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RELEASEDMATHEMATICS ITEMS8This book contains the released Trends in International Mathematics and Science Study(TIMSS) 2011 grade 8 mathematics assessment items. This is not a complete set of allTIMSS 2011 assessment items because some items are kept confidential so that theymay be used in subsequent cycles of TIMSS to measure trends.How Can This Set of Released Items Be Used?In Teacher-designed Assessments. The items in this book present different ways ofmeasuring students’ understanding in various content and cognitive domains. A teachermay use these items to create an assessment according to the needs of the class afterreviewing the items and selecting items of interest.For Feedback on Student Understanding. Studentresponses can be scored accordingto the scoring information provided in the book. Items that coincide with conceptstaught in class allow the teacher to gain feedback on the students’ understanding ofassessed concepts. For example, a teacher might decide to examine the incorrect orpartially correct responses of the class. The teacher might use the items to identifyparticular difficulties or misconceptions experienced by individual students, whichcan serve as the basis for some remedial teaching or focused practice.To Benchmark Student Performance. Theteacher might also compare the percentof students in the class who responded correctly to an item with the percentof students who responded correctly to the same item in other education systemsor in the United States.TIMSS and PIRLS are copyrighted and are registered trademarks of IEA. Released items fromTIMSS and PIRLS assessments are for non-commercial, educational, and research purposes only.Translated versions of items remain the intellectual property of IEA. Although the items are in thepublic domain, please print an acknowledgement of the source, including the year and name of theassessment you are using. If you publish any part of the released items from TIMSS 2011, please usethe following acknowledgement:SOURCE: TIMSS 2011 Assessment. Copyright 2013 International Association for the Evaluation ofEducational Achievement (IEA). Publisher: TIMSS & PIRLS International Study Center, Lynch Schoolof Education, Boston College, Chestnut Hill, MA and International Association for the Evaluation ofEducational Achievement (IEA), IEA Secretariat, Amsterdam, the Netherlands.38331.0513.86070312
USER’S GUIDEGrade 8This book contains TIMSS 2011 released itemsfor grade 8. Each item appears on a single page,on which is provided information about the item’sclassification and about international studentperformance on the item. The items appear in thecontent domain order, as shown in the index on thenext page.Information aboutitem classificationTake a look at the first item on page 1. Acrossthe top are three boxes which identify theitem’s content domain (the subject matter inmathematics that the item assesses), its main topic(the specific topic assessed within that subjectmatter), and its cognitive domain (the cognitive orthinking process assessed). For this item, the contentdomain is number, the main topic is fractions anddecimals, and the cognitive domain is applying.Below the row of boxes and above a boxed-in areaof the page is the item label. For this item, it is Annand Jenny divide 560 zeds. Below the boxed-in areais the item number, which is more commonly usedto identify each item than the item label. Within theboxed-in area is the item as it appeared in studenttest booklets.are shown beneath each item.The correct answer for multiple-choice items issimply a letter code. For example, in the itemM032094 on page 3, the letter code A is the correctanswer. The correct answers for write-in or openended items are explained in a scoring guide. Forexample, the Ann and Jenny divide 560 zeds (page 1)provides an example of a scoring guide, indicatingthe general nature of correct and incorrectCorrect answersresponses. In some cases, partial credit may beawarded and these items will provide guidelinesfor fully correct, partially correct, and incorrectresponses. Sample student responses are providedfor some of the constructed-response items for eachscoring category.Information about internationalstudent performanceIn the table along the right-hand side of the pageare the percent correct statistics for the item.These consist of statistics on the percentage ofstudents in each education system who couldanswer the question correctly. The lists of educationsystems are ordered in terms of this percentage.The international average is included as well.To the right of some of the percent correctstatistics are special symbols that indicate whenan education system scored significantly higheror significantly lower than the internationalaverage. Thus, on the item Ann and Jenny divide560 zeds as an example, an estimated 25 percentof U.S. students could correctly answer this item,a percentage that was not measurably different thanthe international average, after taking into accountthe standard of error associated with the percentcorrect statistic for the United States and for theinternational average.38331.0513.86070312
ITEM INDEXGrade 8Content 052231PageAlgebra (continued)Ann and Jenny divide 560 zeds .14/100 plus 3/1000.3Best estimate of (7.21x3.86)/10.09.4The percentage of caps for sale.536 as a product of prime factors.6Location of N on number line.7Write 3 5/6 in decimal form.8Numbers to get greatest results.10Express 256 X 4096 as power of 4 .12What is K on a number line.13Equivalent expression.14Equivalent fraction for 0.125.15Length of the original pipe.16Complete the missing boxes.17Next line in the pattern.19Packing eggs into boxes.21Which number sentence is true.22Select the decimal equal to 3/5.23Method for subtracting fractions.24Add 42.65 to ent DomainSum of 3 consecutive whole numbers.26m boys and n girls in a parade.27The shadow lengths of four bushes.28Which represents 2x plus 3x.29Jo has 3 metal blocks to weigh.30Cost in zeds for taxi trip of n km.31Find the value of y when t is 9.32If t is a number between 6 and 9.34Simplify 3x/8 plus x/4 plus x/2.35What xy plus 1 mean.37Red&BlackTiles Complete table.38Red&BlackTiles Shape with 64 tiles.40Red&BlackTiles Shape with 49 tiles.41Red&BlackTiles Shape with 44 tiles.42Red&BlackTiles Figure n.43What is the area of the rectangle.45Expression to equivalent to 4(3 x).46What is the value of 2a 2b 4.47Solve the inequality.49Next term in the pattern.51Term number 100 in the pattern.53Term number n in the pattern.55What is the value P.57Value of x in the pattern.59What is the value of x and y.61M042236M042245M052002M052173M052302Simplify the expression.62Equation that satisfies number pairs.63Length of the longest wood piece.64Area of garden’s shaded portion.65Value of y in an 52362M052408Shape made up of same size cubes .67Area of a square is 144 square cm.68Distance between the midpoints.69Degrees minute hand of clock turns.70Figure 1 transformed to 2 and 3.71Value of angle x in figure.72Why PQR is a right angle triangle.73Area of the shaded region in figure.74Shape of cutout figure.75Interior angles of pentagon .76View of shape directly from above.78Which shape has a line of symmetry.80Half-turn around point O.81Length of the rectangular box.82Draw an isosceles triangle.84Measure of angle BOC-DERIVED.86Calculate the area of a square .88Number of books to fill the box.89What is the size of angle B.90Value of angle b.91Data and 207M042260M042269M052429M052503AM052503BHow likely to get pink candy .92Number of times spinner in red area.93Car production graph/time cars made.94Car production graph/avg by hour.96Car production graph/identify time.98Make a pie chart with labels.100Sales of two types of soft drink.103Mean number of staff members.104Median number of staff members.105Change in mean and median.108Number of regular size bottles.110Chance of getting a button.111Complete and label this pie chart.112How likely student voted for Pat.115Long jump competition.116Probability that the marble is red.117Age structures of country X and Y.118Problem of taking care of elderly.12038331.0513.86070312
