released 4 mathematics items

4RELEASED

MATHEMATICS ITEMS

This book contains the released Trends in International Mathematics and Science Study (TIMSS) 2003 grade 4 mathematics assessment items. This is not a complete set of all TIMSS 2003 assessment items because some items are kept confidential so that they may 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 of measuring students’ understanding in various content and cognitive domains. A teacher may use these items to create an assessment according to the needs of the class after reviewing the items and selecting items of interest.

For feedback on student understanding. Student responses can be scored according to the scoring information provided in the book. Items that coincide with concepts taught in class allow the teacher to gain feedback on the students’ understanding of assessed concepts. For example, a teacher might decide to examine the incorrect or partially correct responses of the class. The teacher might use the items to identify particular difficulties or misconceptions experienced by individual students, which can serve as the basis for some remedial teaching or focused practice.

To benchmark student performance. The teacher might also compare the percent of students in the class who responded correctly to an item with the percent of students who responded correctly to the same item in other education systems or in the United States.

18675.0206

TIMSS and PIRLS are copyrighted and are registered trademarks of IEA. Released items from TIMSS 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 the public domain, please print an acknowledgement of the source, including the year and name of the assessment you are using. If you publish any part of the released items from TIMSS 2003, please use the following acknowledgement:

SOURCE: TIMSS 2003 Assessment. Copyright © 2005 International Association for the Evaluation of Educational Achievement (IEA). Publisher: TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College, Chestnut Hill, MA and International Association for the Evaluation of Educational Achievement (IEA), IEA Secretariat, Amsterdam, the Netherlands.

Guide to the Content and Layout of This Book

This book contains the released items from TIMSS 2003. Due to slight revisions in terminology and released information between cycles, the format for the items in each cycle differs slightly. Each item appears on a single page and is accompanied by a number of descriptors.

2003 Content Domains:• Patterns and Relationships• Data• Geometry• Measurement• Number

2003 Cognitive Domains:• Knowing facts and procedures• Using concepts• Solving routine problems• Reasoning

Looking at Symbolic linear equation of magazines, the first item from TIMSS 2003, the content domain (patterns and relationships) and the cognitive domain (solving routine problems) are also accompanied by the main topic (equations and formulas).

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.

• Scoring guide. This form is used to assist in scoring write-in responses. In some cases, partial credit may be awarded and these items will provide guidelines for fully correct, partially correct, and incorrect responses.

Sample student responses are provided for some extended response items.

International benchmarks are provided in a table next to each item. These consist of statistics on the percentage of students 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.

Correct Response:

Main TopicContent Domain Cognitive Domain

Overall Percent Correct

Country average vs. International average:

Higher pNotdifferent OLower q

TIMSS 2003 4th-Grade Mathematics Concepts and Mathematics Items

Singapore 86 pChinese Taipei 81 pHong Kong, SAR 76 pNetherlands 72 pUnited States 72 pJapan 67 pBelgium (Flemish) 67 pLatvia 66 pRussian Federation 66 pEngland 66 pCyprus 65 pMoldova, Republic of 64 pLithuania 62 OHungary 61 OSlovenia 60 OScotland 60 OInternational average 58 OAustralia 56 ONew Zealand 54 qItaly 50 qArmenia 46 qPhilippines 38 qNorway 37 qIran, Islamic Republic of 34 qMorocco 29 qTunisia 20 q

PaTTeRns anD RelaTIOnshIPs

EquationsandFormulas SolvingRoutineProblems

Symboliclinearequationofmagazines

Item Number: M012048

B

Singapore 86 pChinese Taipei 81 pHong Kong, SAR 76 pNetherlands 72 pUnited States 72 pJapan 67 pBelgium (Flemish) 67 pLatvia 66 pRussian Federation 66 pEngland 66 pCyprus 65 pMoldova, Republic of 64 pLithuania 62 OHungary 61 OSlovenia 60 OScotland 60 OInternational average 58 OAustralia 56 ONew Zealand 54 qItaly 50 qArmenia 46 qPhilippines 38 qNorway 37 qIran, Islamic Republic of 34 qMorocco 29 qTunisia 20 q

M012048

C represents the number of magazines that Lina reads each week.

Which of these represents the total number of magazines that Lina reads in

6 weeks?

a 6 + C

b 6 × C

c C + 6

d ( C + C ) × 6

Copyright © 2005 International Association for the Evaluation of Educational Achievement (IEA). 3

Correct Response:







EquationsandFormulas UsingConcepts

Robsoldsomeofhisapples

D

M031220

Rob had 50 apples. He sold some and then had 20 left.

Which of these is a number sentence that shows this?

a C − 20 = 50

b 20 − C = 50

c C − 50 = 20

d 50 − C = 20


Chinese Taipei 89 pJapan 89 pSingapore 89 pHong Kong, SAR 87 pHungary 87 pLithuania 87 pRussian Federation 87 pUnited States 84 pCyprus 83 pLatvia 83 pMoldova, Republic of 81 pBelgium (Flemish) 81 pSlovenia 78 pEngland 78 pNetherlands 76 OAustralia 74 ONew Zealand 74 OInternational average 73 OScotland 72 OArmenia 70 OItaly 67 qNorway 59 qIran, Islamic Republic of 54 qPhilippines 52 qMorocco 33 qTunisia 21 q








EquationsandFormulas UsingConcepts

Thevalueof37timesboxplus6


sCORInGCorrect Response

• 709or703+6

Incorrect Response

• Incorrect(includingcrossedout/erased,straymarks,illegible,orofftask)

F

F

Hong Kong, SAR 48 pRussian Federation 35 pBelgium (Flemish) 29 pNetherlands 27 pJapan 26 pChinese Taipei 24 pLithuania 23 pSingapore 23 pArmenia 22 pItaly 21 OLatvia 21 pHungary 19 OCyprus 17 OMoldova, Republic of 17 OInternational average 17 OAustralia 10 OScotland 10 qSlovenia 9 qEngland 9 qNew Zealand 8 qNorway 8 qUnited States 7 qTunisia 5 qPhilippines 4 qIran, Islamic Republic of 2 qMorocco 2 q


student Responses


Thevalueof37timesboxplus6(continued)Item Number: M031249

Correct Response:

Incorrect Response:


Correct Response:







Patterns Reasoning

Completenumberpattern


a

M011027

Here is a number pattern.

100, 1, 99, 2, 98, C, C, C

What three numbers should go in the boxes?

a 3, 97, 4

b 4, 97, 5

c 97, 3, 96

d 97, 4, 96

Singapore 94 pUnited States 91 pAustralia 88 pEngland 88 pChinese Taipei 85 pHong Kong, SAR 83 pJapan 83 pBelgium (Flemish) 83 pNew Zealand 82 pLithuania 80 pScotland 79 pCyprus 77 pLatvia 73 OMoldova, Republic of 73 ORussian Federation 73 pHungary 70 ONetherlands 70 OSlovenia 69 OInternational average 69 OItaly 58 qPhilippines 56 qArmenia 47 qNorway 46 qMorocco 28 qIran, Islamic Republic of 27 qTunisia 15 q


Correct Response:







Patterns SolvingRoutineProblems

Thenumbertogointhecenterofthetable

C

M031023

4 11 6

9 5

8 3 10

The rule for the table is that numbers in each row and column must addup to the same number. What number goes in the center of the table?

a 1

b 2

c 7

d 12


Hungary 77 pChinese Taipei 75 pJapan 72 pSingapore 72 pLithuania 70 pHong Kong, SAR 69 pCyprus 68 pLatvia 67 pBelgium (Flemish) 67 pMoldova, Republic of 66 pRussian Federation 66 OEngland 65 OScotland 63 ONew Zealand 61 OInternational average 61 ONetherlands 60 OAustralia 59 OSlovenia 59 OItaly 58 OUnited States 58 qArmenia 51 qIran, Islamic Republic of 49 qNorway 48 qPhilippines 43 qTunisia 42 qMorocco 41 q


Correct Response:







Patterns SolvingRoutineProblems

Thedailystarttimesforamovie


C

M031051

The daily start times for showing a movie are listed below:

Show Start Time

1st 2:00 p.m.

