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Release of Spring 2021MCAS Test Itemsfrom theGrade 6 MathematicsPaper-Based TestJune 2021Massachusetts Department ofElementary and Secondary Education
This document was prepared by theMassachusetts Department of Elementary and Secondary EducationJeffrey C. RileyCommissionerThe Massachusetts Department of Elementary and Secondary Education, an affirmative action employer,is committed to ensuring that all of its programs and facilities are accessible to all members of the public.We do not discriminate on the basis of age, color, disability, gender identity, national origin, race, religion, sex orsexual orientation. Inquiries regarding the Department’s compliance with Title IX and other civil rights laws maybe directed to the Human Resources Director, 75 Pleasant St., Malden, MA 02148 781-338-6105. 2021 Massachusetts Department of Elementary and Secondary EducationPermission is hereby granted to copy for non-commercial educational purposes any or all parts ofthis document with the exception of English Language Arts passages that are not designated as inthe public domain. Permission to copy all other passages must be obtained from the copyright holder.Please credit the “Massachusetts Department of Elementary and Secondary Education.”Massachusetts Department of Elementary and Secondary Education75 Pleasant Street, Malden, MA 02148-4906Phone 781-338-3000 TTY: N.E.T. Relay 800-439-2370www.doe.mass.edu
Overview of Grade 6 Mathematics TestThe spring 2021 grade 6 Mathematics test was a next-generation assessment that was administered in two primary formats:a computer-based version and a paper-based version. The vast majority of students took the computer-based test. The paperbased test was offered as an accommodation for students with disabilities who are unable to use a computer, as well as forEnglish learners who are new to the country and are unfamiliar with technology.Most of the operational items on the grade 6 Mathematics test were the same, regardless of whether a student took the computerbased version or the paper-based version. In places where a technology-enhanced item was used on the computer-based test, anadapted version of the item was created for use on the paper test. These adapted paper items were multiple-choice, multiple-select,or short-answer items that tested the same Mathematics content and assessed the same standard as the technology-enhanced item.This document displays released items from the paper-based test. Released items from the computer-based test areavailable on the MCAS Resource Center website at mcas.pearsonsupport.com/released-items.Test Sessions and Content OverviewThe grade 6 Mathematics test was made up of two separate test sessions. Each session included selected-response, shortanswer, and constructed-response questions. On the paper-based test, the selected-response questions were multiple-choiceitems and multiple-select items, in which students select the correct answer(s) from among several answer options.In 2021, due to the COVID-19 pandemic, the Department reduced testing time for students in grades 3–8 through a sessionsampling approach, in which each student took only a portion of each MCAS assessment. Instead of taking two sessions ineach subject, individual students took one session each.Standards and Reporting CategoriesThe grade 6 Mathematics test was based on standards in the five domains for grade 6 in the Massachusetts CurriculumFramework for Mathematics (2017). The five domains are listed below. Ratios and Proportional Relationships The Number System Expressions and Equations Geometry Statistics and ProbabilityThe Massachusetts Curriculum Framework for Mathematics is available on the Department website tics test results are reported under five MCAS reporting categories, which are identical to the five framework domainslisted above.The tables at the conclusion of this document provide the following information about each released and unreleasedoperational item: