MATHEMATICS CONCEPTS MATHEMATICS ITEMS

8&MATHEMATICS CONCEPTSMATHEMATICS ITEMSThe Mathematics Concepts and Mathematics Items book contains the released TIMSS mathematicsassessment items. These are the released items from the 1999 and 2003 assessments (as distinctfrom the secure items, which are kept confidential so that they may be used in subsequent cyclesto monitor trends).Guide to Using the Mathematics Concepts and Mathematics Items MaterialsThe materials contained in this book can be used in a number of ways as a tool to assist teachersin making a formative assessment of student knowledge and skills. Some of these ways includethe following:Teacher-designed formative assessments. A teacher might, for example, decide to examinehow well his or her class can solve routine problems. In such a case, the first step would be toreview the questions in Mathematics Concepts and Mathematics Items, selecting the ones of interest.Ready-to-use versions of these items can be found in the Mathematics Items book. Teachers canprint these items or present them to students on an overhead. Student responses can be scored byreferring to the appropriate page in Mathematics Concepts and Mathematics Items. Teachers can alsocompare the overall percentage of students responding correctly to the international benchmarkfor that item.Feedback on teaching. To the extent that the items coincide with concepts taught, the teachermight follow the same process to gain rapid feedback on the success of the teaching episode.Understanding misunderstandings. Again, a teacher might decide to examine the incorrector partially correct responses of the class for insight into any general misunderstandings, with aview to re-teaching a particular topic or skill.Identifying individual difficulties. In the same way, the teacher might use the items toidentify particular difficulties experienced by individual students, as the basis for some remedialteaching or focused practice.18675.02063

Guide to the Content and Layout of This BookThis book contains the released items from both TIMSS 1999 and TIMSS 2003. Due to slight revisions in terminologyand released information between cycles, the format for the items in each cycle differs slightly. Each item appears ona single page and is accompanied by a number of descriptors.1999 Content Domains: Fractions and number sense Algebra Measurement Geometry Data representation, analysis, and probability2003 Content Domains: Algebra Data Geometry Measurement Number1999 Cognitive Domains: Knowing Using routine procedures Investigating and problem solving Mathematical reasoning Communicating2003 Cognitive Domains: Knowing facts and procedures Using concepts Solving routine problems ReasoningTake a look at Calories in a portion of food from ratio, the name given to the first 1999 item in this book. As specified inboxes at the top of the page, the content domain for this item is fractions and number sense and the cognitive domain isinvestigating and solving problems. Looking at Value of -3x given value of x, the first item from TIMSS 2003 (page 85), thecontent domain (algebra) and the cognitive domain (knowing facts and procedures) are also accompanied by the Main Topic(algebraic expressions).International item numbers identify each item. This number appears just below the item box.Correct answers are shown beneath each item. These correct answers take two forms: Letter code. This form is used for the correct response on multiple-choice items. Calories in a portion of food fromratio provides an example of the letter code type—the correct answer is A. Scoring guide. This form is used to assist in scoring write-in responses. Division of fractions (J12) further alongin the Fractions and number sense domain (page 13), provides an example of the scoring guide approach, indicatingthe general nature of correct and incorrect responses. In some cases, partial credit may be awarded and theseitems will provide guidelines for fully correct, partially correct, and incorrect responses.Sample student responses are provided for TIMSS 2003 extended response items. An example of an actual U.S.eighth-grade student’s response is provided for each scoring category. See item M032557 on page 89.International benchmarks are provided in a table next to each item.These consist of statistics on the percentage ofstudents in each country who answered the question correctly. The countries are ordered in terms of this percentage.The international average is included as well, and this display also indicates which countries scored significantly higher,significantly lower, and not significantly different from this international average.