2nd 3:30 p.m.

3rd 5:00 p.m.

4th ?

If this pattern continues, what is the start time for the 4th show?

a 5:30 p.m.

b 6:00 p.m.

c 6:30 p.m.

d 7:00 p.m.

Japan 90 pSingapore 88 pHong Kong, SAR 86 pEngland 85 pNetherlands 83 pUnited States 83 pBelgium (Flemish) 81 pAustralia 77 pChinese Taipei 74 pNew Zealand 74 pScotland 74 pLithuania 73 pRussian Federation 73 pCyprus 72 pHungary 69 OItaly 68 OLatvia 68 OInternational average 67 OMoldova, Republic of 65 OSlovenia 60 qPhilippines 48 qArmenia 47 qNorway 45 qIran, Islamic Republic of 33 qMorocco 31 qTunisia 28 q


Correct Response:







RelationshipsKnowingFactsandProcedures

Outputofthenumbermachine

B

M031190

A number machine takes a number and operates on it.When the Input Number is 5, the Output Number is 9, as shown below.

When the Input Number is 7, which of these is the Output Number?

a 11

b 13

c 14

d 25

5 × 29

+ 2 − 310 12

InputNumber

OutputNumber


Belgium (Flemish) 72 pHungary 71 pSingapore 69 pJapan 65 pNetherlands 65 pEngland 64 pCyprus 62 pItaly 61 pLatvia 61 pLithuania 61 pHong Kong, SAR 55 pMoldova, Republic of 55 ORussian Federation 55 OChinese Taipei 54 pInternational average 50 OScotland 49 OUnited States 48 ONew Zealand 45 qAustralia 44 qArmenia 41 qSlovenia 36 qNorway 34 qIran, Islamic Republic of 27 qPhilippines 24 qMorocco 22 qTunisia 18 q


Correct Response:






DaTa DataInterpretation Reasoning

Heightsoffourgirlsongraph


B

M012126

The graph shows the heights of four girls.

The names are missing from the graph. Debbie is the tallest. Amy is theshortest. Dawn is taller than Sarah. How tall is Sarah?

a 75 cm

b 100 cm

c 125 cm

d 150 cm

Names of Girls

150

125

75

100

50

Hei

ght

(Cen

tim

eter

s)

0

25

Singapore 84 pLatvia 83 pBelgium (Flemish) 82 pHong Kong, SAR 81 pRussian Federation 81 pChinese Taipei 78 pUnited States 78 pJapan 76 pLithuania 76 pNetherlands 76 pSlovenia 76 pAustralia 74 pItaly 74 pEngland 74 pHungary 73 pNew Zealand 70 OCyprus 68 OInternational average 67 OMoldova, Republic of 66 ONorway 63 OScotland 63 qArmenia 55 qMorocco 39 qIran, Islamic Republic of 36 qTunisia 32 qPhilippines 31 q


Correct Response:






DaTa DataRepresentation SolvingRoutineProblems

Bargraph:whichshows45bottles

B

M011009

Central School had a bottle collection. Children in each class brought emptybottles to school. The principal made a bar graph of the number of bottlesfrom five classes.

Which class collected 45 bottles?

a Miss Barber’s class

b Mr. Chyn’s class

c Mrs. Friedman’s class

d Mr. Mack’s class

Numberof

Bottles

100

80

60

40

20

0Miss

Barber’sClass

Mr.Chyn’sClass

Mrs.Friedman’s

Class

MissGonzalez’s

Class

Mr.Mack’sClass


Hong Kong, SAR 98 pSingapore 98 pChinese Taipei 97 pJapan 97 pUnited States 97 pEngland 96 pAustralia 95 pNetherlands 95 pBelgium (Flemish) 95 pNew Zealand 93 pScotland 92 pLatvia 90 pLithuania 90 pCyprus 89 pHungary 88 pSlovenia 87 pRussian Federation 84 ONorway 83 OInternational average 83 OItaly 82 OMoldova, Republic of 76 qPhilippines 65 qArmenia 53 qMorocco 50 qIran, Islamic Republic of 48 qTunisia 32 q


Correct Response:







Bargraph:whichtwoshow80bottles


a

M011012

Central School had a bottle collection. Children in each class brought emptybottles to school. The principal made a bar graph of the number of bottlesfrom five classes.

Which two classes collected exactly 80 bottles?

a Miss Barber’s and Mrs. Friedman’s classes

b Miss Barber’s and Mr. Mack’s classes

c Mrs. Friedman’s and Miss Gonzalez’s classes

d Miss Gonzalez’s and Mr. Mack’s classes

Miss Mr. Mrs. Miss Mr.Barber’s Chyn’s Friedman’s Gonzalez’s Mack’s

Class Class Class Class Class

Numberof

Bottles

100

80

60

40

20

0

Hong Kong, SAR 98 pSingapore 97 pUnited States 96 pNetherlands 92 pBelgium (Flemish) 91 pAustralia 89 pChinese Taipei 88 pSlovenia 88 pCyprus 85 pJapan 85 pItaly 84 pNew Zealand 84 pEngland 84 pScotland 81 OLatvia 80 ORussian Federation 80 OHungary 78 OInternational average 78 ONorway 76 OLithuania 75 OMoldova, Republic of 75 OPhilippines 64 qArmenia 50 qIran, Islamic Republic of 48 qMorocco 48 qTunisia 35 q


Correct Response:






DaTa DataInterpretation SolvingRoutineProblems

Highesttemperatureonchart

B

M012078

This chart shows temperature readings made at different times onfour days.

TEMPERATURES

6 a.m. 9 a.m. Noon 3 p.m. 8 p.m.

Monday 15˚ 17˚ 20˚ 21˚ 19˚

Tuesday 15˚ 15˚ 15˚ 10˚ 9˚

Wednesday 8˚ 10˚ 14˚ 13˚ 15˚

Thursday 8˚ 11˚ 14˚ 17˚ 20˚

When was the highest temperature recorded?

a Noon on Monday

b 3 p.m. on Monday

c Noon on Tuesday

d 3 p.m. on Wednesday


Japan 95 pChinese Taipei 90 pHong Kong, SAR 89 pNetherlands 89 pHungary 86 pSingapore 85 pUnited States 85 pEngland 85 pBelgium (Flemish) 85 pItaly 82 pLithuania 81 pScotland 81 pAustralia 80 pRussian Federation 80 pLatvia 79 pNew Zealand 78 pSlovenia 76 OInternational average 74 ONorway 73 OCyprus 70 OMoldova, Republic of 65 qArmenia 53 qPhilippines 50 qIran, Islamic Republic of 42 qMorocco 34 qTunisia 31 q



TitleNamePulledfromItem Overall Percent Correct




Colorsofstudents’haironthegraph

M031264

In a class of 30 students, 10 have black hair, 15 have blonde hair, and therest have brown hair. Complete the graph below to show the number ofstudents with brown hair.

Num

ber

of

Stu

den

ts

Hair Color

5

20

15

10

25

Black Blonde Brown

Color of Hair



• Barforbrownhairdrawntothehorizontallineat5

Incorrect Response



Netherlands 93 pBelgium (Flemish) 93 pChinese Taipei 92 pHong Kong, SAR 92 pJapan 90 pSingapore 90 pLatvia 88 pLithuania 87 pEngland 86 pHungary 84 pScotland 83 pRussian Federation 82 pUnited States 82 pCyprus 80 pNew Zealand 80 pSlovenia 79 pAustralia 76 ONorway 75 OInternational average 73 OItaly 71 OMoldova, Republic of 67 qArmenia 50 qPhilippines 29 qIran, Islamic Republic of 28 qMorocco 24 qTunisia 21 q


student Responses

TitleNamePulledfromItemHere(continued)Item Number: M022002A


Colorsofstudents’haironthegraph(continued)Item Number: M031264

Correct Response:

Incorrect Response:







Howmanymorepencilsthanrulerssold




• 2morepencilsthanrulers

Incorrect Response

• 1morepencilthanrulers

• Otherincorrect(includingcrossedout/erased,straymarks,illegible,orofftask)

Japan 89 pEngland 73 pBelgium (Flemish) 72 pNetherlands 70 pUnited States 70 pSingapore 69 pAustralia 66 pScotland 62 pNew Zealand 60 pNorway 55 pLatvia 46 pCyprus 44 OInternational average 39 OHong Kong, SAR 36 OChinese Taipei 35 OLithuania 22 qArmenia 18 qPhilippines 16 qItaly 10 qMoldova, Republic of 7 qRussian Federation 6 qSlovenia 5 qTunisia 4 qMorocco 3 qIran, Islamic Republic of 2 qHungary 0 q

M031265

A store owner decided to check how many pens, pencils, erasers, and rulerswere sold on the day school opened. He made the tally chart below.

