring f respnses entered by cmputer interface, subsectin Illustratins at the dmain level. Slve ne step wrd prblems invlving multiplying multi digit whle numbers. PARCC Int.1 i) The given factrs are such as t require an efficient/standard algrithm (e.g., 726 x 4871). Factrs in the task d nt suggest any bvius ad hc r mental strategy (as wuld be present fr example in a case such as 7250 x 400). ii) Fr purpses f assessment, the pssibilities are 3 digit 4 digit. Slve wrd prblems invlving three tw digit numbers. PARCC 5.Int.2 i) The given factrs are such as t require an efficient/standard algrithm (e.g., 76 x 48 x 39). Factrs in the task d nt suggest any bvius ad hc r mental strategy (as wuld be present fr example in a case such as 50 x 20 x 15). Use parentheses, brackets, r braces in numerical expressins, and evaluate expressins with these symbls (MA10 GR.5 S.1 GLE.2 EO.d.i) (5.CC.OA.1) Use parentheses, brackets, r braces in numerical expressins, and evaluate expressins with these symbls. i) Expressins have depth n greater than tw, e.g., 3 x [5 + (8 2)] is acceptable but 3 x [5 + (8 (4 2)] is nt. Write simple expressins that recrd calculatins with numbers, and interpret numerical expressins withut evaluating them (MA10 GR.5 S.1 GLE.2 EO.d.ii) (5.CC.OA.2) December 13, 2013 Page 20 f 21
6 Cnvert amng different sized standard measurement units within a given measurement system and use these cnversins in slving multi step, real wrld prblems (MA10 GR.5 S.1 GLE.1 EO.d.i, d.ii) (5.CC.OA.1 & 2) Write simple expressins that recrd calculatins with numbers. Fr example, express the calculatin add 8 and 7, then multiply by 2 as 2 X (8 + 7). PARCC i) Nte that expressins elsewhere in CCSS are thught f as recrding calculatins with numbers (r letters standing fr numbers) as well; see fr example 6.EE.2a. See als the first paragraph f the Prgressin fr Expressins and Equatins. Interpret numerical expressins withut evaluating them. Fr example, recgnize that 3 x ( ) is three times as large as withut having t calculate the indicated sum r prduct. PARCC Critical Language: includes the Academic and Technical vcabulary, semantics, and discurse which are particular t and necessary fr accessing a given discipline. EXAMPLE: A student in Language Arts can demnstrate the ability t apply and cmprehend critical language thrugh the fllwing statement: Mark Twain expses the hypcrisy f slavery thrugh the use f satire. A student in can demnstrate the ability t apply and cmprehend critical language thrugh the fllwing statement(s): Academic Vcabulary: When cnverting a 42 centimeters t meters, I first need t remember there are 100 centimeters in 1 meter. This means I will need t divide 42 centimeters by 100 t find ut the equivalent number f meters, because I am dividing by a pwer f ten the digits will remain the same in my answer I simply mve the decimal pint tw places t the left because 100 is 102, thus the answer is 0.42 meters. Measurements, centimeter, meters, inches, feet, cnvert, cnversins, parenthesis, measurement systems, multiplicatin, divisin, relatinship, runding, additin, subtractin, fractins, explain, cmpare, fluently Technical Vcabulary: Dividend, divisr, qutient, tenths, hundredths, thusandths, metric, rder f peratins, expnents, equivalence, units, place value, decimals, pwers f ten, digits, standard algrithm, denminatr, numeratr, prduct, qutient, divisr, factr, qutient, partial prducts December 13, 2013 Page 21 f 21
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