TIMSS 2011 8th-Grade Mathematics Concepts and Mathematics ItemsContent DomainMain TopicCognitive DomainNUMBERFractions and DecimalsApplyingAnn and Jenny divide 560 zedsAnn and Jenny divide 560 zeds between them. If Jenny getsOverall Percent Correctof the money,how many zeds will Ann get?Answer:Item Number: M032064SCORINGCorrect Response 350Incorrect Response 210 5/8 Other incorrect (including crossed out, erased, stray marks, illegible, or off task)Education systemPercentcorrectSingaporeKorea, Rep. ofHong Kong-CHNChinese Taipei-CHNFinlandRussian w ZealandInternational averageUnited nited Arab EmiratesIran, Islamic Rep. ofMacedonia, Rep. ofQatarChileThailandPalestinian Nat’l Auth.LebanonBahrainIndonesiaSaudi ArabiaOmanJordanMoroccoSyrian Arab kingeducation systemPercentcorrectQuebec-CANNorth SADubai-UAEFlorida-USACalifornia-USAAbu rcent higher than International averagePercent lower than International averageCopyright 2013 International Association for the Evaluation of Educational Achievement (IEA).1
TIMSS 2011 8th-Grade Mathematics Concepts and Mathematics ItemsAnn and Jenny divide 560 zeds (continued)M032064Student ResponsesCorrect Response:Answer:Incorrect Response:Answer:Copyright 2013 International Association for the Evaluation of Educational Achievement (IEA).2
TIMSS 2011 8th-Grade Mathematics Concepts and Mathematics ItemsContent DomainMain TopicCognitive DomainNUMBERFractions and DecimalsKnowing4/100 plus 3/1000Overall Percent Correct1000A.0.043B.0.1043C.0.403D.0.43Item Number: M032094Correct Response:AEducation systemPercentcorrectSingaporeKorea, Rep. ofHong Kong-CHNChinese Taipei-CHNRussian azakhstanLithuaniaFinlandUnited Arab yUnited StatesInternational averagePalestinian Nat’l Auth.England-GBRGeorgiaRomaniaThailandMacedonia, Rep. ofQatarNew ZealandIran, Islamic Rep. ofTurkeyJordanNorwayMoroccoSaudi ArabiaBahrainSyrian Arab 94949484847464134Benchmarkingeducation systemPercentcorrectNorth u ent higher than International averagePercent lower than International averageCopyright 2013 International Association for the Evaluation of Educational Achievement (IEA).3
TIMSS 2011 8th-Grade Mathematics Concepts and Mathematics ItemsContent DomainMain TopicCognitive DomainNUMBERFractions and DecimalsKnowingBest estimate of (7.21x3.86)/10.09Which of these is the BEST estimate ofOverall Percent Correct?A.B.C.D.Item Number: M032166Correct Response:BEducation systemPercentcorrectSingaporeHong Kong-CHNUnited StatesRussian FederationFinlandLithuaniaJapanChinese Taipei-CHNSwedenNorwayKorea, Rep. sraelRomaniaInternational averageNew ZealandMalaysiaMacedonia, Rep. ofUnited Arab EmiratesArmeniaGeorgiaThailandSaudi ilePalestinian Nat’l Auth.Iran, Islamic Rep. ofJordanIndonesiaOmanMoroccoSyrian Arab enchmarkingeducation ANDubai-UAEAbu Dhabi-UAEMinnesota-USAConnecticut-USANorth 8786858581807670Percent higher than International averagePercent lower than International averageCopyright 2013 International Association for the Evaluation of Educational Achievement (IEA).4