reporting category, standard(s) covered, item type, and item description. The correct answers for releasedselected-response and short-answer questions are also displayed in the released item table.Reference Materials and ToolsEach student taking the paper-based version of the grade 6 Mathematics test was provided with a plastic ruler and a grade 6Mathematics Reference Sheet. A copy of the reference sheet follows the final question in this document. An image of theruler is not reproduced in the document.During both Mathematics test sessions, the use of bilingual word-to-word dictionaries was allowed for current and formerEnglish learner students only. No calculators, other reference tools, or materials were allowed.1
Grade 6 MathematicsSESSION 1This session contains 10 questions.You may use your reference sheet during this session.You may not use a calculator during this session.DirectionsRead each question carefully and then answer it as well as you can. You must recordall answers in this Test & Answer Booklet.For some questions, you will mark your answers by filling in the circles in yourTest & Answer Booklet. Make sure you darken the circles completely. Do not makeany marks outside of the circles. If you need to change an answer, be sure to eraseyour first answer completely.For other questions, you will need to fill in an answer grid. Directions for completingquestions with answer grids are provided on the next page.If a question asks you to show or explain your work, you must do so to receive fullcredit. Write your response in the space provided. Only responses written within theprovided space will be scored.2
Mathematics Session 1Directions for Completing Questions with Answer Grids1.Work the question and find an answer.2.Enter your answer in the answer boxes at the top of the answer grid.3. Print only one number or symbol in each box. Do not leave a blank box inthe middle of an answer.4. Under each answer box, fill in the circle that matches the number orsymbol you wrote above. Make a solid mark that completely fills thecircle.5.Do not fill in a circle under an unused answer box.6. Fractions cannot be entered into an answer grid and will not be scored.Enter fractions as decimals.7. If you need to change an answer, be sure to erase your first answercompletely.8.See below for examples of how to correctly complete an answer grid.EXAMPLES– 1 4–\ \ \ \\ \ \ \0000000\\\\\\\1 \11 \1 \1 \1 \1 \\222222\\\\\\\ 23 \33 \3 \3 \3 \3 \\444444\\\\\\\ 45 \55 \5 \5 \5 \5 \\666666\\\\\\\ 67 \77 \7 \7 \7 \7 \\888888\\\\\\\ 89 \99 \9 \9 \9 \9 \\65 . 34 8 3 1 6–\ \ \ \\ \ \ \0 \00 \0 \0 \0 \0 \\1 \11 \1 \1 \1 \1 \\2 \22 \2 \2 \2 \2 \\3 \33 \3 \3 \3 \3 \\4 \44 \4 \4 \4 \4 \\5 \55 \5 \5 \5 \5 \\6 \66 \6 \6 \6 \6 \\7 \77 \7 \7 \7 \7 \\8 \88 \8 \8 \8 \8 \\9 \99 \9 \9 \9 \9 \\–\ \ \ \\ \ \ \0 \00 \0 \0 \0 \0 \\1 \11 \1 \1 \1 \1 \\2 \22 \2 \2 \2 \2 \\3 \33 \3 \3 \3 \3 \\4 \44 \4 \4 \4 \4 \\5 \55 \5 \5 \5 \5 \\6 \66 \6 \6 \6 \6 \\7 \77 \7 \7 \7 \7 \\8 \88 \8 \8 \8 \8 \\9 \99 \9 \9 \9 \9 \\39 . 5 5 5 5–\ \ \ \\ \ \ \0000000\\\\\\\1 \11 \1 \1 \1 \1 \\222222\\\\\\\ 23 \33 \3 \3 \3 \3 \\444444\\\\\\\ 45 \55 \5 \5 \5 \5 \\666666\\\\\\\ 67 \77 \7 \7 \7 \7 \\888888\\\\\\\ 89 \99 \9 \9 \9 \9 \\
Mathematics MA282262 OPqSession 1DWhat is the value of this expression when n 5?45 10nA9B11C15D19MA736364876OPwE,CWhich of the following inequalities are true?Select the two correct answers.A 4 7B 4 4C 7 4 D 7 7 E 4 7 4
Mathematics MA735778671eSession 1OPConsider this expression.7110 90What is the value of this expression?Enter your answer in the answer boxes at the top of the answer grid andcompletely fill the matching circles.–\ \ \ \\ \ \ \0000000\\\\\\ \1 \11 \1 \1 \1 \1 \\2222222\\\\\\ \3333333\\\\\\ \4444444\\\\\\ \5555555\\\\\\ \6666666\\\\\\ \7777777\\\\\\ \8888888\\\\\\ \9999999\\\\\\ \5
