Released Test Answer and Alignment Document Mathematics Algebra 1 Performance Based Assessment

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1 Released Test Answer and Alignment Dcument Mathematics Algebra 1 Perfrmance Based Assessment The fllwing pages include the answer key fr all machine-scred items, fllwed by the rubrics fr the hand-scred items. The rubrics shw sample student respnses. Other valid methds fr slving the prblem can earn full credit unless a specific methd is required by the item. In items where the scres are awarded fr full and partial credit, the definitin f partial credit will be cnfirmed during range-finding (reviewing sets f real student wrk). If students make a cmputatin errr, they can still earn pints fr reasning r mdeling. Item Number Answer Key Evidence Statement Key Integrated Curse Alignment 1. B, D F-IF.1 Math 1 2. B F-IF.6-6a 3. A-REI.4b-1 Math 2 4. A-REI.11-1a 5. A-APR.1-1 Math 2 6. A A-CED.4-1 Math 1 PARCC PBA Assessment: Algebra 1 Mathematics Released Test Answer and Rubric Dcument 1

2 7. A-SSE.3a Math 2 r 8. D A-REI F-IF.6-1a 10. F-IF.7a-1 Math Part A: see rubric HS.D.2-6 Math 2 Part B: see rubric 12. Part A: see rubric Math 2 HS.D.2-9 Part B: see rubric 13. See rubric HS.C.2.1 Math Part A: see rubric Part B: see rubric Part C: see rubric HS.D Part A: see rubric Part B: see rubric HS.C Part A: see rubric Part B: see rubric HS.C Part A: see rubric Part B: see rubric HS.C See rubric HS.D.3-1 Math 1 Math 1 Math 1 Math 2 Math 1 PARCC PBA Assessment: Algebra 1 Mathematics Released Test Answer and Rubric Dcument 2

3 #11 Part A Scre Descriptin 2 Student respnse includes the fllwing 2 elements. Mdeling cmpnent 2 pints Valid equatin fr width f the rug Valid explanatin fr the equatin Sample Student Respnse: w(w + 4) 21, where w is the width f rug The area f the rug is A lw, which is 21 square feet. The length is l w + 4. Replacing l with w + 4 and A with 21 gives the equatin w(w + 4) Student respnse includes 1 f the 2 elements. 0 Student respnse is incrrect r irrelevant. Scre Descriptin #11 Part B 4 Student respnse includes the fllwing 4 elements. Mdeling cmpnent 3 pints Determinatin f the riginal length and width f the rug Implementatin f the 1.5 feet brder int the calculatin Wrk t determine the new area Cmputatin cmpnent 1 pint Crrect cmputatin based n wrk Sample Student Respnse: w 2 + 4w 21 0 (w + 7)(w 3) 0 w OR w 3 0 w 7 OR w 3 Since width cannt be negative, the width is 3 feet. S, the length is 7 feet. The 1.5 ft brder wuld add 3 feet t each dimensin. PARCC PBA Assessment: Algebra 1 Mathematics Released Test Answer and Rubric Dcument 3

4 A (3 + 3)(7 + 3) A (6)(10) A square feet Nte: A student can earn full credit fr the mdeling cmpnent in Part B withut explicitly stating the width and length f the rug if the reasning is mathematically apprpriate. 3 Student respnse includes 3 f the 4 elements. 2 Student respnse includes 2 f the 4 elements. 1 Student respnse includes 1 f the 4 elements. 0 Student respnse is incrrect r irrelevant. PARCC PBA Assessment: Algebra 1 Mathematics Released Test Answer and Rubric Dcument 4

5 #12 Part A Scre Descriptin 2 Student respnse includes the fllwing 2 elements. Mdeling cmpnent 2 pints Valid functin Wrk t supprt the functin Sample Student Respnse: f(x) 6x 450 The ttal cst f the prizes is Fr 75 tickets t make $450, they must each cst $6. 1 Student respnse includes 1 f the 2 elements. 0 Student respnse is incrrect r irrelevant. #12 Part B Scre Descriptin 1 Student respnse includes the fllwing element. Cmputatin cmpnent 1 pints Machine Scred: 217 tickets 0 Student respnse is incrrect r irrelevant. PARCC PBA Assessment: Algebra 1 Mathematics Released Test Answer and Rubric Dcument 5

6 #13 Rubric Scre Descriptin 3 Student respnse includes the fllwing 3 elements. Reasning cmpnent 3 pints Crrect identificatin f a as ratinal and b as irratinal Crrect identificatin that the prduct is irratinal Crrect reasning used t determine ratinal and irratinal numbers Sample Student Respnse: A ratinal number can be written as a rati. In ther wrds, a number that can be written as a simple fractin. a can be written as 4. Thus, a is a ratinal number. All numbers that 9 are nt ratinal are cnsidered irratinal. An irratinal number can be written as a decimal, but nt as a fractin. b cannt be written as a fractin, s it is irratinal. The prduct f an irratinal number and a nnzer ratinal number is always irratinal, s the prduct f a and b is irratinal. Yu can als see it is irratinal with my calculatins: 4 ( ) is irratinal. 2 Student respnse includes 2 f the 3 elements. 1 Student respnse includes 1 f the 3 elements. 0 Student respnse is incrrect r irrelevant. PARCC PBA Assessment: Algebra 1 Mathematics Released Test Answer and Rubric Dcument 6