TIMSS 2011 8th-Grade Mathematics Concepts and Mathematics ItemsContent DomainMain TopicCognitive DomainNUMBERRatio, Proportion and PercentApplyingThe percentage of caps for saleOverall Percent CorrectColor of CapsGreen25%White30%Red20%Black15%Blue10%The pie chart shows the percentage of caps for sale at a sporting goods store.If there are 200 caps, what is the total number of caps that are either white orgreen?A.55B.100C.110D.145Item Number: M032595Correct Response:CEducation systemPercentcorrectKorea, Rep. ofSingaporeHong Kong-CHNChinese wedenSloveniaItalyUnited StatesIsraelAustraliaNew ZealandRussian FederationNorwayTurkeyUkraineInternational averageMalaysiaArmeniaChileKazakhstanThailandIran, Islamic Rep. ofQatarUnited Arab EmiratesRomaniaIndonesiaSaudi ArabiaBahrainGeorgiaMacedonia, Rep. ofLebanonTunisiaSyrian Arab RepublicOmanMoroccoPalestinian Nat’l 13Benchmarkingeducation ticut-USANorth bai-UAEAlabama-USAAbu Dhabi-UAE7673676767656563595850424039Percent higher than International averagePercent lower than International averageCopyright 2013 International Association for the Evaluation of Educational Achievement (IEA).5
TIMSS 2011 8th-Grade Mathematics Concepts and Mathematics ItemsContent DomainMain TopicCognitive DomainNUMBERWhole NumbersKnowing36 as a product of prime factorsOverall Percent CorrectWhich of these shows how 36 can be expressed as a product of prime factors?A.6 6B.4 9C.4 3 3D.2 2 3 3Item Number: M032626Correct Response:DEducation systemPercentcorrectKorea, Rep. ofChinese Taipei-CHNSingaporeHong Kong-CHNHungaryRussian FederationItalyThailandUnited StatesUkraineJordanPalestinian Nat’l Auth.ArmeniaTurkeyLebanonIsraelEngland-GBRUnited Arab EmiratesInternational traliaNew ZealandIran, Islamic Rep. ofIndonesiaSaudi ArabiaGhanaKazakhstanJapanMacedonia, Rep. ofOmanLithuaniaMalaysiaBahrainSyrian Arab 7353534323129292913Benchmarkingeducation Indiana-USANorth io-CANAbu cent higher than International averagePercent lower than International averageCopyright 2013 International Association for the Evaluation of Educational Achievement (IEA).6
TIMSS 2011 8th-Grade Mathematics Concepts and Mathematics ItemsContent DomainMain TopicCognitive DomainNUMBERFractions and DecimalsReasoningLocation of N on number lineP0QOverall Percent Correct12P and Q represent two fractions on the number line above.P Q N.Which of these shows the location of N on the number line?A.0PQB.0PC.D.N12Q12PQ12PQ12NN0N0Item Number: M032662Correct Response:DEducation systemPercentcorrectChinese Taipei-CHNHong Kong-CHNSingaporeKorea, Rep. ofJapanRussian FederationSwedenEngland-GBRFinlandPalestinian Nat’l Auth.IsraelOmanSyrian Arab RepublicSaudi ArabiaJordanAustraliaHungaryInternational averageUnited StatesQatarSloveniaBahrainNew ZealandUkraineLebanonMalaysiaLithuaniaMacedonia, Rep. ofIran, Islamic Rep. ofMoroccoItalyNorwayArmeniaUnited Arab 13121210Benchmarkingeducation North ana-USAAbu 9161413Percent higher than International averagePercent lower than International averageCopyright 2013 International Association for the Evaluation of Educational Achievement (IEA).7
TIMSS 2011 8th-Grade Mathematics Concepts and Mathematics ItemsContent DomainMain TopicCognitive DomainNUMBERFractions and DecimalsKnowingWrite 3 5/6 in decimal formWriteOverall Percent Correctin decimal form, rounded to 2 decimal places.Answer:Item Number: M032725SCORINGCorrect Response 3.83Incorrect Response 3.56 Other incorrect (including crossed out, erased, stray marks, illegible, or off task)Education systemPercentcorrectHong Kong-CHNSingaporeKorea, Rep. ofChinese Taipei-CHNJapanTunisiaRussian iaIsraelUnited StatesItalyArmeniaFinlandLithuaniaInternational averageSwedenEngland-GBRUnited Arab EmiratesUkraineMacedonia, Rep. ofNorwayRomaniaMoroccoGeorgiaNew ZealandThailandPalestinian Nat’l Auth.Saudi ArabiaBahrainQatarIndonesiaOmanGhanaChileIran, Islamic Rep. ofJordanSyrian Arab nchmarkingeducation Alberta-CANNorth SAAbu 0Percent higher than International averagePercent lower than International averageCopyright 2013 International Association for the Evaluation of Educational Achievement (IEA).8