How many more pencils than rulers were sold?

Answer: _______________

Pens Pencils Erasers Rulers


student Responses

TitleNamePulledfromItemHere(continued)Item Number: M022002A


Correct Response:

Incorrect Response:

Howmanymorepencilsthanrulerssold(continued)Item Number: M031265


Correct Response:






DaTa Datainterpretation SolvingRoutineProblems

Highandlowtemperaturesforaweek


a

M031333

The graph above shows the daily high and low temperatures for a week.

On which day is the difference between the high and low temperatures thegreatest?

a Monday

b Thursday

c Friday

d Saturday

Temperature for Week

Sun. Mon. Tues. Wed. Thu. Fri. Sat.

25º

40º

35º

30º

45º

20º

Tem

per

ature

Day

High Temp.

Low Temp.

Japan 73 pHong Kong, SAR 69 pBelgium (Flemish) 68 pChinese Taipei 57 pLithuania 56 pNetherlands 56 pEngland 53 pLatvia 48 OSingapore 47 pRussian Federation 44 OInternational average 42 OHungary 41 OCyprus 40 OMoldova, Republic of 39 OScotland 39 ONew Zealand 38 OSlovenia 38 OUnited States 38 qItaly 37 OAustralia 34 qNorway 32 qPhilippines 30 qMorocco 25 qArmenia 22 qIran, Islamic Republic of 16 qTunisia 13 q


Correct Response:






DaTa DataRepresentation UsingConcepts

Thefavoriteicecreamsof30students

C

M031315

Favorite Number ofIce Cream Students

Butterscotch ||||

Chocolate |||| ||||

Strawberry |||| ||||

Vanilla |||| ||

A teacher asked 30 students in her class the flavor of their favoriteice cream. The table above shows how the teacher recorded thestudents’ responses.

In the bar graph below, which ice cream flavor corresponds to the bar thatis labeled X?

a butterscotch

b chocolate

c strawberry

d vanilla

Ice Cream FlavorX

Num

ber

of

Stu

den

ts

10

8

6

4

2

Favorite Ice Cream


Japan 90 pSingapore 82 pEngland 75 pNetherlands 72 pUnited States 69 pHong Kong, SAR 65 pChinese Taipei 61 pScotland 60 pNew Zealand 59 pBelgium (Flemish) 58 pAustralia 57 pCyprus 53 pLatvia 50 OInternational average 47 OHungary 41 qLithuania 37 qNorway 36 qRussian Federation 33 qItaly 30 qMoldova, Republic of 25 qPhilippines 25 qIran, Islamic Republic of 24 qMorocco 24 qSlovenia 22 qArmenia 19 qTunisia 15 q


Correct Response:






GeOMeTRy CongruenceandSimilarityKnowingFactsandProcedures

Congruent figures


C

M011014

Figures that are the same size and shape are called congruent figures.

Which two figures are congruent?

a 1 and 2

b 1 and 3

c 1 and 4

d 3 and 4

1 2 3 4

Latvia 96 pLithuania 95 pSlovenia 94 pUnited States 94 pJapan 93 pRussian Federation 93 pSingapore 93 pBelgium (Flemish) 93 pChinese Taipei 92 pNetherlands 92 pHong Kong, SAR 90 pItaly 89 pEngland 89 pScotland 88 OAustralia 87 OHungary 87 ONew Zealand 86 ONorway 86 OInternational average 85 OCyprus 83 OMoldova, Republic of 83 OIran, Islamic Republic of 69 qArmenia 68 qMorocco 67 qPhilippines 60 qTunisia 59 q







GeOMeTRy CongruenceandSimilarityKnowingFactsandProcedures

Shadeintwotrianglesofdifferentsizes

M031267

Two of the four triangles in the figure above are the same shape butdifferent sizes. Shade in those two triangles.

1

2

3

4

D

AB is parallel to DCB

C

A



• Triangles1and3

Incorrect Response

• Triangles2and4

• Triangles1and2;Triangles3and4;Triangles1and4;ORTriangles2and3


Chinese Taipei 66 pJapan 63 pSingapore 62 pUnited States 57 pEngland 57 pRussian Federation 53 pAustralia 52 pHungary 51 pNew Zealand 51 pBelgium (Flemish) 51 pLithuania 50 pScotland 50 pCyprus 49 pHong Kong, SAR 48 pItaly 46 OSlovenia 45 OInternational average 43 OMoldova, Republic of 39 ONetherlands 39 OLatvia 28 qArmenia 26 qIran, Islamic Republic of 24 qNorway 23 qPhilippines 17 qMorocco 13 qTunisia 11 q


student Responses


Shadeintwotrianglesofdifferentsizes(continued)Item Number: M031267

Correct Response:

Incorrect Response:







GeOMeTRy LinesandAnglesKnowingFactsandProcedures

DrawalineonthegridparalleltolineL

M031327

On the grid, draw a line parallel to line L.

L



• Line(orlines)paralleltoL

Incorrect Response

• LineperpendiculartoLshown


Singapore 94 pBelgium (Flemish) 91 pMoldova, Republic of 74 pUnited States 72 pItaly 69 pHong Kong, SAR 63 pChinese Taipei 58 pHungary 58 pEngland 56 OArmenia 51 OIran, Islamic Republic of 50 OInternational average 50 ORussian Federation 48 OAustralia 47 OJapan 46 qCyprus 43 qNew Zealand 42 qLithuania 40 qMorocco 36 qNorway 36 qLatvia 34 qSlovenia 34 qPhilippines 33 qNetherlands 32 qTunisia 29 qScotland 22 q


student Responses


DrawalineonthegridparalleltolineL(continued)Item Number: M031327

Correct Response:

Incorrect Response:


Correct Response:






GeOMeTRy LocationsandSpatial

RelationshipsReasoning

Rotated 3-dimensional figure

a

M012069

This figure will be turned to a different position.

Which of these could be the figure after it is turned?

a b c d


Norway 60 pLatvia 59 pChinese Taipei 57 pSingapore 54 pBelgium (Flemish) 52 pSlovenia 51 pHungary 50 pItaly 49 pJapan 49 pScotland 49 pEngland 46 ONew Zealand 45 OHong Kong, SAR 43 OInternational average 43 OAustralia 42 ORussian Federation 41 ONetherlands 40 OMoldova, Republic of 39 OUnited States 39 qTunisia 35 qArmenia 34 qLithuania 32 qCyprus 31 qIran, Islamic Republic of 26 qPhilippines 23 qMorocco 20 q


Correct Response:






GeOMeTRy Two-andThree-

DimensionalShapesKnowingFactsandProcedures

Which has flat and curved surface


D

M011006

Here is a cone. Part of its surface is flat and part of its surface is curved.

Which of these solids also has both a flat surface and a curved surface?

a b c d

England 83 pAustralia 81 pScotland 81 pUnited States 74 pNew Zealand 73 pSingapore 72 pItaly 71 pSlovenia 68 pBelgium (Flemish) 66 pHungary 64 pChinese Taipei 62 pHong Kong, SAR 56 OInternational average 55 ONetherlands 53 OMoldova, Republic of 52 OArmenia 49 qJapan 48 qLithuania 46 qCyprus 45 qLatvia 42 qRussian Federation 39 qNorway 35 qIran, Islamic Republic of 31 qTunisia 31 qMorocco 30 qPhilippines 26 q


Correct Response: a






Statementsabouttriangle



M011022

All of the pupils in a class cut out paper shapes. The teacher picked one outand said, “This shape is a triangle.” Which of these statements MUST becorrect?

a The shape has three sides.

b The shape has a right angle.

c The shape has equal sides.

d The shape has equal angles.