Mathematics MA800171425 PArOPSession 1CAn electrician will use the following wires for a project: 4 red wires that are each 36 inches in length 2 blue wires that are each 84 inches in lengthThe electrician wants to cut all the wires into equal-sized pieces of thegreatest possible length.Which of the following is true?AThe greatest length the electrician can cut the wires into is 6 inches. Thetotal number of pieces the electrician will have after the wires are cut is 26.BThe greatest length the electrician can cut the wires into is 6 inches. Thetotal number of pieces the electrician will have after the wires are cut is 51.CThe greatest length the electrician can cut the wires into is 12 inches. Thetotal number of pieces the electrician will have after the wires are cut is 26.DThe greatest length the electrician can cut the wires into is 12 inches. Thetotal number of pieces the electrician will have after the wires are cut is 51.6
Mathematics MA301222tOPSession 1DA new office building will have 640 workers. A construction code requiresthat new buildings have 2 restrooms for every 80 workers in the building.Based on the construction code, what is the total number of restrooms thenew office building must have?A4B8C12D167
Mathematics Session 1This question has three parts. Be sure to label each part of your response.MA713831396 PAyOPA city planner is creating designs for two dog parks.A. The city planner is using a coordinate plane to create the design for thefirst park. The park will be in the shape of a rectangle. These four pointsrepresent the corners of the park. point A: (4, 1) point B: (4, 3) point C: ( 2, 3) point D: ( 2, 1)On the coordinate plane provided in your answer space, plot the fourpoints and then connect them to create the rectangle.B. What are the length and the width, in units, of the rectangle you createdin Part A to represent the park? Show or explain how you got your answer.C. The city planner is using another coordinate plane to create the design forthe second park. T he perimeter of the second park will be the same as the perimeterof the first park. One corner of the second park is represented by the point (1, 2). The second park is in the shape of a square.What could be the coordinates of the other three corners of the secondpark? Show or explain how you got your answer.8
Mathematics yA.Session 1y4321-4 -3 -2 -1 0-1-2-3-491 2 3 4x
Mathematics MA800173241 PAuOPSession 1DWhich of the following number lines shows a point that represents 2–10–4–3–2–10BCD10
Mathematics MA805283567 PABA volleyball team played twenty games this season. This list of data showsthe number of people in attendance at each 35,42,27,46,23Which of the following histograms represents the data?Volleyball Game Attendance10987654321010987654321011–20 21–30 31–40 41–5011–20 21–30 31–40 41–50Number of PeopleNumber of PeopleVolleyball Game Attendance109876543210Volleyball Game AttendanceDNumber of GamesCVolleyball Game AttendanceBNumber of GamesNumber of GamesANumber of GamesiOPSession 110987654321011–20 21–30 31–40 41–5011–20 21–30 31–40 41–50Number of PeopleNumber of People11
Mathematics MA736069855oOPSession 1DConsider this inequality.5c 10Which of the following is a solution to the inequality?A0B1C2D3MA805179243aOPE,BA student collects data by asking students in his math class some questions.Which of the following questions are statistical questions?Select the two statistical questions.AWho is your math teacher?BWhat is your favorite subject?CHow many minutes long is math class?DDid the teacher give a math quiz today?EHow many minutes do you spend on math homework each week?12
Grade 6 MathematicsSESSION 2This session contains 10 questions.You may use your reference sheet during this session.You may not use a calculator during this session.DirectionsRead each question carefully and then answer it as well as you can. You must recordall answers in this Test & Answer Booklet.For some questions, you will mark your answers by filling in the circles in yourTest & Answer Booklet. Make sure you darken the circles completely. Do not makeany marks outside of the circles. If you need to change an answer, be sure to eraseyour first answer completely.For other questions, you will need to fill in an answer grid. Directions for completingquestions with answer grids are provided on the next page.If a question asks you to show or explain your work, you must do so to receive fullcredit. Write your response in the space provided. Only responses written within theprovided space will be scored.13