TIMSS 2011 8th-Grade Mathematics Concepts and Mathematics ItemsWrite 3 5/6 in decimal form (continued)M032725Student ResponsesCorrect Response:Answer:Incorrect Response:Answer:Copyright 2013 International Association for the Evaluation of Educational Achievement (IEA).9
TIMSS 2011 8th-Grade Mathematics Concepts and Mathematics ItemsContent DomainMain TopicCognitive DomainNUMBERWhole NumbersReasoningNumbers to get greatest resultsOverall Percent CorrectPlace the four digits 3, 5, 7, and 9 into the boxes below in the positions thatwould give the greatest result when the two numbers are multiplied.Item Number: M042002SCORINGCorrect Response 93 x 75 OR 75 x 93Incorrect Response 95 x 73 OR 73 x 95 97 x 53 OR 53 x 97 Other incorrect (including crossed out, erased, stray marks, illegible, or off task)Education systemPercentcorrectHong Kong-CHNSingaporeJapanChinese Taipei-CHNNorwayIsraelKorea, Rep. ofNew ZealandEngland-GBRUnited StatesRussian lyKazakhstanInternational averageMalaysiaLithuaniaMacedonia, Rep. ofUkraineTunisiaIran, Islamic Rep. ofArmeniaUnited Arab EmiratesTurkeyThailandPalestinian Nat’l Auth.Syrian Arab RepublicSaudi 3131312102Benchmarkingeducation nesota-USAOntario-CANNorth ai-UAEAbu Dhabi-UAE5148474745423938353433272423Percent higher than International averagePercent lower than International averageCopyright 2013 International Association for the Evaluation of Educational Achievement (IEA).10
TIMSS 2011 8th-Grade Mathematics Concepts and Mathematics ItemsNumbers to get greatest results (continued)M042002Student ResponsesCorrect Response:XIncorrect Response:XCopyright 2013 International Association for the Evaluation of Educational Achievement (IEA).11
TIMSS 2011 8th-Grade Mathematics Concepts and Mathematics ItemsContent DomainMain TopicCognitive DomainNUMBERWhole NumbersApplyingExpress 256 X 4,096 as power of 4Overall Percent CorrectLook at this table:414243444546416642561,0244,096Use the table to express the value of 256 4,096 as a power of 4.A.410B.416C.420D.424Item Number: M042016Correct Response:AEducation systemPercentcorrectHong Kong-CHNLebanonRussian FederationKorea, Rep. ofSingaporeChinese Taipei-CHNItalyUnited StatesUkraineUnited Arab meniaQatarFinlandInternational averageRomaniaEngland-GBRMacedonia, Rep. ofAustraliaSaudi ArabiaJapanIran, Islamic Rep. ofNew estinian Nat’l Auth.TunisiaOmanSwedenSyrian Arab 4443424242414139393939373228Benchmarkingeducation systemPercentcorrectNorth -USAMinnesota-USADubai-UAEAbu 646361595654535243Percent higher than International averagePercent lower than International averageCopyright 2013 International Association for the Evaluation of Educational Achievement (IEA).12
TIMSS 2011 8th-Grade Mathematics Concepts and Mathematics ItemsContent DomainMain TopicCognitive DomainNUMBERFractions and DecimalsKnowingWhat is K on a number line26Overall Percent CorrectK2728Which number does K represent on this number line?A.27.4B.27.8C.27.9D.28.2Item Number: M042024Correct Response:BEducation systemPercentcorrectSingaporeJapanHong Kong-CHNKorea, Rep. ofChinese ithuaniaAustraliaNew ZealandRussian FederationNorwayUnited StatesIsraelMalaysiaItalyUkraineInternational averageThailandChileKazakhstanUnited Arab EmiratesLebanonMacedonia, Rep. udi ArabiaPalestinian Nat’l Auth.MoroccoJordanSyrian Arab RepublicIndonesiaOmanIran, Islamic Rep. rkingeducation nesota-USANorth ai-UAEAbu rcent higher than International averagePercent lower than International averageCopyright 2013 International Association for the Evaluation of Educational Achievement (IEA).13
