Released Test Answer and Alignment Document Mathematics Grade 8 Performance Based Assessment

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1 Released Test Answer and Alignment Dcument Mathematics Grade 8 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 1. A 8.EE EE.7b 3. C, D 8.F F G.1a 6. D 8.G.1b 7. Part A: A 8.G.4 Part B: B PARCC PBA Assessment: Grade 8 Mathematics Released Test Answer and Rubric Dcument 1

2 8. C 8.EE EE.8a 8. C 8.EE EE.8a 10. A 8.EE C 8.EE See rubric 8.C Part A: see rubric 8.C.6 Part B: see rubric 14. See rubric 8.D Part A: see rubric 8.C.3.3 Part B: see rubric 16. Part A: see rubric 8.C.6 Part B: see rubric 17. Part A: see rubric 8.D.2 Part B: see rubric Part C: see rubric 18. Part A: see rubric 8.D.3 Part B: see rubric Part C: see rubric PARCC PBA Assessment: Grade 8 Mathematics Released Test Answer and Rubric Dcument 2

3 #12 Rubric Scre Descriptin 3 Student respnse includes the fllwing 3 elements. Cmputatin cmpnent = 1 pint Crrect cnclusin abut the equatin with an apprpriate explanatin f why the cnclusin is valid Reasning cmpnent = 2 pints Crrectly uses the distributive prperty t simplify bth sides f the equatin Crrectly cmbines like terms, resulting in a false equatin in which the variable has been eliminated and tw nn-equal numbers appear n ppsite sides f the equal sign Sample Student Respnse: -2(11-12x) = -4(1-6x) x = x Subtracting 24x frm each side x -24x = x -24x -22 = -4 This is impssible, since -22 is nt equal t -4. Therefre, there is n slutin t the equatin. 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: Grade 8 Mathematics Released Test Answer and Rubric Dcument 3

4 # 13 Part A Scre Descriptin 2 Student respnse includes the fllwing 2 elements. Cmputatin cmpnent = 1 pint Determines bth percentage increases Reasning cmpnent = 1 pint Crrectly reasns that the student s claim is justified Sample Student Respnse: Percent increase frm 1998 t 2000 is ( )/ Percent increase frm 2011 t 2013 is ( )/ The percent increase fr bth perids is abut 5%, s the student s claim can be justified. 1 Student respnse includes 1 f the 2 elements. 0 Student respnse is incrrect r irrelevant. Scre Descriptin #13 Part B 2 Student respnse includes the fllwing 2 elements. Cmputatin cmpnent = 1 pint Determines the percent errr f the predictin, 0.8% Reasning cmpnent = 1 pint Crrectly reasns that the newspaper s claim is crrect Sample Student Respnse: The percent errr f the predictin was 0.8%. ( ) = Since 0.8% is less than 2%, the newspaper s claim was crrect. 1 Student respnse includes 1 f the 2 elements. 0 Student respnse is incrrect r irrelevant. PARCC PBA Assessment: Grade 8 Mathematics Released Test Answer and Rubric Dcument 4

5 #14 Rubric Scre Descriptin 3 Student respnse includes the fllwing 3 elements. Cmputatin cmpnent = 1 pint Determines the unit price fr bth gas statins Mdeling cmpnent = 2 pints Determines that gas statin P charges mre fr gasline Crrectly mdels determining the unit prices and the gas statin that charges mre fr gasline. Sample Student Respnse: Based n the unit prices, Gas Statin P charges mre fr gasline. The unit price fr Gas Statin P is $4.00 per galln since the cnstant linear graph fr Gas Statin P shws the pint (5, 20), which means it csts $20 fr 5 gallns f gas. The table fr Gas Statin M shws that 10 gallns cst $38, s the unit price fr Gas Statin M is 38 / 10 = $3.80 per galln. 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: Grade 8 Mathematics Released Test Answer and Rubric Dcument 5

6 #15 Part A Scre Descriptin 1 Student respnse includes the fllwing element. Reasning cmpnent = 1 pint Crrectly reasns why KJN and LJM are bth cngruent Sample Student Respnse: KJN is cngruent t LJM because they are the same angle since they exactly verlap. 0 Student respnse is incrrect r irrelevant. Scre Descriptin #15 Part B 2 Student respnse includes the fllwing element. Reasning cmpnent = 2 pints crrect pair f crrespnding cngruent angles, JKN and JLM r JNK and JML crrectly reasns why the given pair f angles is cngruent Sample Student Respnse: JKN is cngruent t JLM OR JNK is cngruent t JML Either line segment JL r line segment JM is a transversal t the parallel line segments KN and LM. When tw parallel lines are intersected by a transversal, crrespnding angles frmed by the transversal are cngruent. The pair f angles is als crrespnding in terms f their lcatins in KJN and LJM. 1 Student respnse includes 1 f the 2 elements. 0 Student respnse is incrrect r irrelevant. PARCC PBA Assessment: Grade 8 Mathematics Released Test Answer and Rubric Dcument 6

