2000-2001 Sample Form Mathematics Scoring Key · 2000-2001 Sample Form Mathematics Scoring Key Item...

2000-2001 Sample FormMathematicsScoring Key

Item #CorrectAnswer

Cluster,Macro*

KnowledgeSkill*

ProblemSolvingSkill*

Power Base Elements*

1 B 1A 06 10 Problem Solving, Numerical Operations, Estimation

2 D 2A 07 11 Problem Solving, Connections, Reasoning

3 B 3A 05 08 Problem Solving, Connections, Numerical Operations

4 D 4B 10 Reasoning, Numerical Operations

5 C 2B 11 12 Problem Solving, Communication, Reasoning, Tools/Technology

6 B 3B 09 Connections, Reasoning, Numerical Operations

7 A 2C 01 13 Problem Solving, Reasoning, Numerical Operations, Measurement

8 B 1A 04 10 Connections, Reasoning, Tools/Technology, Numerical Operations, Estimation

9 B 4B 11 13 Problem Solving, Connections, Reasoning, Tools/Technology, Numerical Operations

10 A 4A 06 Connections, Reasoning

11 A 4B 01 Problem Solving, Reasoning

12 B 1B 15 25 Problem Solving, Connections, Reasoning, Tools/Technology, Numerical Operations, Estimation

13 See rubric 1B 17 Communication, Reasoning, Numerical Operations

14 See rubric 2C 06 13 Problem Solving, Communication, Connections, Reasoning, Tools/Technology, Numerical Operations,Measurement

15 D 2B 11 Reasoning

16 B 4A 09 10 Problem Solving, Connections, Reasoning, Numerical Operations, Measurement

17 C 2B 02 Connections, Numerical Operations

18 C 3A 04 Connections, Numerical Operations

19 C 1C 05 Connections, Reasoning, Tools/Technology, Numerical Operations

20 C 1A 06 10 Problem Solving, Connections, Reasoning, Numerical Operations, Estimation

21 A 1B 0422 A 3A 04 08 Problem Solving, Connections, Numerical Operations

23 A 4B 06 17 Problem Solving, Connections, Reasoning

24 C 4A 09 Problem Solving, Connections, Reasoning, Numerical Operations

25 D 3B 06 11 Problem Solving, Reasoning

26 See rubric 3D 07 10 Problem Solving, Communication, Tools/Technology, Numerical Operations

27 See rubric 4B 08 14 Problem Solving, Communication, Connections, Reasoning, Tools/Technology, Numerical Operations

28 B 1B 13 Numerical Operations,

29 B 4A 09 10 Problem Solving, Connections, Reasoning, Tools/Technology, Numerical Operations

30 A 1A 04 10 Problem Solving, Numerical Operations, Estimation

31 C 3B 09 Reasoning, Tools/Technology, Numerical Operations

32 D 3C 09 14 Problem Solving, Reasoning

33 B 2C 10 13 Problem Solving, Reasoning, Numerical Operations, Measurement

34 B 4B 01 Problem Solving, Reasoning

35 A 1B 19 23 Problem Solving, Connections, Numerical Operations

36 A 2A 03 Reasoning

37 B 4B 08 Problem Solving, Reasoning, Numerical Operations

38 B 1C 04 08 Problem Solving, Reasoning, Numerical Operations

39 See rubric 3A 01 08 Problem Solving, Communication, Connections, Reasoning, Numerical Operations

40 See rubric 2C 10 13 Problem Solving, Communication, Connections, Reasoning, Tools/Technology, Numerical Operations,Measurement

Scoring Instructions

Official scores for open-ended items on a live test are derived from two independent readings of each student response. If you do notplan to use a second scorer, simply assign the same score twice. Responses that are unintelligible, not in English, off topic, notresponsive, or only a partial fragment are assigned a score of zero points. If you have difficulty deciding on a score point or feel aparticular response lies between two score points on the rubric, you may assign “split” scores (i.e., 2 and 3). Based on the item type, thetwo scores are either added together or averaged (which can result in half-points) in computing the total number of points earned.

To compute the total score, add the following:• Count one point for each correct answer on all multiple-choice items. (maximum 34 points possible)• Scores for open-ended items 13, 14, 26, 27, 39, and 40 (average of two scores for each item – minimum of 0, maximum of 3

points possible for each item or 18 maximum total points possible).