TIMSS 2011 8th-Grade Mathematics Concepts and Mathematics ItemsContent DomainMain TopicCognitive DomainNUMBERFractions and DecimalsApplyingEquivalent expressionThe fractionsandWhat is the value ofA.6B.7C.11Overall Percent Correctare equivalent.?D. 14Item Number: M042031Correct Response:AEducation systemPercentcorrectKorea, Rep. ofSingaporeChinese Taipei-CHNHong Kong-CHNJapanIsraelRussian FederationSloveniaUnited StatesFinlandUnited Arab EmiratesLithuaniaSaudi tional averageMalaysiaHungaryItalyChileMacedonia, Rep. ofAustraliaUkraineEngland-GBRQatarPalestinian Nat’l Auth.Syrian Arab RepublicTunisiaBahrainNew ZealandNorwayTurkeyGeorgiaOmanThailandIran, Islamic Rep. 939383534343231Benchmarkingeducation systemPercentcorrectNorth ADubai-UAEOntario-CANAlberta-CANCalifornia-USAAbu rcent higher than International averagePercent lower than International averageCopyright 2013 International Association for the Evaluation of Educational Achievement (IEA).14
TIMSS 2011 8th-Grade Mathematics Concepts and Mathematics ItemsContent DomainMain TopicCognitive DomainNUMBERFractions and DecimalsKnowingEquivalent fraction for 0.125Overall Percent CorrectWhich fraction is equivalent to 0.125?A.B.C.D.Item Number: M042032Correct Response:BEducation systemPercentcorrectKorea, Rep. ofSingaporeChinese Taipei-CHNLebanonHong Kong-CHNRussian FederationSloveniaJapanKazakhstanFinlandUnited meniaIsraelUkraineInternational averagePalestinian Nat’l Auth.United Arab EmiratesMoroccoAustraliaRomaniaJordanSaudi ArabiaGeorgiaThailandEngland-GBRMacedonia, Rep. ofBahrainQatarTurkeyIran, Islamic Rep. ofNew ZealandNorwaySyrian Arab 95858585654545346Benchmarkingeducation systemPercentcorrectNorth California-USAOntario-CANColorado-USADubai-UAEAbu rcent higher than International averagePercent lower than International averageCopyright 2013 International Association for the Evaluation of Educational Achievement (IEA).15
TIMSS 2011 8th-Grade Mathematics Concepts and Mathematics ItemsContent DomainMain TopicCognitive DomainNUMBERFractions and DecimalsApplyingLength of the original pipeOverall Percent Correct1A workman cut off 5 of a pipe. The piece he cut off was 3 meters long.How many meters long was the original pipe?A.8mB. 12 mC. 15 mD. 18 mItem Number: M042041Correct Response:CEducation systemPercentcorrectKorea, Rep. ofJapanChinese Taipei-CHNSingaporeFinlandHong Kong-CHNSwedenItalyRussian gland-GBRNew ZealandUnited StatesIran, Islamic Rep. ofKazakhstanUkraineTurkeyHungaryInternational averageArmeniaThailandMalaysiaMacedonia, Rep. ofTunisiaUnited Arab EmiratesRomaniaPalestinian Nat’l nGhanaSyrian Arab RepublicOmanSaudi enchmarkingeducation erta-CANMinnesota-USANorth ma-USAAbu Dhabi-UAE8888858482807977767069686055Percent higher than International averagePercent lower than International averageCopyright 2013 International Association for the Evaluation of Educational Achievement (IEA).16
TIMSS 2011 8th-Grade Mathematics Concepts and Mathematics ItemsContent DomainMain TopicCognitive DomainNUMBERRatio, Proportion and PercentKnowingComplete the missing boxesOverall Percent CorrectPeter, James, and Andrew each had 20 tries at throwing balls into a basket.Complete the missing boxes below.NameNumber ofSuccessful ShotsPeter10 out of 20James15 out of 20Andrewout of 20Percentage ofSuccessful Shots50 %80%Item Number: M042059SCORINGCorrect Response 75 and 16, both correctPartially Correct Response Only 75 correct Only 16 correctIncorrect Response Incorrect (including crossed out, erased, stray marks, illegible, or off task)Education systemPercentcorrectSingaporeKorea, Rep. ofHong Kong-CHNChinese Taipei-CHNJapanIsraelRussian FederationUnited nd-GBRNew ZealandHungaryItalyNorwayMalaysiaInternational averageUnited Arab iaChileQatarMacedonia, Rep. ofBahrainIran, Islamic Rep. ofIndonesiaGeorgiaTunisiaThailandPalestinian Nat’l Auth.Syrian Arab RepublicSaudi 1817121111108Benchmarkingeducation nesota-USAAlberta-CANOntario-CANNorth olorado-USADubai-UAECalifornia-USAAbu Dhabi-UAEAlabama-USA81797775
8 RELEASED MATHEMATICS ITEMS This book contains the released Trends in International Mathematics and Science Study (TIMSS) 2011 grade 8 mathematics assessment items. This is not a complete set of all TIMSS 2011 assessment items because some items are kept confidential so that they may
