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X. Mathematics, Grade 4

Grade 4 Mathematics TestTest Sessions and Content OverviewThe spring 2016 grade 4 Mathematics test was made up of two separate test sessions. Each session included: Twenty-one common items, including multiple-choice, short-answer, and open-response questions. Thesecommon items are the items on which each student’s 2016 MCAS Mathematics score will be based. Three items developed by the Partnership for Assessment of Readiness for College and Careers (PARCC),including multiple-choice, multiple-select, and open-response questions. Students’ performance on these PARCCitems will not be factored into their MCAS scores.Approximately half of the common test items are shown on the following pages as they appeared in test booklets.The PARCC items are not being released in this document. The Department will post information about these items to theStudent Assessment webpage in a separate document. See page 4 of the Introduction to this document for more informationabout the inclusion of PARCC items in the 2016 MCAS tests.Standards and Reporting CategoriesThe common items in the spring 2016 grade 4 Mathematics test assessed standards in the five domains for grade 4 in theMassachusetts Curriculum Framework for Mathematics (March 2011). The grade 4 standards can be found on pages 43–47in the Framework, and the five domains are listed below. Operations and Algebraic Thinking Number and Operations in Base Ten Number and Operations—Fractions Measurement and Data GeometryThe 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 frameworkdomains listed above.The tables at the conclusion of this chapter indicate each released and unreleased common item’s reporting category andthe framework standard it assesses. The correct answers for released multiple-choice and short-answer questions are alsodisplayed in the released item table.Standards and reporting categories for the PARCC items in the grade 4 Mathematics test will be listed in a separatedocument, which will be posted to the Student Assessment webpage.Reference Materials and ToolsEach student taking the grade 4 Mathematics test was provided with a plastic ruler and a grade 4 Mathematics ToolKit. The tool kit pieces and an image of the ruler are not reproduced in this publication.During both Mathematics test sessions, the use of bilingual word-to-word dictionaries was allowed for current andformer English language learner students only. No calculators, other reference tools, or materials were allowed.155

Grade 4 MathematicsSession 1You may use your tool kit and MCAS ruler during this session.You may not use a calculator during this session.DIRECTIONSThis session contains six multiple-choice questions, two short-answer questions, and two openresponse questions. Mark your answers to these questions in the spaces provided in your StudentAnswer Booklet.ID:303326 A Common1 ID:286768 A Common2 Jane, Frank, and Denise each cut alength of ribbon. Jane’s ribbon is 0.5 meter long.Jessica is thinking of a number. Shelisted some of the factors of her numberin the box shown below. Frank’s ribbon is 0.39 meter long.2, 3, 4, 6 Denise’s ribbon is 0.4 meter long.Which of the following could beJessica’s number?Which statement about the lengths ofthe ribbons is true?A. 12A. Jane’s ribbon is longer thanFrank’s ribbon.B. 14C. 16B. Denise’s ribbon is longer thanJane’s ribbon.D. 18C. Frank’s ribbon is longest.D. Denise’s ribbon is shortest.156

Mathematics Session 1Questions 3 and 4 are short-answer questions. Write your answers to these questions in the boxesprovided in your Student Answer Booklet. Do not write your answers in this test booklet. You may doyour figuring in the test booklet.ID:293514 SA3005 perpend lines.eps CommonUse your MCAS ruler to answer question 3.3 In your Student Answer Booklet, draw two lines that are perpendicular.ID:307311 Common4 Devin wrote a number in expanded form, as shown below.500, 00090, 0003, 00020Write Devin’s number in standard form.1578

Mathematics Session 1Question 5 is an open-response question. BE SURE TO ANSWER AND LABEL ALL PARTS OF THE QUESTION.Show all your work (diagrams, tables, or computations) in your Student Answer Booklet.If you do the work in your head, explain in writing how you did the work.Write your answer to question 5 in the space provided in your Student Answer Booklet.ID:302489 Common5 Carl sold cookies and pies at a bake sale to earn money. A bag of cookies sells for 3. A pie sells for 8.a. Carl sold 4 bags of cookies and 2 pies during the first hour of the bake sale. What is thetotal amount of money, in dollars, Carl earned during the first hour of the bake sale?Show or explain how you got your answer.b. Ms. O’Hara bought 2 bags of cookies and 1 pie from Carl. She paid with a 20 bill. Whatis the total amount of change, in dollars, Ms. O’Hara should receive? Show or explain howyou got your answer.Vanessa sold cakes at the same bake sale.c. Mr. Stanley bought 1 bag of cookies and 2 pies from Carl. Mr. Stanley also spent 11 tobuy a cake from Vanessa at the bake sale. Write an equation to show m, the total amountof money, in dollars, Mr. Stanley spent at the bake sale.d. Solve the equation you wrote in part (c) to find the total amount of money, in dollars,Mr. Stanley spent at the bake sale. Show your work.158

Mathematics Session 1Mark your answers to multiple-choice questions 6 through 9 in the spaces provided in your StudentAnswer Booklet. Do not write your answers in this test booklet. You may do your figuring in the testbooklet.ID:311536 C CommonID:287236 EBH2095.eps [opt a01, b01 C Common6 7 Which of the following shapes hasexactly two lines of symmetry?When rounded to the nearest thousand,the number of people who attended aconcert is 18,000.Which of the following could be thenumber of people who attended theconcert?A.A. 17,264B. 17,428B.C. 18,135D. 18,526C.D.159