7 #16 Part A Scre Descriptin 2 Student respnse includes the fllwing element. Reasning cmpnent = 2 pints Determines whether the claim is always true, smetimes true, r never true Crrectly reasns that the claim is smetimes true Sample Student Respnse: Cary s claim is smetimes true. Fr example, when 4 is substituted fr m, = -1. If the value f m is a number that is greater than 5, such as 6 where = 1, then the expressin results in a psitive number. (Accept alternative valid explanatins.) 1 Student respnse includes 1 f the 2 elements. 0 Student respnse is incrrect r irrelevant. Scre Descriptin #16 Part B 2 Student respnse includes the fllwing element. Reasning cmpnent = 2 pints Determines whether the claim is always true, smetimes true, r never true Crrectly reasns that the claim is always true Sample Student Respnse: Phillip s claim is always true because p and p are ppsites. The sum f ppsites is always 0. That makes the expressin which will always be psitive 5. The value f p des nt matter ( -7) = = 5 and ( -3) = = = 5 and = 5 since the ppsite f 0 is 0. (Accept alternative valid explanatins.) 1 Student respnse includes 1 f the 2 elements. 0 Student respnse is incrrect r irrelevant. PARCC PBA Assessment: Grade 8 Mathematics Released Test Answer and Rubric Dcument 7

8 #17 Part A Scre Descriptin 1 Student respnse includes the fllwing element. Cmputatin cmpnent = 1 pint Machine Scred: Selects nly the fllwing tw ptins: 1/24 cup f milk is used t make each muffin 1 cup f milk is used t make every 24 muffins 0 Student respnse is incrrect r irrelevant. Scre Descriptin #17 Part B 3 Student respnse includes the fllwing 3 elements. Cmputatin cmpnent = 1 pint Indicates that 32 batches f muffins can be made with 1 galln f milk Mdeling cmpnent = 2 pints Crrect strategy t find the ttal number f cups in a galln Nte: Prviding the crrect number f cups in a galln is sufficient t satisfy this element. Crrect strategy t find the number f batches f muffins that can be made with 1 galln f milk Sample Student Respnse: There are 2 cups in a pint, 2 pints in a quart, and 4 quarts in a galln, s there are = 16 cups in a galln. One cup f milk is needed fr 24 muffins, s 1 galln f milk can make = 384 muffins. This means that = 32 batches f muffins can be made using 1 galln f milk. Nte: The student may shw mdeling using nly equatins. If the equatins shwn represent a valid mdeling prcess, credit shuld be awarded. 2 Student respnse includes 2 f the 3 elements. PARCC PBA Assessment: Grade 8 Mathematics Released Test Answer and Rubric Dcument 8

9 1 Student respnse includes 1 f the 3 elements. 0 Student respnse is incrrect r irrelevant. Scre Descriptin #17 Part C 2 Student respnse includes the fllwing elements. Cmputatin cmpnent = 1 pint Indicates 7.5 gallns f milk are needed t make 96 muffins every day fr 30 days Mdeling cmpnent = 1 pint Crrect strategy t find the number f gallns f milk needed t make 96 muffins each day fr 30 days Sample Student Respnse: The bakery makes = 8 batches f muffins each day. In 30 days, the bakery makes 30 8 = 240 batches. Since 32 batches can be made with 1 galln f milk, 240 batches can be made with = 7.5 gallns f milk. Ntes: The student may receive mdeling pints if the student shws a sufficient mdeling prcess fr sme r all f the parts indicated but makes ne r mre cmputatinal errrs resulting in incrrect answer(s). The student may receive cmputatin pints if he r she cmputes the crrect answer(s) t ne r all f the parts but shws n wrk r insufficient wrk t indicate a crrect mdeling prcess. The student may nt receive mre than 2 ttal pints (acrss all parts) fr mdeling if the explanatins, while sufficient t indicate that the student has a crrect prcess, cntain nnsense statements. 1 Student respnse includes 1 f the 2 elements. 0 Student respnse is incrrect r irrelevant. PARCC PBA Assessment: Grade 8 Mathematics Released Test Answer and Rubric Dcument 9

10 #18 Part A Scre Descriptin 1 Student respnse includes the fllwing element. Cmputatin cmpnent = 1 pint Graphs a line that passes thrugh the pints (0, 0) and (6, 90) Nte: The student may chse any tw pints n the crrect line t receive credit. 0 Student respnse is incrrect r irrelevant. Scre Descriptin #18 Part B 1 Student respnse includes the fllwing element. Mdeling cmpnent = 1 pint Explains what the slpe f the line represents Sample Student Respnse: The slpe f the line represents the amunt f mney that is saved each week fr the first six weeks. Ntes: The student des nt have t mentin what the slpe f the line is in rder t get the mdeling pint. The student may get 1 mdeling pint fr a crrect explanatin f what the slpe represents that references an incrrect slpe based n his r her respnse t Part A. 0 Student respnse is incrrect r irrelevant. PARCC PBA Assessment: Grade 8 Mathematics Released Test Answer and Rubric Dcument 10

11 #18 Part C Scre Descriptin 1 Student respnse includes the fllwing element. Mdeling cmpnent = 1 pint Shws r explains hw t use the line drawn in Part A t determine the number f weeks it will take fr Mindy t have $150 saved and states the assumptin that the mney is still saved at a cnstant rate after week 6 Sample Student Respnse: I can extend the line t when y = 150 t find the number f weeks it takes Mindy t save $150. By ding that, I assume that the rate f change in the amunt f mney saved each week is still cnstant after week 6. Ntes: Many valid respnses are pssible. As lng as it is clear that the student knws the rate at which Mindy saves mney is assumed t be cnstant and hw t determine the number f weeks given a dllar amunt saved, credit shuld be awarded. The student des nt have t determine the number f weeks in rder t get the mdeling pint; the student nly needs t explain hw t determine the number f weeks. The student may receive 1 mdeling pint fr a crrect explanatin that references an incrrect slpe based n his r her respnse t Part A. 0 Student respnse is incrrect r irrelevant. PARCC PBA Assessment: Grade 8 Mathematics Released Test Answer and Rubric Dcument 11

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