Australia 79 pLatvia 82 pNetherlands 82 pSingapore 82 pChinese Taipei 81 pHong Kong, SAR 81 pRussian Federation 81 pItaly 79 pNew Zealand 79 pUnited States 79 pEngland 79 pMoldova, Republic of 74 OBelgium (Flemish) 74 pLithuania 73 OScotland 72 OCyprus 71 OInternational average 71 ONorway 70 OArmenia 68 OJapan 68 OSlovenia 66 OIran, Islamic Republic of 61 qHungary 58 qPhilippines 48 qMorocco 47 qTunisia 33 q









Indicatesgeometricshapesinthepicture


sCORInGFully Correct Response

• Any three of square, rectangle, triangle, trapezoid, diamond/rhombus, kite correctly identified

• Anytwooftheabovepluscircle

Partially Correct Response

• Any two of the above correctly identified

• Anyoneoftheabovepluscircle

Incorrect Response

• Incorrect(includingcrossedout/erased,straymarks,illegibleorofftask)

M031269

In the picture there are a number of geometric shapes, like circles, squares,rectangles, and triangles. For example, the sun looks like a circle.

Draw lines to three other different objects in the picture and write whatshapes they look like.

circle

sun

Belgium (Flemish) 81 pChinese Taipei 80 pNew Zealand 74 pEngland 72 pAustralia 71 pHong Kong, SAR 70 pUnited States 70 pItaly 68 pJapan 68 pMoldova, Republic of 68 pCyprus 67 pLatvia 67 pNetherlands 67 pSingapore 66 pScotland 64 pRussian Federation 62 OHungary 60 OSlovenia 60 OInternational average 59 OLithuania 57 ONorway 45 qArmenia 35 qIran, Islamic Republic of 30 qPhilippines 26 qTunisia 23 qMorocco 11 q


student Responses


Indicatesgeometricshapesinthepicture(continued)Item Number: M031269

Fully Correct Response:




student Responses (continued)

Partially Correct Response:




student Responses (continued)

Incorrect Response:







a. GeOMeTRy Two- and Three-Dimensional shapes Knowing Facts and Procedures

B.GEOmETRy Two-andThree-DimensionalShapes KnowingFactsandProcedures

C.NUmBER FractionsandDecimals KnowingFactsandProcedures

Geometrytiles:blacktriangle

Item Number: M031347A


TIMSS 2003 Released Items: Fourth Grade Mathematics

UniqueID M031347A Subject M Grade 4 MSBlock M09 MSBlockSeq 05A

A: Codes for Triangle Pattern

Code Response Item: M031347A

Correct Response

0

or

Incorrect Response

70 Used two triangle tiles but created two small black triangles

79 Other incorrect (including crossed out/erased, stray marks, illegible, or off task)

Nonresponse

99 Blank

Incorrect Response

• Usedtwotriangletilesbutcreatedtwosmallblacktriangles


M031347

A. Use 2 of the triangle tiles to make one large black triangle. Then showwhat you did with your tiles by shading in your triangle below.

Shade in YourTriangle Here

B. Use all 4 triangle tiles to make a black square. Then show what you didwith your tiles by shading in your square below.

Shade in YourSquare Here

C. What fraction of the figure is shaded in part B above?

Answer: ___________________

Questions for Geometry Tiles continue.

Japan 78 pLatvia 64 pLithuania 61 pRussian Federation 61 pHong Kong, SAR 60 pItaly 59 pChinese Taipei 57 pNetherlands 55 pCyprus 54 pNew Zealand 52 pEngland 52 pBelgium (Flemish) 52 pAustralia 51 pNorway 50 OScotland 48 OSlovenia 47 OInternational average 45 OSingapore 44 OUnited States 42 OHungary 41 OMoldova, Republic of 38 qArmenia 15 qTunisia 11 qPhilippines 10 qIran, Islamic Republic of 9 qMorocco 6 q

or


student Responses


Geometrytiles:blacktriangle(continued)Item Number: M031347A

Correct Response:

Incorrect Response:







A.GEOmETRy Two-andThree-DimensionalShapes KnowingFactsandProcedures

B. GeOMeTRy Two- and Three-Dimensional shapes Knowing Facts and Procedures

C.NUmBER FractionsandDecimals KnowingFactsandProcedures

Geometrytiles:blacksquare

Item Number: M031347B



UniqueID M031347B Subject M Grade 4 MSBlock M09 MSBlockSeq 05B

B: Codes for Square Pattern

Code Response Item: M031347B

Correct Response

10

Incorrect Response

70 Used four triangle tiles but did not create a black square


Nonresponse

99 Blank

Incorrect Response

• Usedfourtriangletilesbutdidnotcreateablacksquare


M031347






Answer: ___________________


Japan 71 pNetherlands 60 pLithuania 57 pRussian Federation 57 pBelgium (Flemish) 55 pChinese Taipei 54 pEngland 54 pAustralia 52 pNew Zealand 52 pItaly 51 pScotland 48 pCyprus 47 pNorway 47 OHong Kong, SAR 46 pHungary 45 OSingapore 45 OSlovenia 44 OUnited States 42 OInternational average 42 OMoldova, Republic of 37 OLatvia 33 qTunisia 15 qIran, Islamic Republic of 13 qArmenia 10 qPhilippines 7 qMorocco 5 q


student Responses


Geometrytiles:blacksquare(continued)Item Number: M031347B

Correct Response:

Incorrect Response:







A.GEOmETRy Two-andThree-DimensionalShapes KnowingFactsandProcedures

B.GEOmETRy Two-andThree-DimensionalShapes KnowingFactsandProcedures

C. nuMBeR Fractions and Decimals Knowing Facts and Procedures

Geometrytiles:fractionshaded

Item Number: M031347C


• ½orequivalent

• Correct fraction based on incorrect figure in part

Incorrect Response

• ¼


M031347






Answer: ___________________


Singapore 73 pHong Kong, SAR 70 pChinese Taipei 61 pJapan 56 pEngland 49 pUnited States 48 pCyprus 45 pBelgium (Flemish) 45 pHungary 38 pNetherlands 38 pNew Zealand 36 OAustralia 34 OInternational average 33 OLatvia 28 qScotland 28 qItaly 26 qLithuania 24 qNorway 23 qRussian Federation 21 qSlovenia 18 qIran, Islamic Republic of 17 qMoldova, Republic of 17 qPhilippines 14 qArmenia 5 qTunisia 3 qMorocco 1 q


student Responses


Geometrytiles:fractionshaded(continued)Item Number: M031347C

Correct Response:

Incorrect Response:








DimensionalShapesSolvingRoutineProblems

Drawlineonrectangle/2triangles



• Onediagonaldrawn

Incorrect Response

• Onehorizontalorverticallinedrawn

• Otherincorrect(includingcrossedout/erased,straymarks,illegibleorofftask)

M031272

A. Draw 1 straight line on this rectangle to divide it into 2 triangles.

B. Draw 1 straight line on this rectangle to divide it into 2 rectangles.

C. Draw 2 straight lines on this rectangle to divide it into 1 rectangle and2 triangles.

Hong Kong, SAR 95 pChinese Taipei 93 pJapan 92 pLatvia 92 pRussian Federation 91 pLithuania 90 pMoldova, Republic of 83 pSingapore 83 pBelgium (Flemish) 83 pNetherlands 82 pCyprus 80 pNew Zealand 80 pEngland 80 pHungary 79 pAustralia 79 OSlovenia 79 OScotland 79 pInternational average 75 OItaly 74 OUnited States 74 ONorway 68 qArmenia 57 qIran, Islamic Republic of 55 qTunisia 50 qMorocco 40 qPhilippines 21 q


student Responses


Drawlineonrectangle/2triangles(continued)Item Number: M031272A

Correct Response:

Incorrect Response:









Drawlineonrectangle/2rectangles



• Onehorizontalorverticallinedrawn

Incorrect Response

• Incorrect(includingcrossedout/erased,straymarks,illegibleorofftask)

M031272




Hong Kong, SAR 99 pChinese Taipei 95 pSingapore 94 pLatvia 93 pLithuania 92 pRussian Federation 92 pAustralia 91 pJapan 91 pBelgium (Flemish) 91 pHungary 89 pNew Zealand 89 pSlovenia 89 pEngland 89 pScotland 89 pUnited States 88 pCyprus 86 pItaly 86 pNetherlands 85 OMoldova, Republic of 84 OInternational average 83 OIran, Islamic Republic of 76 qNorway 74 qArmenia 58 qTunisia 58 qMorocco 52 qPhilippines 34 q


student Responses


Correct Response:

Incorrect Response:

Drawlineonrectangle/2rectangles(continued)Item Number: M031272B









Drawlineonrectangle/1rectangle,2triangles



• Twolinescorrectlydrawntoshowasmallerrectangleandtwotriangles

Incorrect Response

• Attemptmadewithtwolinesdrawnbutdrawingdoesnotshowalinedividingtherectangleinto2rectangleswithadiagonalaccuratelydrawninoneofthem

• Otherincorrect(includingcrossedout/erased,straymarks,illegibleorofftask)

M031272




Hong Kong, SAR 85 pChinese Taipei 84 pJapan 75 pSingapore 71 pRussian Federation 68 pLatvia 66 pCyprus 59 pLithuania 59 pHungary 52 pBelgium (Flemish) 52 pNetherlands 50 OAustralia 47 OInternational average 47 OMoldova, Republic of 45 OEngland 45 ONew Zealand 44 OSlovenia 44 OScotland 41 qArmenia 35 qUnited States 34 qItaly 33 qNorway 27 qTunisia 20 qMorocco 16 qIran, Islamic Republic of 15 qPhilippines 11 q


student Responses


Correct Response:

Incorrect Response:

Drawlineonrectangle/1rectangle,2triangles(continued)Item Number: M031272C


Correct Response:






MeasuReMenT AttributesandUnitsKnowingFactsandProcedures

Weightofanadult


C

M011023

Which of these could be the weight (mass) of an adult?

a 1 kg

b 6 kg

c 60 kg

d 600 kg

Chinese Taipei 91 pSingapore 90 pJapan 89 pLatvia 89 pLithuania 88 pNetherlands 87 pRussian Federation 87 pHungary 86 pItaly 82 pHong Kong, SAR 81 pMoldova, Republic of 81 pBelgium (Flemish) 80 pAustralia 79 pNew Zealand 78 pNorway 78 pArmenia 76 pCyprus 76 pInternational average 72 OSlovenia 61 qUnited States 54 qEngland 54 qScotland 50 qIran, Islamic Republic of 45 qMorocco 44 qPhilippines 36 qTunisia 32 q


Correct Response:







Unitstomeasuremassofegg

C

M012023

What units would be best to use to measure the weight (mass) of an egg?

a centimeters

b milliliters

c grams

d kilograms


Japan 91 pNetherlands 88 pCyprus 83 pLithuania 82 pSingapore 82 pLatvia 81 pEngland 80 pBelgium (Flemish) 80 pHong Kong, SAR 78 pItaly 77 pHungary 76 pRussian Federation 75 pMoldova, Republic of 74 pInternational average 69 OChinese Taipei 68 OAustralia 67 ONew Zealand 67 OArmenia 65 ONorway 59 qSlovenia 59 qScotland 55 qUnited States 54 qIran, Islamic Republic of 50 qMorocco 47 qTunisia 43 qPhilippines 40 q


Correct Response: a







Whichcouldequal150milliliters


M031338

Which of these could equal 150 milliliters?

a The amount of water in a cup

b The length of a kitten

c The weight of an egg

d The area of a coin

Chinese Taipei 87 pHong Kong, SAR 86 pLithuania 82 pSingapore 81 pJapan 75 pHungary 74 pRussian Federation 72 pEngland 72 pCyprus 71 pLatvia 69 pBelgium (Flemish) 69 pItaly 68 pMoldova, Republic of 68 pSlovenia 63 OInternational average 61 OAustralia 60 OScotland 60 ONetherlands 59 ONew Zealand 55 qUnited States 48 qArmenia 41 qNorway 39 qPhilippines 36 qMorocco 32 qTunisia 28 qIran, Islamic Republic of 25 q


Correct Response:






MeasuReMenT AttributesandUnits Reasoning

Whichhaslargestarea

C

M011005

Which of these figures has the largest area?

a

b

c

d


Australia 85 pChinese Taipei 96 pJapan 94 pHong Kong, SAR 91 pSingapore 88 pLatvia 86 pScotland 86 pBelgium (Flemish) 84 pNetherlands 83 pRussian Federation 82 OMoldova, Republic of 81 OUnited States 81 pHungary 80 OLithuania 80 OArmenia 79 OCyprus 79 OItaly 79 ONew Zealand 79 OEngland 78 OInternational average 78 OSlovenia 77 OIran, Islamic Republic of 72 qMorocco 65 qNorway 65 qTunisia 46 qPhilippines 43 q


Correct Response:







B

The length of the films

MeasuReMenT AttributesandUnits SolvingRoutineProblems

M031008

Simon wants to watch a film that is between 21

1 and 2 hours long.

Which of the following films should he choose?

a a 59-minute film

b a 102-minute film

c a 121-minute film

d a 150-minute film

Singapore 46 pEngland 42 pHungary 41 pNetherlands 38 pAustralia 37 pHong Kong, SAR 37 pRussian Federation 37 pUnited States 34 pBelgium (Flemish) 33 OChinese Taipei 32 OLithuania 30 OSlovenia 30 OInternational average 30 ONew Zealand 29 ONorway 29 OScotland 28 OLatvia 27 OItaly 26 qMoldova, Republic of 26 OCyprus 25 qJapan 25 qArmenia 22 qIran, Islamic Republic of 22 qPhilippines 22 qTunisia 17 qMorocco 16 q


Correct Response:






MeasuReMenT Tools,techniques,

andformulasKnowingFactsandProcedures

Howmuchdidtemperaturerise

D

M011013

When Tracy left for school, the temperature was minus 3 degrees.

At recess, the temperature was 5 degrees.

How many degrees did the temperature rise?

a 2 degrees

b 3 degrees

c 5 degrees

d 8 degrees

10

0

-10

10

0

-10

10

0

-10

10

0

-10


Netherlands 78 pEngland 76 pBelgium (Flemish) 76 pHungary 74 pJapan 71 pLatvia 70 pItaly 66 pNorway 65 pLithuania 63 pRussian Federation 63 pChinese Taipei 60 OScotland 59 OHong Kong, SAR 58 OInternational average 57 OCyprus 55 OMoldova, Republic of 55 OSlovenia 54 OSingapore 53 qUnited States 52 qArmenia 51 qNew Zealand 49 qAustralia 46 qIran, Islamic Republic of 46 qPhilippines 44 qMorocco 29 qTunisia 27 q







MeasuReMenT Tools,techniques,

andformulasKnowingFactsandProcedures

DrawatrianglewithABasthebase



• Trianglewithtwonewsidesequal(i.e.meetingonorwithin2mmofthegridlinethatistheperpendicularbisectorofAB)

Incorrect Response

• Trianglewithtwonewsidesunequal


M031322

Draw a triangle in the grid so that the line AB is the base of the triangleand the two new sides are the same length as each other.

A B

Hong Kong, SAR 95 pLatvia 84 pJapan 80 pNew Zealand 80 pAustralia 77 pItaly 77 pRussian Federation 77 pSingapore 77 pBelgium (Flemish) 77 pLithuania 74 pEngland 73 pHungary 72 pScotland 71 OChinese Taipei 70 OMoldova, Republic of 67 OInternational average 67 OSlovenia 64 OUnited States 63 qNorway 58 qCyprus 57 qArmenia 56 qIran, Islamic Republic of 48 qPhilippines 45 qMorocco 42 qTunisia 28 qNetherlands 0 q


student Responses


Correct Response:

Incorrect Response:

DrawatrianglewithABasthebase(continued)Item Number: M031322


Correct Response:






MeasuReMenT Tools,Techniques,

andFormulasReasoning

Distanceonmap


C

M012065

One centimeter on the map represents 8 kilometers on the land.