TIMSS 1999 8th-Grade Mathematics Concepts and Mathematics ItemsContent DomainCognitive DomainFractions and Number SenseInvestigatingand Solving ProblemsOverall Percent CorrectCalories in portion of food from ratioIf there are 300 calories in 100 g of a certain food, how manycalories are there in a 30 g portion of this food?A. 90B. 100C. 900D. 1000E. 9000Item Number: B08SingaporeKorea, Rep. ofHong Kong, SARChinese TaipeiSlovak RepublicMalaysiaBelgium (Flemish)Czech RepublicRussian FederationThailandSloveniaCyprusMacedonia, Rep. andsLatvia (LSS)EnglandInternational AverageTunisiaNew ZealandBulgariaUnited StatesTurkeyIsraelIran, Islamic coPhilippinesSouth 6969696868666666656362565654534237Country average vs.International average:HigherNot differentLowerCorrect Response:A3 O O O OOOOOOOOOOOOO

TIMSS 1999 8th-Grade Mathematics Concepts and Mathematics ItemsContent DomainCognitive DomainFractions and Number SenseUsing Complex ProceduresOverall Percent CorrectFigure showing equivalent fractionsSingaporeHong Kong, SARKorea, Rep. ofJapanChinese TaipeiMalaysiaBelgium United StatesCyprusRussian ernational AverageNew ZealandIran, Islamic Rep.MoldovaHungaryBulgariaSlovak RepublicLithuaniaJordanLatvia (LSS)Czech RepublicTurkeyChileIndonesiaMacedonia, Rep. ofRomaniaTunisiaSouth AfricaMoroccoItem Number: 4535252514948464646464544332923Country average vs.International average:HigherNot differentLowerCorrect Response:A4 O OOOOOOOOOO O

TIMSS 1999 8th-Grade Mathematics Concepts and Mathematics ItemsContent DomainCognitive DomainFractions and Number SenseKnowingOverall Percent CorrectSmallest decimal fractionSingaporeHong Kong, SARKorea, Rep. ofNetherlandsJapanFinlandChinese TaipeiBelgium (Flemish)LithuaniaCanadaSlovak RepublicCzech RepublicMalaysiaSloveniaAustraliaHungaryRussian FederationUnited StatesLatvia (LSS)BulgariaInternational AverageEnglandThailandNew usJordanMacedonia, Rep. ofChileIran, Islamic Rep.PhilippinesIndonesiaTurkeySouth AfricaWhich of these is the smallest number?A. 0.625B. 0.25C. 0.375D. 0.5E. 0.125Item Number: 3373431312928272625141010996Country average vs.International average:HigherNot differentLowerCorrect Response:E5 O OOOOOOO

TIMSS 1999 8th-Grade Mathematics Concepts and Mathematics ItemsContent DomainCognitive DomainFractions and Number SenseUsing Complex ProceduresOverall Percent CorrectSmallest simple fractionHong Kong, SARSingaporeJapanNetherlandsFinlandChinese TaipeiCanadaKorea, Rep. ofBelgium (Flemish)AustraliaUnited StatesSloveniaNew ZealandIsraelCyprusEnglandHungarySlovak RepublicCzech RepublicMalaysiaInternational AverageTunisiaLatvia (LSS)Russian onia, Rep. ofIran, Islamic Rep.ThailandPhilippinesTurkeyMoldovaIndonesiaSouth AfricaMoroccoChileWhich of these fractions is smallest?1A. ––62B. ––31C. ––31D. ––2Item Number: 9595150474644434239393838282521Country average vs.International average:HigherNot differentLowerCorrect Response:A6 O OOOOOOO

TIMSS 1999 8th-Grade Mathematics Concepts and Mathematics ItemsContent DomainCognitive DomainFractions and Number SenseKnowingOverall Percent CorrectEstimate of point P on number lineJapanSingaporeFinlandNetherlandsEnglandHong Kong, SARBelgium (Flemish)CanadaAustraliaChinese TaipeiUnited StatesKorea, Rep. ofSlovak RepublicHungaryNew ZealandMalaysiaSloveniaLatvia (LSS)Russian FederationItalyInternational AverageCzech eyChileRomaniaJordanPhilippinesMacedonia, Rep. ofIndonesiaCyprusMoroccoTunisiaSouth AfricaIran, Islamic Rep.Item Number: 4636361595453535149464443403832Country average vs.International average:HigherNot differentLowerCorrect Response:B7 O OOOOO