Mathematics Session 1ID:311541 MCAS1415 Gr04 Math VP30.e B Common8 ID:311555 MCAS1415 Gr04 Math VP57 A A Common9 Nathan is using the area model below tosolve a problem.101010Kendall drew a 100 angle from thecenter of a circle, as shown below.6100 31036Which problem is represented by thewhole area model?A. 126B. 1613C. 209D. 6030What fraction of the circle doesKendall’s angle turn through?160A.100360B.100260C.100180D.10090

Mathematics Session 1Question 10 is an open-response question. BE SURE TO ANSWER AND LABEL ALL PARTS OF THE QUESTION.Show all your work (diagrams, tables, or computations) in your Student Answer Booklet.If you do the work in your head, explain in writing how you did the work.Write your answer to question 10 in the space provided in your Student Answer Booklet.ID:307322 Common10 Erin uses28yard of string to make 1 bracelet. Erin will make 6 bracelets.a. How many yards of string will Erin use to make 6 bracelets? Show or explain how you gotyour answer.Erin uses38yard of string to make 1 necklace. Erin will make 5 necklaces.b. How many yards of string will Erin use to make 5 necklaces? Show or explain how yougot your answer.c. The total number of yards of string Erin will use for 6 bracelets and 5 necklaces isbetween what two whole numbers? Show or explain how you got your answer.161

Grade 4 MathematicsSession 2You may use your tool kit and MCAS ruler during this session.You may not use a calculator during this session.DIRECTIONSThis session contains ten multiple-choice questions and one short-answer question. Mark youranswers to these questions in the spaces provided in your Student Answer Booklet.ID:311532 D Common11 ID:280085 B Common12 Which of these numbers has a 5 whosevalue is ten times the value of the 5 in7359?Darlene has 16 toy spiders. She hasone-half as many toy beetles as shehas toy spiders.Which of the following equations canbe used to find b, the total number oftoy beetles Darlene has?A. 5268B. 4652C. 3005D. 2511162A. 162bB. 162bC. 1612bD. 1612b

Mathematics Session 2ID:307325 MCAS13 M04 11 ART.eps C Common13 ID:301804 B Common14 Gianna drew an X on two sides of atriangle, as shown below.A class of 29 students is taking a fieldtrip to the zoo. Each ticket to the zoocosts 15.Which of these expressions can be used tofind the total cost, in dollars, of the ticketsto the zoo?XXWhich statement is true about the sidesthat Gianna drew an X on?A. The sides are parallel.B. The sides are perpendicular.C. The sides form an acute angle.D. The sides form an obtuse angle.163A. (2910)(295)B. (2910)(295)C. (2910)(295)D. (2910)(295)

Mathematics Session 2ID:218905 D CommonID:298098 IS062 triangles.eps [opt B Common15 16 Which of these is a right triangle?A.The recipe on a box of pancake mixtells how many cups of pancake mix areneeded to make different numbers ofpancakes, as shown in the table below.Pancake Recipe60 Cups ofPancake Mix123456B.90 C.Number ofPancakes8162432?120 D.Based on the information in the table,how many pancakes can be made with6 cups of pancake mix?140 A. 39B. 40C. 46D. 48164

Mathematics Session 2Question 17 is a short-answer question. Write your answer to this question in the box provided inyour Student Answer Booklet. Do not write your answer in this test booklet. You may do your figuringin the test booklet.ID:307030 MCAS13 M04 MD 24 ART.eps Common17 Some angles are shown in the diagram below.GH30 EJ50 FAngle EFG has a measure of 50 , and angle GFH has a measure of 30 . The sum of the measuresof angles EFG, GFH, and HFJ is 120 .What is the measure, in degrees, of angle HFJ ?165

Mathematics Session 2Mark your answers to multiple-choice questions 18 through 21 in the spaces provided in your StudentAnswer Booklet. Do not write your answers in this test booklet. You may do your figuring in the testbooklet.ID:298082 IS046 rainfall line plot. B Common18 Brendan made a line plot showing the weekly rainfall, in inches, for his town one summer.His line plot is shown below.0XXXXX1211 —12—XXX22 —12XX33 —12XX44 —12X55 —126Weekly Rainfall(in inches)Which of these expressions can Brendan use to find the difference, in inches, between thegreatest weekly rainfall and the least weekly rainfall that he recorded for his town?A. 1 2112112112B. 5 21C. 5 2D. 612166

Mathematics Session 2ID:307073 C Common19 ID:247750 EBH542 garden version2.ep B Common20 Jacob wrote the expression shown below.6107100Parvati’s GardenWhich of these is equivalent to theexpression Jacob wrote?A.610710B.60107100C.601007100D.6010070100A diagram of Parvati’s garden and thelengths of all its sides are shown below.1 yard2 yards5 yards8 yards6 yards6 yardsParvati wants to put a fence around herwhole garden. What is the least numberof yards of fence she will need?A. 24 yardsB. 28 yardsC. 36 yardsD. 48 yards167

Mathematics Session 2ID:301819 D Common21 Olivia’s height is 1.34 meters. What isOlivia’s height in centimeters?A. 0.0134 centimeterB. 0.134 centimeterC. 13.4 centimetersD. 134.0 centimeters168

Massachusetts Comprehensive Assessment SystemGrade 4 Mathematics Tool KitDuring testing, students were provided with tool kit pieces to answer test items that arenot released.169