About how far apart are Oxford and Smithville on the land?

a 4 km

b 16 km

c 35 km

d 50 km

Oxford

Hatboro

Indian River

Smithville

1 cm = 8 km

Netherlands 69 pSingapore 62 pJapan 61 pBelgium (Flemish) 61 pHong Kong, SAR 60 pLithuania 59 pLatvia 57 pHungary 55 pRussian Federation 52 pEngland 51 pChinese Taipei 49 pAustralia 46 ONew Zealand 45 OInternational average 45 OItaly 44 OMoldova, Republic of 44 OUnited States 41 qSlovenia 38 qCyprus 37 qNorway 36 qScotland 35 qArmenia 33 qMorocco 26 qIran, Islamic Republic of 21 qTunisia 21 qPhilippines 20 q







Complete the figure with an area of 13 cm2


andFormulasReasoning

M031298

The squares in the grid above have areas of 1 square centimeter. Draw linesto complete the figure so that it has an area of 13 square centimeters.

1 cm

1cm



• Linesdrawntogiveareaof13squarecm

Incorrect Response

• Errorduetocountinghalfsquaresasfullsquarecentimeters

• One line drawn to close given figure

• Symmetrical figure drawn


Japan 68 pChinese Taipei 66 pHong Kong, SAR 52 pLatvia 43 pSingapore 43 pLithuania 40 pNetherlands 37 pMoldova, Republic of 35 pCyprus 34 pRussian Federation 30 OAustralia 29 OEngland 29 OScotland 29 OInternational average 29 OBelgium (Flemish) 28 OHungary 26 OArmenia 25 OUnited States 24 qItaly 22 qNew Zealand 15 qIran, Islamic Republic of 11 qSlovenia 11 qNorway 10 qMorocco 9 qTunisia 9 qPhilippines 5 q


student Responses


Correct Response:

Incorrect Response:

Complete the figure with an area of 13 cm2(continued)Item Number: M031298


Correct Response:







andFormulasSolvingRoutineProblems

Whenismary’strip

C

M011017

Here is a calendar for December.

Mary’s birthday is on Thursday, December 2. She is going on a trip exactly3 weeks later. On what date will she go on the trip?

a December 16th

b December 21st

c December 23rd

d December 30th

DECEMBER

S M T W T F S

1 2 3 4

5 6 7 8 9 10 11

12 13 14 15 16 17 18

19 20 21 22 23 24 25

26 27 28 29 30 31


Japan 83 pEngland 82 pBelgium (Flemish) 81 pNetherlands 79 pScotland 79 pHong Kong, SAR 76 pAustralia 75 pChinese Taipei 75 pSingapore 75 pUnited States 75 pNew Zealand 74 pLatvia 69 pHungary 67 ORussian Federation 67 OItaly 66 OSlovenia 66 OLithuania 65 OMoldova, Republic of 64 OInternational average 64 ONorway 62 OCyprus 61 OArmenia 51 qPhilippines 36 qIran, Islamic Republic of 31 qMorocco 26 qTunisia 25 q


Correct Response:








Perimeterofrectangle


D

M011025

Here is a rectangle with length 6 centimeters and width 4 centimeters. Thedistance right around its shape is called its perimeter.

Which of these gives the perimeter of the rectangle in centimeters?

a 6 + 4

b 6 × 4

c 6 × 4 × 2

d 6 + 4 + 6 + 4

6 cm

4 cm

Singapore 93 pLatvia 77 pLithuania 73 pRussian Federation 72 pArmenia 66 pUnited States 64 pHong Kong, SAR 62 pMoldova, Republic of 62 pBelgium (Flemish) 61 pAustralia 57 pHungary 57 pItaly 57 pCyprus 53 OEngland 52 OInternational average 51 OChinese Taipei 42 qNew Zealand 39 qNorway 39 qPhilippines 39 qScotland 36 qNetherlands 35 qIran, Islamic Republic of 34 qSlovenia 33 qJapan 25 qTunisia 25 qMorocco 21 q


Correct Response:








Betty’saveragedrivingspeed

C

M031097

The distance from one town to another is 180 km. If Betty has to drive thedistance in 3 hours, what must her average speed be in kilometers perhour?

a 180 × 3

b 180 + 3

c 180 ÷ 3

d 180 − 3


Hong Kong, SAR 83 pLatvia 80 pRussian Federation 74 pChinese Taipei 73 pJapan 73 pLithuania 65 pNetherlands 62 pSingapore 59 pBelgium (Flemish) 56 pArmenia 54 pHungary 53 OMoldova, Republic of 53 OInternational average 48 OCyprus 39 qSlovenia 37 qUnited States 37 qEngland 36 qItaly 34 qNew Zealand 32 qAustralia 31 qNorway 30 qScotland 29 qTunisia 28 qMorocco 27 qIran, Islamic Republic of 26 qPhilippines 25 q


Correct Response:








Georgepracticedsoccer6daysaweek


D

M031178

George practiced soccer six days a week.

For 3 of the days he practiced for 45 minutes each day.

For 3 of the days he practiced for 20 minutes each day.

In hours and minutes, what is the total amount of time George practiced onthese six days?

a 2 hours 20 minutes

b 2 hours 55 minutes

c 3 hours 5 minutes

d 3 hours 15 minutes

Singapore 64 pChinese Taipei 61 pRussian Federation 57 pJapan 53 pLithuania 53 pHong Kong, SAR 50 pLatvia 49 pHungary 44 pEngland 42 OBelgium (Flemish) 41 OInternational average 37 OUnited States 36 OMoldova, Republic of 35 OArmenia 34 OAustralia 33 OItaly 33 ONetherlands 33 OSlovenia 32 OCyprus 31 qNew Zealand 28 qScotland 27 qNorway 24 qMorocco 17 qPhilippines 15 qIran, Islamic Republic of 13 qTunisia 11 q


Correct Response:







andFormulasUsingConcepts

Volumeofstackofcubes

D

M011010

Jasmine made a stack of cubes of the same size. The stack had 5 layers andeach layer had 10 cubes. What is the volume of the stack?

a 5 cubes

b 15 cubes

c 30 cubes

d 50 cubes


Chinese Taipei 93 pHong Kong, SAR 91 pNetherlands 85 pSingapore 85 pRussian Federation 82 pLithuania 80 pLatvia 79 pBelgium (Flemish) 75 pJapan 73 pMoldova, Republic of 70 pItaly 67 OUnited States 67 pEngland 65 OHungary 64 OInternational average 63 OAustralia 61 OCyprus 61 OScotland 60 ONew Zealand 56 qArmenia 53 qSlovenia 53 qNorway 46 qIran, Islamic Republic of 36 qMorocco 29 qTunisia 28 qPhilippines 26 q


Correct Response:






NuMbeR FractionsandDecimalsKnowingFactsandProcedures

Sumoftwonumberswithdecimals


b

Singapore 97 pChinese Taipei 97 pJapan 96 pBelgium (Flemish) 91 pLithuania 87 pHong Kong, SAR 86 pNetherlands 85 pItaly 77 pEngland 73 pUnited States 72 pRussian Federation 72 OHungary 72 pMoldova, Republic of 69 OLatvia 69 OInternational average 67 OArmenia 67 OPhilippines 62 qAustralia 58 qScotland 55 qCyprus 52 qNew Zealand 49 qSlovenia 48 qNorway 45 qMorocco 42 qIran, Islamic Republic of 37 qTunisia 31 q

M011008

What is the sum of 2.5 and 3.8 ?

a 5.3

b 6.3

c 6.4

d 9.5


Correct Response:







Subtractionwithdecimals


e

Singapore 94 pHong Kong, SAR 84 pChinese Taipei 83 pRussian Federation 81 pLatvia 79 pArmenia 74 pItaly 74 pLithuania 73 pJapan 72 pMoldova, Republic of 72 pUnited States 72 pBelgium (Flemish) 71 pNetherlands 69 pCyprus 65 OHungary 63 OInternational average 61 OScotland 51 qTunisia 47 qSlovenia 44 qEngland 43 qMorocco 41 qPhilippines 40 qIran, Islamic Republic of 38 qNorway 38 qAustralia 35 qNew Zealand 28 q

M011015

Subtract: 4.03−1.15

a 5.18

b 4.45

c 3.12

d 2.98

e 2.88


Correct Response:







Fractiontodecimal


C

M011020

Which of these means

7

10?

a 70

b 7

c 0.7

d 0.07

Singapore 95 pHong Kong, SAR 78 pChinese Taipei 74 pBelgium (Flemish) 73 pCyprus 65 pUnited States 62 pJapan 60 pItaly 58 pMoldova, Republic of 52 pPhilippines 49 pLithuania 48 pEngland 46 OInternational average 43 OAustralia 42 OArmenia 42 ORussian Federation 39 ONew Zealand 37 qNetherlands 29 qMorocco 23 qScotland 22 qHungary 17 qNorway 17 qIran, Islamic Republic of 16 qTunisia 15 qLatvia 12 qSlovenia 8 q







A. NuMbeR Fractions and Decimals Knowing Facts and Procedures

B.NumBer FractionsandDecimals reasoning

GeometryTiles:½black


SCORINGCorrect Response

• Drawsapatternmadeupof2blacktilesandtwowhitetiles.Seeexamplesbelow.


UniqueID M031348A Subject M Grade 4 MSBlock M09 MSBlockSeq 06A

A: Codes for 4-Tile Pattern without Triangles

Code Response Item: M031348A

Correct Response

10 Draws a pattern made up of 2 black tiles and two white tiles. See examples below.

Incorrect Response

70 Shaded 21 of the figure but used triangle tiles

71 Shaded 41 of the figure

72 Shaded 43 of the figure


Nonresponse

99 Blank

Incorrect Response


M031348_1

Making Fractions

A. WITHOUT using any triangle tiles, place 4 tiles so that

12

of a square

shape is black. Then shade in the square below to show what you did

with your tiles.

Shade in Here

B. Place 8 tiles so that

5

8 of the rectangle shape is black. Then shade in the

rectangle below to show what you did with your tiles.

Shade in Here

End of Geometry Tiles section.

Singapore 56 pBelgium (Flemish) 51 pEngland 49 pUnited States 48 pNetherlands 46 pJapan 45 pNew Zealand 44 pHong Kong, SAR 43 pAustralia 42 pCyprus 39 pHungary 39 OLatvia 37 pScotland 36 OLithuania 35 OInternational average 33 OChinese Taipei 32 ORussian Federation 32 ONorway 31 OItaly 30 OMoldova, Republic of 28 qSlovenia 24 qPhilippines 16 qArmenia 11 qIran, Islamic Republic of 7 qMorocco 4 qTunisia 4 q


Student Responses


GeometryTiles:½black(continued)Item Number: M031348A

Correct Response:

Incorrect Response:







GeometryTiles:½black

A.NumBer FractionsandDecimals KnowingFactsandProcedures

b. NuMbeR Fractions and Decimals Reasoning



• Anyfigureusing3black,1white,and4triangletiles:


• ½5 8 ofthefigureshadedwithoutusingcorrecttiles

Incorrect Response

• ½ofthefigureshaded


M031348_1

Making Fractions

A. WITHOUT using any triangle tiles, place 4 tiles so that

12

of a square

shape is black. Then shade in the square below to show what you did

with your tiles.

Shade in Here

B. Place 8 tiles so that

5

8 of the rectangle shape is black. Then shade in the

rectangle below to show what you did with your tiles.

Shade in Here

End of Geometry Tiles section.

Japan 13 pLatvia 13 pEngland 13 pBelgium (Flemish) 13 pAustralia 11 pSingapore 11 pNew Zealand 10 pRussian Federation 10 OChinese Taipei 8 OCyprus 8 OLithuania 8 ONetherlands 8 OUnited States 8 OHong Kong, SAR 7 OScotland 7 OInternational average 7 OItaly 6 ONorway 5 OHungary 4 qIran, Islamic Republic of 1 qMoldova, Republic of 1 qPhilippines 1 qSlovenia 1 qTunisia 1 qArmenia 0 qMorocco 0 q

85


Student Responses


GeometryTiles:½black(continued)Item Number: M031348B

Correct Response:

Incorrect Response:

85


Correct Response:







D

Fractionofcakeleft

NuMbeR FractionsandDecimals SolvingRoutineProblems

M012119

Janis, Maija, and their mother were eating a cake. Janis ate

1

2 of the cake.

Maija ate

1

4 of the cake. Their mother ate

1

4 of the cake.

How much of the cake is left?

a

3

4

b

1

2

c

1

4

d None

Singapore 83 pEngland 83 pHong Kong, SAR 82 pNew Zealand 74 pLithuania 73 pScotland 70 pAustralia 68 pUnited States 65 pBelgium (Flemish) 65 pNetherlands 63 ORussian Federation 63 OHungary 61 OMoldova, Republic of 61 OItaly 60 OLatvia 60 OInternational average 59 OSlovenia 58 OCyprus 54 qChinese Taipei 51 qNorway 49 qArmenia 48 qIran, Islamic Republic of 48 qJapan 47 qMorocco 32 qPhilippines 32 qTunisia 24 q







NuMbeR FractionsandDecimals SolvingroutineProblems

½of600ballsinabox



• 200

Incorrect Response


M031065

There are 600 balls in a box, and

1

3 of the balls are red.

How many red balls are in the box?

Answer: _______________ red balls

Lithuania 85 pSingapore 84 pLatvia 82 pBelgium (Flemish) 82 pRussian Federation 78 pMoldova, Republic of 68 pCyprus 64 pHong Kong, SAR 64 pArmenia 63 pNetherlands 63 pHungary 62 pJapan 56 pChinese Taipei 55 pInternational average 49 OItaly 43 qEngland 41 qScotland 40 qUnited States 38 qNew Zealand 34 qSlovenia 32 qAustralia 30 qTunisia 24 qNorway 19 qPhilippines 14 qIran, Islamic Republic of 9 qMorocco 7 q

3


Student Responses


Correct Response:

Incorrect Response:

½of600ballsinabox(continued)Item Number: M031065

3


Correct Response:






NuMbeR FractionsandDecimals SolvingroutineProblems

WhatfractionofcakeJohnate


b

M031216

A cake was cut into 8 pieces of equal size. John ate 3 pieces of the cake.What fraction of the cake did John eat?

a 1

8

b 3

8

c 3

5

d 8

3

Chinese Taipei 97 pHong Kong, SAR 93 pSingapore 89 pBelgium (Flemish) 89 pJapan 88 pUnited States 86 pCyprus 85 pNetherlands 83 pEngland 80 pAustralia 79 pNew Zealand 77 pLithuania 73 pItaly 72 OScotland 71 OLatvia 69 OInternational average 69 OHungary 64 qNorway 62 qIran, Islamic Republic of 58 qRussian Federation 58 qArmenia 53 qPhilippines 52 qMoldova, Republic of 46 qSlovenia 42 qTunisia 28 qMorocco 27 q


Correct Response:






b


Whichfigurehasone-halfblackdots

NuMbeR FractionsandDecimals usingConcepts

M011001

In which figure are one-half of the dots black?

a b c d

Belgium (Flemish) 97 pNetherlands 97 pHungary 95 pMoldova, Republic of 91 pRussian Federation 90 pHong Kong, SAR 90 pLithuania 89 pSingapore 89 pJapan 88 pItaly 88 pArmenia 86 pNorway 85 pAustralia 85 pLatvia 84 pEngland 84 pNew Zealand 84 pUnited States 79 pScotland 76 O

International average 75 OIran, Islamic Republic of 66 qCyprus 56 qMorocco 47 qTunisia 46 qChinese Taipei 42 qPhilippines 37 q


Correct Response:






3of4squaresshaded


C


M011016

In this diagram, 2 out of every 3 squares are shaded.