Total of 52 maximum points possible.

Clusters/Macros1. Number Sense, Concepts and Applications.

1.A. Make Appropriate Estimations and Approximations.1.B. Understand Numbers, Our Numeration System and Their Applications in Real-World Situations.1.C. Use Ratios, Proportions and Percents in a Variety of Situations.

2. Spatial Sense and Geometry.2.A. Recognize, Identify and Represent Spatial Relationships and Geometric Properties.2.B. Apply the Principles of Congruence, Similarity, Symmetry, Geometric Transformations and Coordinate

Geometry.2.C. Apply the Principles of Measurement and Geometry to Solve Problems Involving Direct and Indirect

Measurement.

3. Data Analysis, Probability, Statistics and Discrete Mathematics.3.A. Predict, Determine, Interpret and Use Probabilities.3.B. Collect, Organize, Represent, Analyze and Evaluate Data.3.C. Apply the Concepts and Methods of Discrete Mathematics to Model and Explore a Variety of Practical

Situations.3.D. Use Iterative Patterns and Processes to Describe Real-World Situations and Solve Problems.

4. Patterns, Functions and Algebra4.A. Recognize, Create and Extend a Variety of Patterns and Use Inductive Reasoning to Understand and

Represent Mathematical and Other Real-World Phenomena.4.B. Use Algebraic Concepts and Processes to Concisely Express, Analyze and Model Real-World Situations.

*Refer to the Directory of Test Specifications and Sample Items for the Grade Eight Proficiency Assessment (GEPA)and the High School Proficiency Assessment (HSPA) in Mathematics, published by the New Jersey Department ofEducation in February, 1998 for further information.

2000-2001 GEPA Sample FormMathematics

Score Interpretation Guide

The New Jersey Department of Education is pleased to provide the 2000-2001 GEPA Sample Forms as tools for gaugingstudent achievement prior to the live administration of these tests. Although the sample forms contain previouslytested items and are built to specifications similar to the “real” test, they are not the “real” test. As such, these sampleforms are not intended to predict student scores on the GEPA. There are several reasons for this:

1. Student performance on these or any test will vary from day to day.2. The sample forms will be given under less standardized conditions than the conditions used for the live tests.3. The sample forms will be scored locally without the extensive training and accuracy controls used to score

the live tests.4. Continued instruction will occur in the time between the administration of the sample form and the live test.

However, these sample forms can be used to screen for students who may have difficulty reaching the Proficientlevel. Also, by examining items that a student or group of students (e.g., a classroom) answer incorrectly, teacherscan identify possible strengths and weaknesses in specific skills. The scoring key provides links to the CoreCurriculum Content Standards and the Directory of Test Specifications and Sample Items to help you understand thecontent, skill and process domains that each item represents.

Individual student performance on these sample forms can be interpreted as follows:

Level Score Range Indication1 0 – 21.5 There is a good chance that the student would not

score at the Proficient level.2 22 – 31.5 There is a good chance that the student would score

just above or just below the Proficient level cut-score.3 32 – 52 There is a good chance that the student is at or above

the Proficient level

The New Jersey Department of Education highly recommends that teachers use sample form results as only onepiece of information when determining the instructional needs of a student or group of students.

2000-2001 GEPA Sample TestMathematics

Item 13 Scoring Rubric

3 points – The student plots and labels both points accurately, names a decimal and afraction between 0.6 and 4/5 and clearly explains why the chosen numbersmeet the requirement.

2 points – The student plots and labels both points accurately and names a decimal and afraction between 0.6 and 4/5 but the explanation is vague, incomplete, ormissing.

OR The student plots and labels both points accurately and names either a decimalor a fraction with a clear explanation.

OR The student fails to plot one or both points or plots them incorrectly but namesa decimal and a fraction between 0.6 and 4/5 with a clear explanation.

1 point – The response fails to meet the requirements of a "2" but shows some evidenceof understanding or begins to answer the question; for example, the studentcorrectly plots and labels the two given points.

0 points – The response shows insufficient understanding of the problem's essentialmathematical concepts.