7 #14 Part A Scre Descriptin 2 Student respnse includes the fllwing 2 elements. Mdeling cmpnent 2 pints Crrect equatin fr Office Essentials Crrect equatin fr Everything Office Sample Student Respnse: M 2, n represents the mnthly earnings fr the Office Essentials jb. M 2, n represents the mnthly earnings fr the Everything Office jb. 1 Student respnse includes 1 f the 2 elements. 0 Student respnse is incrrect r irrelevant. #14 Part B Scre Descriptin 2 Student respnse includes the fllwing 2 elements. Mdeling cmpnent 2 pints Fr Office Essentials, the cnclusin that Marcella must sell at least 12 machines per mnth in rder t meet her gal, with supprting wrk Fr Everything Office, the cnclusin that Marcella must sell at least 14 machines per mnth in rder t meet her gal, with supprting wrk Sample Student Respnse: Fr each cmpany, write and slve an inequality. PARCC PBA Assessment: Algebra 1 Mathematics Released Test Answer and Rubric Dcument 7

8 Office Essentials 2, n M 2, n 4, n 1,500 n 12 Everything Office 2, n M 2, n 4, n 2,000 n Fr Office Essentials, the result n 12 means that Marcella must sell at least 12 ffice machines per mnth in rder t earn a ttal f at least $4,000. At Everything Office, the result 1 3 n 13 must be interpreted within the cntext f the prblem as n 14, since it is impssible t sell ne-third f an ffice machine. S Marcella must sell at least 14 ffice machines per mnth in rder t earn a ttal f at least $4, Student respnse includes 1 f the 2 elements. 0 Student respnse is incrrect r irrelevant. Scre Descriptin #14 Rubric Part C 2 Student respnse includes the fllwing 2 elements. Mdeling cmpnent 2 pints Calculatins r reasning t shw that the ttal earnings at the tw cmpanies are equal when 20 machines are sld The cnclusin that the ttal earnings fr the Everything Office jb are greater than the ttal earnings fr the Office Essentials jb when the representative sells any number f ffice machines greater than 20, with supprting wrk. Sample Student Respnse: Use the equatins frm Part A t frm a system f equatins. M 2, n M 2, n Slve the system by substituting 2, n fr M in the first equatin and then slving the resulting equatin fr n. PARCC PBA Assessment: Algebra 1 Mathematics Released Test Answer and Rubric Dcument 8

9 2, n 2, n 2, n 2,500 25n 500 n 20 In bth cases, the value f M is 5,000 when 20 is substituted fr n. S the ttal earnings at Everything Office equal the ttal earnings at Office Essentials when 20 ffice machines are sld. T find the interval f machines sld fr which the ttal earnings at Everything Office are greater than the ttal earnings at Office Essentials, I can set up the inequality: 2, n > 2, n 25n > 500 n > 20 When Marcella sells mre than 20 machines her earnings at Everything Office are greater than at Office Essentials. 1 Student respnse includes 1 f the 2 elements. 0 Student respnse is incrrect r irrelevant. PARCC PBA Assessment: Algebra 1 Mathematics Released Test Answer and Rubric Dcument 9

10 #15 Part A Scre Descriptin 1 Student respnse includes the fllwing element. Cmputatin cmpnent 1 pint Web Site A Web Site B Week 1: Week 2: Week 3: Week 4: Week 5: Week 6: Week 7: 1, Week 8: 3,200 1,075 Nte: All values must be crrect t earn the pint. 0 Student respnse is incrrect r irrelevant. #15 Part B Scre Descriptin 2 Student respnse includes the fllwing 2 elements. Reasning cmpnent 2 pints Valid reasning abut the nature f the data fr Web Site A Valid reasning abut the nature f the data fr Web Site B Sample Student Respnse: Jse s claim is nt crrect abut Web Site A. A linear mdel assumes that the rate f change is cnstant fr each ne-week increment. Lking at the data in the table, the change frm Week 1 t Week 2 is 25, the change frm Week 2 t Week 3 is 50, and the change frm Week 3 t Week 4 is 100. The change in visitrs frm ne week t the next is nt cnstant; the change in visitrs frm ne PARCC PBA Assessment: Algebra 1 Mathematics Released Test Answer and Rubric Dcument 10

11 week t the next is tw times the change in the previus week. Such data are better suited fr an expnential mdel. Jse s claim is crrect abut Web Site B. The rate f change in the number f visitrs frm ne week t the next is cnstant. The change frm ne week t the next is 150 visitrs each week. 1 Student respnse includes 1 f the 2 elements. 0 Student respnse is incrrect r irrelevant. PARCC PBA Assessment: Algebra 1 Mathematics Released Test Answer and Rubric Dcument 11

