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The Pennsylvania System of SchoolAssessmentMathematicsItem and Scoring Sampler2016–2017Grade 6Pennsylvania Department of Education Bureau of Curriculum, Assessment and Instruction—September 2016

TABLE OF CONTENTSINFORMATION ABOUT MATHEMATICSIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1General Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Pennsylvania Core Standards (PCS). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1What Is Included. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Purpose and Uses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Item Format and Scoring Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Item Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Testing Time and Mode of Testing Delivery for the PSSA. . . . . . . . . . . . . . . . . . . . . . . . . . . 2Mathematics Reporting Categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2General Description of Scoring Guidelines for Mathematics Open-Ended Questions. . . . . 4Item and Scoring Sampler Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Grade 6 Formula Sheet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Mathematics Test Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7PSSA MATHEMATICS GRADE 6Multiple-Choice Items . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Open-Ended Question. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Item-Specific Scoring Guideline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Mathematics—Summary Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35PSSA Grade 6 Mathematics Item and Scoring Sampler—September 2016ii

INFORMATION ABOUT MATHEMATICSINTRODUCTIONGeneral IntroductionThe Pennsylvania Department of Education provides districts and schools with tools to assist indelivering focused instructional programs aligned with the Pennsylvania Core Standards (PCS).These tools include Academic Standards, Assessment Anchor documents, assessment handbooks,and content-based item and scoring samplers. This Item and Scoring Sampler is a useful tool forPennsylvania educators in preparing local instructional programs. It can also be useful in preparingstudents for the statewide assessment.Pennsylvania Core Standards (PCS)This sampler contains examples of test questions that are aligned to the new Pennsylvania CoreStandards-based 2013 PSSA Assessment Anchors and Eligible Content. The Mathematics, Reading,and Writing PSSA transitioned to PCS-based operational Mathematics and English Language Artsassessments starting with the spring 2015 PSSA administration.The 2013 PCS-aligned Assessment Anchor and Eligible Content documents are posted on thisportal:¾¾ www.education.pa.gov [Hover over “K–12,” select “Assessment and Accountability,” andselect “Pennsylvania System of School Assessment (PSSA).” Then select “AssessmentAnchors” from the “Other Materials” list on the right side of the screen.]What Is IncludedThis sampler contains test questions (items) that have been written to align to the AssessmentAnchors that are based on the Pennsylvania Core Standards (PCS). The test questions provide anidea of the types of items that will appear on an operational, PCS-based PSSA. Each sample testquestion has been through a rigorous review process to ensure alignment with the AssessmentAnchors.Purpose and UsesThe items in this sampler may be used as examples for creating assessment items at the classroomlevel, and they may also be copied and used as part of a local instructional program.1 Classroomteachers may find it beneficial to have students respond to the open-ended item in this sampler.Educators can then use the sampler as a guide to score the responses either independently ortogether with colleagues within a school or district.Item Format and Scoring GuidelinesThe multiple-choice (MC) items have four answer choices. Each correct response to an MC item isworth one point.Each open-ended (OE) item is designed to take approximately ten to fifteen minutes to complete.1 Thepermission to copy and/or use these materials does not extend to commercial purposes.PSSA Grade 6 Mathematics Item and Scoring Sampler—September 20161

INFORMATION ABOUT MATHEMATICSDuring the administration of the PSSA, students are given additional time as necessary to completethe test items. Each OE item in mathematics is scored using an item-specific scoring guidelinebased on a 0–4-point scale. In this sampler, every item-specific scoring guideline is combined withexamples of student responses that represent each score point to form a practical, item-specificscoring guide.This sampler also includes the General Description of Scoring Guidelines for Mathematics OpenEnded Questions that students will have access to during a PSSA mathematics administration.The general description of scoring guidelines can be distributed to students for use during localassessments and can also be used by educators when scoring local assessments.2Item AlignmentAll PSSA items are aligned to statements and specifications included in the Assessment Anchorsand Eligible Content Aligned to the Pennsylvania Core Standards. The mathematics content, processskills, directives, and action statements included in the PSSA mathematics questions align with theAssessment Anchor Content Standards. The Eligible Content statements represent the limits of thecontent of the mathematics questions.Testing Time and Mode of Testing Delivery for the PSSAThe PSSA is delivered in traditional paper-and-pencil format as well as in an online format. Theestimated time to respond to a test question is the same for both methods of test delivery. During anofficial testing administration, students are given additional time as necessary to complete the testquestions. The following table shows the estimated response time for each item type.Mathematics Item TypeMCOEEstimated Response Time(minutes)210 to 15Mathematics Reporting CategoriesThe Assessment Anchors are organized into four classifications as listed below.A Numbers and OperationsB Algebraic ConceptsC GeometryD Data Analysis and ProbabilityThese four classifications are used throughout the grade levels. In addition to these classifications,there are five Reporting Categories for each grade level. The first letter of each Reporting Categoryrepresents the classification; the second letter represents the Domain as stated in the Common CoreState Standards for Mathematics. Listed below are the Reporting Categories for Grade 6.2The permission to copy and/or use these materials does not extend to commercial purposes.PSSA Grade 6 Mathematics Item and Scoring Sampler—September 20162