Mathematics Session 2Directions for Completing Questions with Answer Grids1.Work the question and find an answer.2.Enter your answer in the answer boxes at the top of the answer grid.3. Print only one number or symbol in each box. Do not leave a blank box inthe middle of an answer.4. Under each answer box, fill in the circle that matches the number orsymbol you wrote above. Make a solid mark that completely fills thecircle.5.Do not fill in a circle under an unused answer box.6. Fractions cannot be entered into an answer grid and will not be scored.Enter fractions as decimals.7. If you need to change an answer, be sure to erase your first answercompletely.8.See below for examples of how to correctly complete an answer grid.EXAMPLES– 1 4–\ \ \ \\ \ \ \0000000\\\\\\\1 \11 \1 \1 \1 \1 \\222222\\\\\\\ 23 \33 \3 \3 \3 \3 \\444444\\\\\\\ 45 \55 \5 \5 \5 \5 \\666666\\\\\\\ 67 \77 \7 \7 \7 \7 \\888888\\\\\\\ 89 \99 \9 \9 \9 \9 \\4 8 3 1 6–\ \ \ \\ \ \ \0 \00 \0 \0 \0 \0 \\1 \11 \1 \1 \1 \1 \\2 \22 \2 \2 \2 \2 \\3 \33 \3 \3 \3 \3 \\4 \44 \4 \4 \4 \4 \\5 \55 \5 \5 \5 \5 \\6 \66 \6 \6 \6 \6 \\7 \77 \7 \7 \7 \7 \\8 \88 \8 \8 \8 \8 \\9 \99 \9 \9 \9 \9 \\65 . 3–\ \ \ \\ \ \ \0 \00 \0 \0 \0 \0 \\1 \11 \1 \1 \1 \1 \\2 \22 \2 \2 \2 \2 \\3 \33 \3 \3 \3 \3 \\4 \44 \4 \4 \4 \4 \\5 \55 \5 \5 \5 \5 \\6 \66 \6 \6 \6 \6 \\7 \77 \7 \7 \7 \7 \\8 \88 \8 \8 \8 \8 \\9 \99 \9 \9 \9 \9 \\149 . 5 5 5 5–\ \ \ \\ \ \ \0000000\\\\\\\1 \11 \1 \1 \1 \1 \\222222\\\\\\\ 23 \33 \3 \3 \3 \3 \\444444\\\\\\\ 45 \55 \5 \5 \5 \5 \\666666\\\\\\\ 67 \77 \7 \7 \7 \7 \\888888\\\\\\\ 89 \99 \9 \9 \9 \9 \\
Mathematics MA307272sOPSession 2AA family drank 4 gallons of juice over 5 weeks. During this time period,at what rate did the family drink juice?A4gallon per week5B5gallons per week4C1 gallon per weekD9 gallons per week15
Mathematics MA800160765dOPSession 2F,D,AConsider this expression.6x 24Which of the following are equivalent to the expression?Select the three equivalent expressions.A6(x 4)B6(x 24)C3(12 2x)D2(3x 12)E3x 3 20 4xF4x 12 2x 1216
Mathematics MA736370121 PAfOPSession 2CConsider this expression.25 36Which of the following is the quotient of the expression?A1018B1215C1512D181017
Mathematics Session 2This question has four parts. Be sure to label each part of your response.MA703249688gOPOn Monday, there were 18 chickens and 12 sheep in a field. There wereno other animals in the field.A. What was the ratio of chickens to sheep in the field on Monday?B. For every 2 sheep in the field on Monday, how many chickens were in thefield? Show or explain how you got your answer.C. The ratio 3:5 can also be used to describe a relationship between theanimals in the field on Monday. What relationship could this ratio describe?Show or explain how you got your answer.D. On Tuesday, there were 4 more sheep in the field. Write a ratio to showthe relationship between the number of sheep and the total number ofanimals in the field on Tuesday. Show or explain how you got your answer.18
Mathematics Session 2g19
Mathematics MA800180478 PAhOPSession 2DThe length of a yellow ribbon is 6.75 inches. The length of a green ribbon isgreater than the length of the yellow ribbon.Which of the following number lines shows the graph of an inequality thatrepresents all the possible lengths, in inches, of the green 678910BCD20
Mathematics MA736071864jOPSession 2DA teenager is saving money to buy a snowboard. The snowboard costs 132, including sales tax. The teenager has already saved 23.Which of the following equations could be used to find m, the remainingamount of money, in dollars, the teenager must save to buy the snowboard?Am 13223B23m 132Cm 23 132Dm 23 13221