GEPA MathItem: 13Score: 3

1 & 215 Sample #:.

path Ck I eu -b+,, +

J&C

. 8).‘19 Score: 3

16 .

l 11111111111111 lllllllll1llIlI,-1 0

$ 0.6 +�t

&a rl, - 0.6 ;‘s qua\ a$- yy.. L 1~~~~1 7s cJ-@cw Sk 0.6

Be 4- 2- 3ctwa5--ct- T5 quaI F s3 r kifi-z-+ .I5 3d%f- &.a+- -“s 0

G-7Score: 3

GEPA MathItem: 13Score: 3Sample #: 3

4 .

. IIIIIIIIIIIIIIIIIIIIII.11IlIIII.l.-1 0 -,;@$ 1

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P-2

13 .

GEPA MathItem: 13Score: 2Sample #: 1 & 2

4 IlllllrlllllllllIIIII~l~l hll 1,-1 0 q1

3 c,5 - 73,\u-

5o *x aa4 ‘ ccy c&qIn ‘-e cc/eeq +Ae/ ‘cc’0t- :

Score: 2- - - 10 533 3 LII., \o E Ti3 \o lo $5330.

. IlllllllllllllllllIIIIIlIIIIIIl*-l.h~~0~‘4.,&le 13 16 \a 1

3 10(0

t-- %5 -- $0 4t 3la s = IO

a , 6 = +.& 5.0 - k. 1% “d‘ 5cb -

50 rt- ‘.--lo c-

6-G

czc-&dL& (,.#.z.-\a

G-4 Score: 2


12... llllllllllllll ll1l1~l~lll~l~~ +

-1 0 00; -& ’

71;0 JOwent f&ma I rumba A+

are y=J~ #mr) 0.6 an&! /es &f-7 3

OIce 0.7 c2nc.l -f$)1 knou

J-+QJ-f&71 each ot my nclmbe.fsace thct, O/6 ctnJ /es ib

$7 ~~CLAU~C, 4 &v&3\ by 5 *YJ~ OX50 +b only &iml +A*+ cdc( be

qmb- +hn ‘0.6 L& /a f+w 0.8’ is“0.y lJhcf7 T- 3oC Q#7 I- ~$pre$ fhd-5 &o eq/Mais 0,7 afJ f&J- is /lo!d2: 3Of lb M~f&f-s T c&J,

Score: 2

G-5


5 .

4 llllllllllllll Il~I~~lIlIllllI.-1 0 5 +!.- '

3 0,7-L 1-1 15 In b&fee/l

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Score: 1

6 .

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-1 o&1&-I I ,

1 y.: 5

e708

08 I’S two b-3e’tl-m 46 b m\lfv-than y/s

Score: 1

G-2


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Score: I

G-3t . .

GEPA MathItem: 13Score: 0Sample #: 1,2 & 3

1 .-1 0 1

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an(j

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c Oh\ 4-Score: 0

2 .

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- - - - - - .-______- - - - - Score: 0

2 .4 IlllIllllllllll~lll~ILlll’llllI’

-1 0 1

P-I



3 points – The student finds area of 148 square yards. Diagram is clearly marked toshow how floor was divided. For each section an appropriate formula iscorrectly used although actual work may not be shown. Diagram may belabeled with needed dimensions or their correctness may be determined fromtheir use in the formulas. Any flaws are minor. (One mislabeled dimensionor one computational error is considered a minor flaw.)

2 points – The student displays a reasonable method for finding the area but shows apattern of errors in computation,

OR finds the area of one section inappropriately. (Includes both misapplication ofa formula and failing to correctly determine a needed dimension.)

1 point – The response fails to meet the requirements of a "2" but shows some evidenceof understanding or begins to answer the question; for example, correctlyfinds area of one subsection of floor.

0 points – The response is irrelevant, inappropriate, or otherwise without merit.

1A 12yd

10yd

\

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Score: 3

GIO

15 .

6yd .

10yd

\8yd


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2 a’oI

72w5. 59/YJ

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w(.,’zJj&

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Score: 3

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GEPA MathItem: 14

16 .12yd

Score: 3Sample #: 3

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Score: 3

K’’

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pgs

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t&5--

tis

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’


22 yd

1 2 y d

L

1Oyd

\8yd yher, ve‘- -cl% d-‘lc’. -I\

\Ii+ 0’l-k .@3,‘tsc-

~~Pe~~6y) T/w?Gnd +c

-neb pt3L :@ t-&3-~~%~~.., &)bpG;o$

say c! --’ iI

D

\6 &tp i-&g-6 =G-+k rp9Cb qkag++ Qb0q

! e=L- sat-p;* k&& m&)jyI\6 X8 tb $“f+ lag l-k&ASc-b~~cf 6. f~,gcd-- a..