12 #16 Part A Scre Descriptin 2 Student respnse includes the fllwing 2 elements. Reasning cmpnent 1 pint crrect explanatin that the slpe is equal between any tw pints n a given line and that each slpe must equal 2, since that is the slpe f the given line Cmputatin cmpnent 1 pint crrect calculatin f m 2 fr the slpes f AB, BC, and AC Sample Student Respnse: Calculate each slpe. AB : (2b 3) (2a 3) 2b 3 2 a ( 3) b a b a 2b 2 a+ ( 3) ( 3) b a 2b 2 a+ ( 3) + 3 b a 2b 2a b a 2( b a) 2 b a BC : PARCC PBA Assessment: Algebra 1 Mathematics Released Test Answer and Rubric Dcument 12

13 (2c 3) (2b 3) 2c 3 2 b ( 3) c b c b 2c 2 b+ ( 3) ( 3) c b 2c 2 b+ ( 3) + 3 c b 2c 2b c b 2( c b) 2 c b AC : (2c 3) (2a 3) 2c 3 2 a ( 3) c a c a 2c 2 a+ ( 3) ( 3) c a 2c 2 a+ ( 3) + 3 c a 2c 2a c a 2( c a) 2 c a Each rati equals 2. Amy is crrect. All the slpes are equal. Nte: A student can als receive a scre f 2 by demnstrating a cmplete understanding, using apprpriate mathematical reasning/wrk. 1 Student respnse includes 1 f the 2 elements. Nte: A student can als receive a scre f 1 by demnstrating a partial understanding, using apprpriate mathematical reasning/wrk. 0 Student respnse is incrrect r irrelevant. Scre Descriptin #16 Part B 2 Student respnse includes the fllwing 2 elements. PARCC PBA Assessment: Algebra 1 Mathematics Released Test Answer and Rubric Dcument 13

14 Reasning cmpnent 2 pints crrect explanatin that ( 1, 1) is nt n the graph f y 2x 3 crrect explanatin that (1, 1) is n the graph f y 2x 3 Sample Student Respnse: T determine whether a pint lies n the graph f an equatin, substitute the crdinates f the pint int the equatin. If the crdinates f the pint make the equatin true, then the pint is n ( 1, 1) 1 2( 1) 3 the graph f the equatin Therefre, ( 1, 1) is nt n the graph. (1, 1) 1 2(1) Therefre, (1, 1) is n the graph. 1 Student respnse includes 1 f the 2 elements. 0 Student respnse is incrrect r irrelevant. PARCC PBA Assessment: Algebra 1 Mathematics Released Test Answer and Rubric Dcument 14

15 #17 Part A Scre Descriptin 2 Student respnse includes the fllwing 2 elements. Reasning cmpnent 1 pint Algebraic r written explanatin fr slving the equatin Cmputatin cmpnent 1 pint Slutin f x 2 r -14 Sample Student Respnse: Slutin 1: 2 Slutin 2: 14 1 Student respnse includes 1 f the 2 elements. 0 Student respnse is incrrect r irrelevant. #17 Part B Scre Descriptin 2 Student respnse includes the fllwing 2 elements. Reasning cmpnent 1 pint PARCC PBA Assessment: Algebra 1 Mathematics Released Test Answer and Rubric Dcument 15

16 Valid explanatin Cmputatin cmpnent 1 pint Slutin f c 36 Sample Student Respnse: There wuld be nly ne slutin if the factrs f the plynmial are the same. If the factrs are the same, then the identity can be used. The middle term is 12, s c wuld have t be the square f half f that number. Therefre c 36 1 Student respnse includes 1 f the 2 elements. 0 Student respnse is incrrect r irrelevant. PARCC PBA Assessment: Algebra 1 Mathematics Released Test Answer and Rubric Dcument 16

17 #18 Rubric Scre Descriptin 3 Student respnse includes the fllwing 3 elements. Mdeling cmpnent 2 pints crrect equatin, w h accurate use f ntatin and vcabulary t supprt crrect calculatins and mathematical reasning, identifying variables as needed Cmputatin cmpnent 1 pint crrect applicatin f the mdel t make an accurate predictin Sample Student Respnse: If the burn rate is believed t be cnstant, determine the average burn rate fr the eight candles as the rati f weight lss per hur. unces lst ver three-hurs unces lst per hur n average Fr 0 hurs, the weight f each candle is 16 unces. Therefre, w h. This mdel can be used t predict the weight f the candle when h, the number f hurs f burning, is 5. PARCC PBA Assessment: Algebra 1 Mathematics Released Test Answer and Rubric Dcument 17

18 w (5) Accrding t the mdel, the weight f the candle after 5 hurs f burning wuld be abut unces. 2 Student respnse includes 2 f the 3 elements. 1 Student respnse includes 1 f the 3 elements. 0 Student respnse is incrrect r irrelevant. PARCC PBA Assessment: Algebra 1 Mathematics Released Test Answer and Rubric Dcument 18

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