Mathematics MA800440516 PAkOPSession 2BA plumber charges a rate of 45 for each hour of work.Which of the following is true?AAn expression that represents the amount, in dollars, that the plumberwill charge for x hours of work is 45x. At this rate, for 2 hours of workthe plumber will charge 47.BAn expression that represents the amount, in dollars, that the plumberwill charge for x hours of work is 45x. At this rate, for 2 hours of workthe plumber will charge 90.CAn expression that represents the amount, in dollars, that the plumberwill charge for x hours of work is 45 x. At this rate, for 2 hours of workthe plumber will charge 47.DAn expression that represents the amount, in dollars, that the plumberwill charge for x hours of work is 45 x. At this rate, for 2 hours of workthe plumber will charge 90.22
Mathematics Session 2This question has two parts.MA624254582 OPlB,XThis list shows the number of countries outside the United States that12 students in Mr. Miller’s class have visited.3, 1, 9, 5, 2, 0, 0, 2, 6, 1, 6, 1Part ABased on the list, what is the median number of countries outside theUnited States that Mr. Miller’s students have visited?A1B2C3D9Part BBased on the list, what is the mean number of countries outside theUnited States that Mr. Miller’s students have visited?Enter your answer in the answer boxes at the top of the answer grid andcompletely fill the matching circles.–\ \ \ \\ \ \ \0 \00 \0 \0 \0 \0 \\1 \11 \1 \1 \1 \1 \\2 \22 \2 \2 \2 \2 \\3 \33 \3 \3 \3 \3 \\4 \44 \4 \4 \4 \4 \\5 \55 \5 \5 \5 \5 \\6 \66 \6 \6 \6 \6 \\7 \77 \7 \7 \7 \7 \\8 \88 \8 \8 \8 \8 \\9 \99 \9 \9 \9 \9 \\23
Mathematics MA800162299;OPSession 2CThe owner of a furniture store orders 6 chairs for every table she orders.Which of the following equations can be used to find c, the total number ofchairs she will order when she orders t tables?A6c tBt 6 cC6t cDc 6 t24
Mathematics MA713679240 PA2)OPSession 2AWhich of the following equations is true?A8 23B92 18C12 62D73 2125
Massachusetts Comprehensive Assessment SystemGrade 6 Mathematics Reference SheetCONVERSIONS1 cup 8 fluid ounces1 inch 2.54 centimeters1 pound 16 ounces1 pint 2 cups1 meter1 pound1 quart 2 pints1 mile 5280 feet1 kilogram1 gallon 4 quarts1 mile 1760 yards1 ton 2000 pounds1 gallon1 mile1 liter3.785 liters0.264 gallon39.37 inches0.454 kilogram2.2 pounds1.609 kilometers1 kilometer0.62 mile1 liter 1000 cubic centimetersAREA (A) FORMULASVOLUME (V) FORMULASsquare . . . . . . . . . . . A s 2right rectangular prism . . . . . V lwh(l length; w width; h height)rectangle . . . . . . . . . A bhORORV BhA lw(B area of base; h height)parallelogram . . . . . . A bhtriangle . . . . . . . . . . A 1 bh2(b length of base; h height)26
Grade 6 MathematicsSpring 2021 Released Operational mType*14Expressions and Equations6.EE.A.2SRDetermine the value of an expression given thevalue of a variable.D24The Number System6.NS.C.7SRInterpret inequalities using absolute values ofintegers.C,E35The Number System6.NS.B.2SAFind the quotient of two multi-digit numbers.79CDItem Description46The Number System6.NS.B.4SRFind the greatest common factor of two numbersto solve a real-world problem.57Ratios and ProportionalRelationships6.RP.A.3SRSolve a ratio problem based on a given realworld context.CorrectAnswer**68Geometry6.G.A.3CRSolve problems on a coordinate plane by plottingpoints, finding the distance between points,and finding the coordinates of points given thedistance between them.710The Number System6.NS.C.6SRDetermine which number line shows a point thatrepresents a given negative decimal.D811Statistics and Probability6.SP.B.4SRChoose a histogram to represent a given setof data.B912Expressions and Equations6.EE.B.5SRDetermine the value of the variable in aninequality.D1012Statistics and Probability6.SP.A.1SRIdentify multiple statistical questions.1115Ratios and ProportionalRelationships6.RP.A.2SRSolve a unit-rate problem based on a given realworld context.1216Expressions and Equations6.EE.A.4SRIdentify expressions that are equivalent to agiven variable expression.1317The Number System6.NS.A.1SRCalculate the quotient