,2 o-~a,~dG(\pcv se-bf-t-d l&t %aq

zw +a $c+ Play&!F,\a\a

Score: - 2

G-7

.

11 .

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yoo bve +3 d&k 4&j

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as 1 hcde done, --ken,

one VW* W&& bp~4.1

mfiy )dS me. TTJ q t)SW&n 'fsFlce7 bbe\k+be -

Sk, ok m& Qcu\&* Sheacpc, ' -the h+&\ nwr*bec& y&dS come -b r-18. -Qe m& +bn Ch'de *isnuCn\Oec h, 3 +O eqk\-he squat ya& -fF),!sCoYnes so 4q L3 yb.?

Score: 2

G8


1 2 y d

6yd

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Score: 1

G-41

1 .

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22 yd

12yd

8yd


Tbv ‘,fi ‘tk 5 LcR( 0r2J--d .)

12yd

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Score: 0

8yd S&-e: 0

10 .

9

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2

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3 points – The student uses a correct strategy to find the correct time (1:00) at whichAmy can buy the coat. The explanation is clear and complete. The responsemay have a minor computational error.

2 points – The student states that Amy can buy the coat at 1:00. The explanation isvague but shows that the student knows how to calculate successive pricereductions of 10%. The response may have minor errors.

1 point – The student shows some understanding of reducing prices by 10%, but theresponse may have major errors.


---


10 .

T m,\~~,l;d a65 b, ,9 hwm ii- py

1,. ave l@Jo oi yob o,,lv par cbc 907’0 04 ;+

ewy G\w ,‘J fi ned rf;ce, -J; k-f??+ mu I+,: I,,,j

6 Y 3 ,,t;l +-h c rwm erh La5 I, &xJ ,TAp\ 1

CbkT+ e J AC mAl\nbtr d 3 i,mCJ JJr m i4 I++l;el, M&

-km ;& LWJJ 4 c&M

Score: 3

G-5

13 .65 65 , .~s.JJ~

‘- 630 %!I K 410 4a m

$2 033% A05 -3

+?A6C-..-.-x 49

52%i 5z$+Ez- 4+#

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rsl 3wi \\ be bb1-e fo by +k

eo> In 4 hours OJi +m pri+ fJ$ ~~72, m,> ‘\s y~s~~~~ by +-&i n3

10 p~fccn+ & * mw> ptrze

-3 Score: 3

Cr

11 .


Score: 3

G-6


-r gd- d&$ k=@Qds~ JjoJ IM~wqy afhfy,o; +hKs pzYp$?$ -+$.?a p-%k 04 *a 0-d\pd J ~~-t’;’* pa -A 1

oil yL-+- -b * l&t q&i?+% QC IQ&)$ 1

Score: 2

9 .

G-3

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Score: 2

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8

t$JGk Qb .g&Jo (jpJI &\: GF (f&J f+(-J/&,,fltj I-ii\ b- qb’ 4~ bh,+~,

‘3 m&G; i&\, &’ i..’ ‘{-!\2SL. cib A-*($ && &p&r% -t,,\.. \A -&I J&c aJF&py- fi&$&. ~yz+?+& C.(-Jg-&?pc +P- \q &-- hw \ .T- [I I- d--t& Qo.> (g

Score: 2

G-4

-

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GEPA MathematicsItem: 26Score: 1Sample #: 1,2 8z 3

Score: 1

5 .\a:ou BY? d-Q l&I! k CA4 Iv + $.te da

x CDLId lo% “+ G5 9-w J&ffi&C&J f.&+nO,Lr\kr hyrt;ll ;f -LAdk6 o r 1~~s .