TIMSS 1999 8th-Grade Mathematics Concepts and Mathematics ItemsContent DomainCognitive DomainFractions and Number SenseInvestigatingand Solving ProblemsOverall Percent CorrectAverage speed from distance and timeA runner ran 3000 m in exactly 8 minutes. What was his averagespeed in meters per second?A. 3.75B. 6.25C. 16.0D. 37.5E. 62.5Item Number: F07SingaporeChinese TaipeiHong Kong, SARJapanMalaysiaRussian FederationBelgium (Flemish)Korea, Rep. ofSlovak aInternational AverageRomaniaCanadaCzech RepublicTurkeyFinlandAustraliaLatvia (LSS)MoldovaUnited StatesThailandIndonesiaIsraelTunisiaMacedonia, Rep. ofNew ZealandItalyCyprusEnglandJordanIran, Islamic Rep.ChileMoroccoSouth ry average vs.International average:HigherNot differentLowerCorrect Response:B8 O O O OOOOOOOOO

TIMSS 1999 8th-Grade Mathematics Concepts and Mathematics ItemsContent DomainCognitive DomainFractions and Number SenseUsing Complex ProceduresOverall Percent CorrectNumber between two decimal fractionsWhich of these numbers is between 0.07 and 0.08?A. 0.00075B. 0.0075C. 0.075D. 0.75Item Number: F09SingaporeNetherlandsKorea, Rep. ofBelgium (Flemish)JapanChinese TaipeiHong Kong, SARFinlandCanadaAustraliaSloveniaSlovak RepublicEnglandLithuaniaCzech RepublicMalaysiaUnited StatesHungaryRussian FederationNew ZealandBulgariaLatvia (LSS)International AverageItalyIsraelMacedonia, Rep. aMoroccoJordanTurkeyPhilippinesSouth AfricaIran, Islamic 59575656545352484240393735343331Country average vs.International average:HigherNot differentLowerCorrect Response:C9 O OOOOO

TIMSS 1999 8th-Grade Mathematics Concepts and Mathematics ItemsContent DomainCognitive DomainFractions and Number SenseKnowingOverall Percent CorrectFraction of circle shadedNetherlandsBelgium (Flemish)EnglandHong Kong, SARSingaporeCanadaAustraliaNew ZealandUnited StatesChinese ch RepublicMalaysiaCyprusInternational AverageKorea, Rep. ofRussian FederationSlovak RepublicItalyLatvia oroccoIran, Islamic Rep.ChilePhilippinesLithuaniaTurkeyMacedonia, Rep. ofSouth AfricaItem Number: 8444340403939343332323131282726Country average vs.International average:HigherNot differentLowerCorrect Response:C10 O OOOOOOOOOO

TIMSS 1999 8th-Grade Mathematics Concepts and Mathematics ItemsContent DomainCognitive DomainFractions and Number SenseKnowingOverall Percent CorrectFigure showing fraction of shaded squareSingaporeBelgium (Flemish)Hong Kong, SARNetherlandsCanadaJapanChinese TaipeiFinlandKorea, Rep. ofCyprusUnited StatesMalaysiaAustraliaEnglandNew ZealandHungarySloveniaIran, Islamic Rep.IsraelSlovak RepublicThailandInternational AverageLatvia (LSS)Czech RepublicItalyRussian FederationBulgariaChileJordanTurkeyMacedonia, Rep. iaSouth AfricaMoroccoItem Number: 563615957545349484645434131217Country average vs.International average:HigherNot differentLowerCorrect Response:E11 O OOOOOOO

TIMSS 1999 8th-Grade Mathematics Concepts and Mathematics ItemsContent DomainCognitive DomainFractions and Number SenseUsing Complex ProceduresOverall Percent CorrectSum closest to 691 208SingaporeBelgium (Flemish)JapanNetherlandsHong Kong, SARCanadaUnited StatesHungaryKorea, Rep. ofSloveniaEnglandCzech RepublicAustraliaFinlandSlovak RepublicChinese TaipeiNew ZealandMalaysiaLatvia (LSS)BulgariaCyprusLithuaniaRussian FederationIsraelInternational AverageMacedonia, Rep. ileIran, Islamic Rep.IndonesiaPhilippinesMoroccoSouth AfricaThe sum 691 208 is closest to the sumA. 600 200B. 700 200C. 700 300D. 900 200Item Number: 3807977777473676666655854534337Country average vs.International average:HigherNot differentLowerCorrect Response:B12 O OOOOOO