of two fractions.1418Ratios and ProportionalRelationships6.RP.A.1CRSolve a real-world problem by interpreting andfinding ratios based on a given ratio relationship.1520Expressions and Equations6.EE.B.8SRDetermine which number line shows the graphof an inequality that represents a constraint in agiven real-world context.D1621Expressions and Equations6.EE.B.7SRDetermine which equation represents a givenreal-world context.D1722Expressions and Equations6.EE.B.6SRDetermine which sentences about a givenreal-world context include an expression andinformation that represent the context.B1823Statistics and Probability6.SP.B.5SADetermine the median and mean of a set of data.1924Expressions and Equations6.EE.C.9SRChoose a two-variable equation that bestrepresents a given real-world context.C2025Expressions and Equations6.EE.A.1SREvaluate numerical expressions involvingwhole-number exponents.AB,EAA,D,FCB;3* Mathematics item types are: selected-response (SR), short-answer (SA), and constructed-response (CR).** Answers are provided here for selected-response and short-answer items only. Sample responses and scoring guidelines for any constructedresponse items will be posted to the Department’s website later this year.27
Grade 6 MathematicsSpring 2021 Unreleased Operational tem Description21The Number System6.NS.B.3SRAdd and subtract decimals within a real-world context.22Ratios and ProportionalRelationships6.RP.A.2SADetermine the unit rate within a real-world context.23Statistics and Probability6.SP.B.5SRCalculate the mean of a given set of data.24Expressions andEquations6.EE.B.7CRWrite and solve equations that model a real-world problem.25Ratios and ProportionalRelationships6.RP.A.1SRDetermine which relationship can be represented by a given ratio.26Expressions andEquations6.EE.A.3SRUse the distributive property to identify an equivalent expression withina real-world context.27Expressions andEquations6.EE.B.8SRIdentify the inequality which represents a constraint within a real-worldcontext.28Expressions andEquations6.EE.A.3SRUse the distributive property to determine equivalent expressions given avariable expression.29Geometry6.G.A.1SAFind the area of a right triangle and decompose a polygon into triangles tochoose the sentence that best describes its area.30Ratios and ProportionalRelationships6.RP.A.1SRDetermine which statement describes a given ratio relationship in a realworld context.31Statistics and Probability6.SP.A.2SRDetermine the interquartile range of data displayed in a box plot.32Expressions andEquations6.EE.A.3SRUse properties of operations to identify an equivalent equation.33Ratios and ProportionalRelationships6.RP.A.3SRDetermine the volume of a liquid by using rate and ratio reasoning withina real-world context.34Statistics and Probability6.SP.A.1SRIdentify multiple statistical questions.35The Number System6.NS.C.8CRSolve problems on a coordinate plane by finding the distance betweenpoints, plotting points, and finding the coordinates of a point given itsdistance from a different point.36The Number System6.NS.C.5SRDetermine which real-world situation can be best represented by anegative number.37Geometry6.G.A.4SAUse the net of a square pyramid to find its surface area.38Ratios and ProportionalRelationships6.RP.A.3SRCompare unit rates given a ratio in a real-world context involving money.39Statistics and Probability6.SP.B.5SRDetermine which statements correctly describe data represented in a dotplot.40Geometry6.G.A.2SRDetermine the number of cubes with fractional edge lengths that would fitin a given right rectangular prism in a real-world context.* Mathematics item types are: selected-response (SR), short-answer (SA), and constructed-response (CR).28
The grade 6 Mathematics test was based on standards in the five domains for grade 6 in the . Massachusetts Curriculum . Framework for Mathematics (2017). The five domains are listed below. Ratios and Proportional Relationships The Number System Expressions and Equations Geometry Statistics and Probability The