Score: 1

61.. ,. _

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Score: 1


1 she ;\x hh.4 e \ne/ COhSl \ie A++&I\ ,,.& bejvs.0~

a+- r\;ooaqh, a/\

Score: 0

2 .6s

.-to’/,3-9 000 I.& fq,

@Yf? $ I hwf*- 1 6 I*

6 ‘L 15lo% ) 1 )\ouf

.iTI”)-LI hour

hEi, l)-glur;q /

fi ’IO’ I 1

1 h0t.qJGY3! /ol/, >

1 hod

G-l

Score: 0


3 .sG\c SkDdd. be =k)k hq+ Q&

u2.t .‘Lt; .!@ :y lx> ‘ELA’SC .:- ’*++YL &- -’ ss/dk- SJr .q,oomimd .-euh hbwr 4--r. Q’- <cc cpc5 CioLfJfl

I@/& ad + \(a0 v-c v““’ 0; \’.y dw-m 50 sne c-oQ\A ““1 kT-

Score: 0



3 points – The student provides a complete response, clearly describing how column D isderived from C (d = 3 x C) and how F is derived from D and E (F = D x E),giving the correct numbers in one row of the table based on the numbers incolumn C doubling, and stating that the numbers in columns D and F woulddouble if the numbers in column C doubled.

2 points – The student provides a nearly complete response in which 1 part of thequestion may be missing or incorrect.

1 point – The student describes how at least one of the columns D or F was derivedusing words or formulas. (Just using numbers is not sufficient).

OR The student shows some understanding of how entries in the spreadsheetaffect other entries.



Score: 3

13 .

, skllirg pf+&$ I Mi;+ COS+ e 3

q-w v ..:.-: f-f ..: :.:+; pe&&= &h-- price I ho- sol4

lh)/ UeW a(ou$~id C&W ’Scoie: 3

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Score: 2

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G-6

: . _^_ _... : :;z-:z-e ; A+.*. I-.-d- ..

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Score: 2

11

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Se\qng .&in ~~[a;l-c qk clrzd p-K! by “‘“‘p

xlJ~^s p’u by/. 3 ,

&&j&( , c qoo MJ\hQ~ C~kAn~ D q cn3-u-i uu &\ \C + a &no SA dci ct-qg

,,sf gu !QZaa

8 --IL Xhy t3y\” 4-npud MM@- A.@

tr\\-k c2cxl!d-. Low dz; (j;,J i-/flu jc( g 1fi-J

4r-kc LA,%.. ‘5 +<,pwl ,+ CrdKd * c.L-)p?cm ti d 4-0 da&@- G;1sot

0 at/

<%30743 o 270 =59+ JoI

! --.a

Score: 2

G-7


4Sample #: 1 & 2

l gl& ~*/$L+.. &$ ~4 2~3, 7; ye+ sej.,�flj pf;f&; .

-$+ i�j kow fivc4 ☺she y+ -&☺f +.bm

Score: 1

5 .

Skip- &54pJs dv tiaK& a pW+so .~:F’c,+h)p (JnI‘$- cosb EisPs,ghC

w;\ 1 hm b ,q+sc hw wch .she SC//s -f++@@M I&-,

..

&horn~ .

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d

Sellihq~ $;4;-

,: !’

2v

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G-3 Score: 1

, 6 .


,I2 .0 .36 = 33 : 3 3% ;aLtta;e --~~:L :r 1. ;.

Thp amount ncriv( d &t&/j On dk tmmin4+

&. sold ad J&c ,,uhLJ p’cr .

A B c 0 5 F

Score: 1


Score: 0

n

@pm& I gM4G- @U /e+ OwI

G-lScore: 0

t.


3 Sample #: 3.

I /Pr /n A AL / \r )c/*&VA-JJ j c&f+ F-+ --

I 4..4 ’ &< ..= . . .:y $

vi/G&

qs+*gcd y-y ’ .:3s4Q r, 0- ..& 1

4 ,,,-3 + I’& lg 0

$Kas16o..qq

Score: 0

G-2



3 points – The student states that Bob is wrong (or that each person has an equal chanceof winning), that Sandra is wrong (or that it is more likely that someone fromSales will win than someone from Credit) and gives clear, completeexplanations of both statements.

2 points – The student states that Bob is wrong and that Sandra is wrong. Oneexplanation is clear and complete. The other explanation is vague,incomplete, or missing, but not incorrect, contradictory, or irrelevant.

1 point – The response fails to meet the requirement for a 2, but shows someunderstanding of probability and/or fairness.

0 points – The student states that both Bob and Sandra are wrong, but explanations aremissing or do not show understanding.

OR The response shows insufficient understanding of the problem's essentialmathematical concepts.