INFORMATION ABOUT MATHEMATICSA-N The Number SystemA-R Ratios and Proportional RelationshipsB-E Expressions and EquationsC-G GeometryD-S Statistics and ProbabilityExamples of multiple-choice and open-ended items assessing these categories are included in thisbooklet.PSSA Grade 6 Mathematics Item and Scoring Sampler—September 20163

INFORMATION ABOUT MATHEMATICSGeneral Description of Scoring Guidelines for Mathematics Open-Ended Questions4: The response demonstrates a thorough understanding of mathematial concepts and proceduresrequired by the task.The response provides correct answer(s) with clear and complete mathematical procedures shownand a correct explanation, as required by the task. Response may contain a minor “blemish” oromission in work or explanation that does not detract from demonstrating a thorough understanding.3: The response demonstrates a general understanding of the mathematical concepts andprocedures required by the task.The response and explanation (as required by the task) are mostly complete and correct. Theresponse may have minor errors or omissions that do not detract from demonstrating a generalunderstanding.2: The response demonstrates a partial understanding of the mathematical concepts and proceduresrequired by the task.The response is somewhat correct with partial understanding of the required mathematical conceptsand/or procedures demonstrated and/or explained. The response may contain some work that isincomplete or unclear.1: The response demonstrates a minimal understanding of the mathematical concepts andprocedures required by the task.0: The response has no correct answer and insufficient evidence to demonstrate any understandingof the mathematical concepts and procedures required by the task for that grade level.Reponse may show only information copied from the question.Special Categories within zero reported separately:BLK (blank) Blank, entirely erased, or written refusal to respondOTOff taskLOEResponse in a language other than EnglishILIllegiblePSSA Grade 6 Mathematics Item and Scoring Sampler—September 20164

INFORMATION ABOUT MATHEMATICSItem and Scoring Sampler FormatThis sampler includes the test directions and scoring guidelines that appear in the PSSAMathematics assessments. Each multiple-choice item is followed by a table that includes thealignment, the answer key, the depth of knowledge (DOK) level, the percentage3 of studentswho chose each answer option, and a brief answer option analysis or rationale. The open-endeditem is followed by a table that includes the item alignment, DOK level, and mean student score.Additionally, each of the included item-specific scoring guidelines is combined with sample studentresponses representing each score point to form a practical, item-specific scoring guide. TheGeneral Description of Scoring Guidelines for Mathematics Open-Ended Questions used to developthe item-specific scoring guidelines should be used if any additional item-specific scoring guidelinesare created for use within local instructional programs.Example Multiple-Choice Item Information TableItem InformationAlignmentAssigned AAECAnswer KeyCorrect AnswerDepth of KnowledgeAssigned DOKp-value APercentage of students who selected each optionp-value BPercentage of students who selected each optionp-value CPercentage of students who selected each optionp-value DPercentage of students who selected each optionOption AnnotationsBrief answer option analysis or rationaleExample Open-Ended Item Information TableAlignment:Assigned AAECDepth of Knowledge:Assigned DOKMean Score3 Allp-value percentages listed in the item information tables have been rounded.PSSA Grade 6 Mathematics Item and Scoring Sampler—September 20165