1GEPA Math

Item: 39Score: 3L,..Sample #: 1 & 2

. ..- .-

12 _ __ _. .__ _ _. .--.&:-L-$-.+ ** q w---_.~__

--[-,i;;;&&((@& /LH& & w ?I &cc’/Lp;. .,e .c, ,py:,3

l-2%& w &&$; .; -”

: -Score: 3

. . I:: ( Score: 3::-. .- :.. .T-T.-. .%; ‘...T,.f i‘ L .:---.; -5:.rT .. -‘zYr:w:y, ”-‘A‘ ix-’ _ CL

G-6


G-7

..‘-?&zzEF _. ..- -..--8. .~.~~Z~~~.~s-.i~co~~~~ . &\3 O&-p.*$. <-“:-, _;. h 2’ LLi..l.-

sm is ~~~~;~~~~~~~~~

-. r- ry$&jy &+&YlQh,~.T” --‘I- ...er::-ciii-c.iL- . . . -/._ ,

_ .1 _ _ ..~,,~--, ,,&;;. :__ ^.. ._~~~~~~~,~~~~ .;~o-~, Sieve ales hcs ~~arget nail. ~-~-_ -. 1

..- . .f’. y&;+), 4, ,j Inoe [;&[y +b. G se m w;&& .--; :

:-,-:

._1.-z. --z-- 1

Score: 2


..- .._ .-_ .___ A -.____ _. _ .

s&n& -i 5 .‘,“,p&&rr-+ +#& i 5 \ 5 Ll G kR$.-

( i Ed, Q, \, fl &\~L*z--;].;;; .. .., 5q:_t)\4ryQ ; 5 k yf&%M+.h&~~ $4,~_ .T-T-- ..--.~w&vlq ~lftj L\Q5 .y’-,lf+jlt\ - Score: 2

G4C.

I ‘4 GEPA MathItem: 39Score: 2Sample #: 3

-

Score: 2 -

6 .

.::. .- .,. . _..i

.’ .._ :.‘-. “--.“‘--” ’Score: 1 ”


G-3

4 .

i


Score: 1


Score: 0

&rJq~&i . \o et kU%L kL .‘t* ‘-- \ 6A-.,e.Txe..__ _ I

-. G-3 5&&-;4 ~&d .oF n ,. -. .----., *,.,.- -

. N~--~---~-~a~~~ ‘; :f;,.

%- c oe-y\j n(.jf clo{ f & , &-zc+---F;cS;f--_. - .__-__. .-

OF -a$ -$ 67\Q, web cm \oe 9;&,,I

tin3 &do cd : ac o-\\ ) *hs Q, w,,t&-dQ..q Q&Q\k ‘;n CT&,-t\

Score: 0

C.

_ 3. JE9^_ . 1%

- - I.[ FgQ $5 w If, jq+& ,! j-& ; .:&h . ..b&e (icQip

L&s pqxL _. sFbly\: c:;i& kl ..: : :-j .,...- .;:+ ._ .- ,-I .- .. ._ _ _ . . . .’: I4

A, YeS, sfiw tS rib+. $i.. t&. ~+i- &cdel

wr in i%~q- j-wu~ &I % : I&.~‘~ i k. tic9t--b/n c&d-.

Score: 0


c



Sample Answer – 08MMGJ188O

Volume = 3 x 8 x 12 = 288 cu. in.Surface area = 2 (3 x 8 + 3 x 12 + 8 x 12) = 312 sq. in.A new box can be 8 in. by 6 in. by 6 in.

Volume of new box: 8 x 6 x 6 – 288 cu. in.Surface area of new box: 2 (8 x 6 + 8 x 6 + 6 x 6) = 264 sq. in. < 312 sq. in.Other solutions include 4 x 6 x 12, 4 x 8 x 9, etc.

3 points – The student correctly computes the volume and surface area of the originalbox and state the dimensions of a box that has the same volume but lesssurface area. Any flaws are minor.

2 points – The student uses correct techniques to find both the volume and surface areaof the original box and makes some attempt to design a new box.

1 point – The student uses a correct technique for finding either the volume of the boxor the area of at least one of its sides.

0 points – The response is irrelevant, inappropriate, or otherwise without merit.


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2000-2001 Sample Form Mathematics Scoring Key · 2000-2001 Sample Form Mathematics Scoring Key Item...

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