INFORMATION ABOUT MATHEMATICSGrade 6 Formula Sheet2016Grade 6Formulas that you may need to work questions on this test are found below. You may refer back tothis page at any time during the mathematics test.A graphic of a triangle with the base labeled B and the height labeled H.A 1/2 bhA graphic of a rectangle with the length labeled L and the width labeled W.A lwA graphic of a square with one side labeled S.A S squaredA graphic of a parallelogram with the base labeled B and the height labeled H.A bhA graphic of a trapezoid with the height labeled H, the top labeled B sub 1, and the bottom labeled Bsub 2.A 1/2 h (b sub 1 b sub 2)A graphic of a rectangular prism with the length labeled L, the width labeled W, and the heightlabeled H.V lwhSA 2lw 2lh 2whA graphic of a cube with one edge labeled S.V s s sSA 6 s squaredA graphic of a triangular prism with the width labeled W. The edges around the triangular face arelabeled A, B, and C. The height of the triangular face is H.SA ah aw bw cwPSSA Grade 6 Mathematics Item and Scoring Sampler—September 20166

INFORMATION ABOUT MATHEMATICSMATHEMATICS TEST DIRECTIONSOn the following pages are the Mathematics questions.You may not use a calculator for question 1. You may use a calculator for all other questions on thistest.Directions for Multiple-Choice Questions:Some questions will ask you to select an answer from among four choices.For the multiple-choice questions:First solve the problem on scratch paper.Choose the correct answer and record your choice in the answer booklet.If none of the choices matches your answer, go back and check your work for possible errors.Only one of the answers provided is the correct response.Directions for Open-Ended Questions:Some questions will require you to write your response.For the open-ended questions:These questions have more than one part. Be sure to read the directions carefully.You cannot receive the highest score for an open-ended question without completing all tasks inthe question. For example, if the question asks you to show your work or explain your reasoning, besure to show your work or explain your reasoning in the space provided.If the question does not ask you to show your work or explain your reasoning, you may use thespace provided, but only those parts of your response that the question speciﬁcally asks for will bescored.Write your response in the appropriate location within the response box in the answer booklet. Someanswers may require graphing, plotting, labeling, drawing, or shading. If you use scratch paper, besure to transfer your ﬁnal response and any needed work or reasoning to the answer booklet.PSSA Grade 6 Mathematics Item and Scoring Sampler—September 20167

PSSA MATHEMATICS GRADE 6Question 1 in this sampler is to be solved without the use of a calculator.MULTIPLE-CHOICE ITEMS1.Divide: 3/4 2/3A. 1/2B. 8/9C. 9/8D. 2Item InformationAlignmentA-N.1.1.1Answer KeyCDepth of Knowledge1p-value A28%p-value B12%p-value C52% (correct answer)p-value D8%Option AnnotationsA.B.C.D.multiplies 3/4 2/3inverts 3/4 instead of 2/3 prior to multiplyingcorrectinverts both fractions prior to multiplyingPSSA Grade 6 Mathematics Item and Scoring Sampler—September 20168

PSSA MATHEMATICS GRADE 6A calculator is permitted for use in solving questions 2–17 in this sampler.2.Greg’s social studies grade is based on two quizzes, two tests, and one project. The tablebelow shows Greg’s scores on these items, as well as each item’s weight in determining his finalgrade.Greg’s Social Studies ScoresItemScoreWeightquiz 1781quiz 2901test 1852test 2892project924To determine his final grade, Greg’s teacher multiplies each score by its weight, adds theproducts together, and then divides the sum by 10. What is Greg’s final grade?A. 79.9B. 86.8C. 88.4D. 92.0Item InformationAlignmentA-N.2.1.1Answer KeyCDepth of Knowledge2p-value A8%p-value B13%p-value C69% (correct answer)p-value D10%Option AnnotationsA.B.C.D.enters (78 90 1) (85 89 2) (92 4); order of operations errorfinds the average of the scorescorrectthinks project grade is final grade because it has greatest weightPSSA Grade 6 Mathematics Item and Scoring Sampler—September 20169

PSSA MATHEMATICS GRADE 63.Kiah plotted the locations of her home and the city of Huntingdon on the number line shownbelow.A number line is shown. The numbers below the number line are negative 9, negative 6, negative3, 0, 3, 6, 9. The point at 0 is labeled Kiah’s Home. The point at 6.75 is labeled Huntingdon.Williamsburg is the same distance from Kiah’s home as Huntingdon, but it is in the oppositedirection. Which statement best describes how to find the location of Williamsburg on thenumber line?A. The opposite of 6.75 is –6.75, so Williamsburg is at –6.75.B. The sum of 6.75 and 6.75 is 13.5, so Williamsburg is at 13.5.C. The numbers 6.75 and –6.75 are the same, so Williamsburg is at 6.75.D. Opposites, such as 6.75 and –6.75, sum to zero, so Williamsburg is at 0.Item InformationAlignmentA-N.3.1Answer KeyADepth of Knowledge2p-value A76% (correct answer)p-value B8%p-value C8%p-value D8%Option AnnotationsA.B.C.D.correctsums the measurements togetherthinks of absolute valueswrong property, fails to identify Kiah’s home as 0PSSA Grade 6 Mathematics Item and Scoring Sampler—September 201610

PSSA MATHEMATICS GRADE 64.James measures the water level from the top of a dock twice a day. The water level in themorning is –2 feet. The water level in the afternoon is –6.5 feet. Which statement about therelationship between the two measurements is true?A. A water level of –6.5 feet is higher than a water level of –2 feet, as –6.5 –2.B. A water level of –2 feet is lower than a water level of –6.5 feet, as –2 –6.5.C. A water level of –6.5 feet is the same as a water level of –2 feet, as –6.5 –2.D. A water level of –2 feet is higher than a water level of –6.5 feet, as –2 –6.5.Item InformationAlignmentA-N.3.2.1Answer KeyDDepth of Knowledge1p-value A15%p-value B11%p-value C6%p-value D68% (correct answer)Option AnnotationsA. thinks –6.5 feet is higher than –2 feet because –6.5 is “more” negative than–2B. thinks –2 is lower than –6.5 in terms of water level, but inequality is correctC. thinks measurements are the same since they are both negativeD. correctPSSA Grade 6 Mathematics Item and Scoring Sampler—September 201611

PSSA MATHEMATICS GRADE 65.The ratio of the number of boys to the number of girls in the cast of a school play is 1 : 5. Whichstatement must describe the cast of the play?A. There are exactly 6 students in the cast.B. There is 1 boy for every 5 girls in the cast.C. There are 4 more girls than boys in the cast.D. There is 1 boy out of the 5 students in the cast.Item InformationAlignmentA-R.1.1.1Answer KeyBDepth of Knowledge1p-value A15%p-value B64% (correct answer)p-value C8%p-value D13%Option AnnotationsA.B.C.D.thinks ratio shows total numbercorrectthinks 5 – 1mistakes ratio of boys to girls for ratio of boys to all students in the castPSSA Grade 6 Mathematics Item and Scoring Sampler—September 201612

PSSA MATHEMATICS GRADE 66.For a recipe, Harris uses 2 cups of white sugar for each cup of brown sugar. How many cups ofbrown sugar does Harris use when he uses 1 cup of white sugar?A. 1/2B. 1C. 1 1/2D. 2Item InformationAlignmentA-R.1.1.2Answer KeyADepth of Knowledge2p-value A71% (correct answer)p-value B10%p-value C10%p-value D9%Option AnnotationsA.B.C.D.correctthinks the cups of brown sugar is a constantsubtracts 1/2 from 2reverses the original ratioPSSA Grade 6 Mathematics Item and Scoring Sampler—September 201613

PSSA MATHEMATICS GRADE 67.Jasmine earns 36 for 4 hours of baby-sitting. She charges a constant hourly rate. Which tablecorrectly shows the amount Jasmine earns baby-sitting for different numbers of hours?A.Jasmine’s Baby-Sitting EarningsNumber of HoursAmount Earned ( )218436654872B.Jasmine’s Baby-Sitting EarningsNumber of HoursAmount Earned (

Standards-based 2013 PSSA Assessment Anchors and Eligible Content . The Mathematics, Reading, and Writing PSSA transitioned to PCS-based operational Mathematics and English Language Arts assessments starting with the spring 2015 PSSA administration . The 2013 PCS-aligned Assessment Anchor