Which diagram has 3 out of every 4 squares shaded?

a

c

b

d

Singapore 77 pBelgium (Flemish) 74 pJapan 73 pLithuania 71 pHong Kong, SAR 70 pItaly 68 pNetherlands 65 pUnited States 63 pEngland 63 pCyprus 60 pMoldova, Republic of 60 pChinese Taipei 59 pSlovenia 56 OInternational average 55 OScotland 54 OAustralia 51 ONew Zealand 51 ONorway 46 qRussian Federation 46 qHungary 45 qLatvia 45 qArmenia 43 qIran, Islamic Republic of 43 qPhilippines 33 qMorocco 25 qTunisia 22 q


Correct Response:







e

Figureshowingfractionofshadedsquare


M012044

Which shows

23

of the square shaded?

a b c d e

Singapore 93 pHong Kong, SAR 86 pUnited States 82 pChinese Taipei 81 pBelgium (Flemish) 79 pJapan 76 pCyprus 75 pNetherlands 73 pEngland 67 pAustralia 62 pLatvia 60 ONew Zealand 59 OInternational average 57 OHungary 56 OLithuania 56 OItaly 55 OScotland 52 qPhilippines 50 qRussian Federation 49 qIran, Islamic Republic of 47 qMoldova, Republic of 43 qSlovenia 34 qArmenia 29 qNorway 29 qMorocco 13 qTunisia 12 q


Correct Response:






D


mariacollectedsoftdrinkbottles

NuMbeR ratio,Proportions,

andPercentSolvingroutineProblems

M031108

For every soft drink bottle that Fred collected, Maria collected 3.Fred collected a total of 9 soft drink bottles. How many did Maria collect?

a 3

b 12

c 13

d 27

Chinese Taipei 74 pHong Kong, SAR 74 pLithuania 67 pSingapore 67 pJapan 65 pNetherlands 63 pEngland 60 pBelgium (Flemish) 59 pCyprus 58 pUnited States 55 pHungary 52 ORussian Federation 52 OInternational average 49 OScotland 47 OArmenia 46 OSlovenia 46 OMoldova, Republic of 43 OAustralia 42 qItaly 40 qNew Zealand 40 qNorway 40 qLatvia 38 qIran, Islamic Republic of 28 qTunisia 21 qMorocco 20 qPhilippines 20 q


Correct Response:






NuMbeR WholeNumbersKnowingFactsandProcedures

Numberroundedto600


D

M011019

Which number would be rounded to 600 when rounded to the nearesthundred?

a 62

b 160

c 546

d 586

e 660

Singapore 87 pChinese Taipei 86 pNetherlands 86 pJapan 85 pEngland 84 pHungary 83 pHong Kong, SAR 82 pUnited States 80 pAustralia 78 pScotland 78 pBelgium (Flemish) 78 pMoldova, Republic of 70 pNew Zealand 70 pCyprus 68 pInternational average 64 OLithuania 61 ONorway 59 OItaly 53 qMorocco 52 qLatvia 50 qArmenia 46 qRussian Federation 45 qSlovenia 39 qTunisia 38 qPhilippines 20 qIran, Islamic Republic of 11 q


Correct Response:







Whichnumberisit


b

M011021

What number equals 3 ones + 5 tens + 4 hundreds + 60 thousands?

a 6,453

b 60,453

c 64,530

d 354,060

e 604,530

Singapore 88 pNetherlands 85 pJapan 84 pChinese Taipei 83 pHungary 83 pLatvia 80 pRussian Federation 80 pUnited States 80 pBelgium (Flemish) 80 pItaly 72 pCyprus 70 OLithuania 69 OEngland 68 OInternational average 68 OIran, Islamic Republic of 63 OAustralia 62 qNew Zealand 62 qHong Kong, SAR 61 qSlovenia 61 qNorway 60 qMoldova, Republic of 59 qMorocco 53 qScotland 52 qTunisia 51 qPhilippines 45 qArmenia 42 q


Correct Response:






b



expressnumberinwords

M011024

Which of these is a name for 9,740 ?

a Nine thousand seventy-four

b Nine thousand seven hundred forty

c Nine thousand seventy-four hundred

d Nine hundred seventy-four thousand

Chinese Taipei 98 pHong Kong, SAR 98 pSingapore 97 pJapan 96 pEngland 95 pBelgium (Flemish) 95 pNetherlands 92 pItaly 91 pLithuania 91 pUnited States 91 pLatvia 90 pRussian Federation 90 pAustralia 89 OHungary 88 OMoldova, Republic of 87 ONew Zealand 87 OScotland 87 OInternational average 86 OCyprus 85 OSlovenia 81 qNorway 80 qArmenia 79 qPhilippines 79 qIran, Islamic Republic of 72 qMorocco 64 qTunisia 50 q


Correct Response:







Whichnumberisequal


b

M011028

Which number is equal to eight tens plus nine tens ?

a 17

b 170

c 1,700

d 17,000

Chinese Taipei 91 pSingapore 87 pHungary 85 pMoldova, Republic of 84 pHong Kong, SAR 80 pNetherlands 77 pLatvia 75 pLithuania 73 pNew Zealand 73 pEngland 73 pArmenia 72 pRussian Federation 72 pBelgium (Flemish) 70 pJapan 69 pAustralia 67 ONorway 65 OUnited States 65 OInternational average 65 OScotland 64 OCyprus 54 qSlovenia 53 qItaly 51 qIran, Islamic Republic of 34 qMorocco 29 qPhilippines 28 qTunisia 27 q








15times9



• 135

Incorrect Response


M031305

15 × 9 =

Answer: _______________

Chinese Taipei 94 pSingapore 93 pHong Kong, SAR 91 pRussian Federation 90 pMoldova, Republic of 88 pLithuania 87 pJapan 86 pLatvia 86 pNetherlands 86 pArmenia 85 pHungary 85 pBelgium (Flemish) 84 pCyprus 76 pItaly 75 OUnited States 73 OInternational average 72 OTunisia 68 OSlovenia 67 OIran, Islamic Republic of 61 qPhilippines 59 qEngland 59 qScotland 54 qAustralia 45 qNew Zealand 41 qMorocco 36 qNorway 30 q


Student Responses


Correct Response:

Incorrect Response:

15times9(continued)Item Number: M031305








204dividedby4



• 51

Incorrect Response


M031306

204 ÷ 4 =

Answer: _______________

Hong Kong, SAR 93 pSingapore 91 pChinese Taipei 90 pRussian Federation 90 pHungary 86 pMoldova, Republic of 85 pJapan 84 pLatvia 82 pLithuania 82 pBelgium (Flemish) 77 pCyprus 72 pItaly 71 pArmenia 70 pNetherlands 65 OInternational average 63 OUnited States 55 qTunisia 47 qIran, Islamic Republic of 46 qEngland 46 qScotland 42 qSlovenia 41 qPhilippines 38 qAustralia 33 qNew Zealand 33 qNorway 27 qMorocco 17 q


Student Responses


Correct Response:

Incorrect Response:

204dividedby4(continued)Item Number: M031306









• 227

Incorrect Response


ThenumberLiashouldaddto142toget369

NuMbeR WholeNumbers reasoning

M031130

Lia is practicing addition and subtraction problems. What number shouldLia add to 142 to get 369?

Answer: _____________

Singapore 88 pHungary 86 pRussian Federation 85 pChinese Taipei 83 pLithuania 83 pHong Kong, SAR 82 pJapan 81 pLatvia 79 pBelgium (Flemish) 72 pUnited States 71 pNetherlands 69 pArmenia 64 OCyprus 64 OMoldova, Republic of 64 OInternational average 62 OEngland 59 OItaly 57 OSlovenia 54 qAustralia 52 qScotland 51 qNew Zealand 46 qIran, Islamic Republic of 39 qNorway 37 qTunisia 29 qPhilippines 28 qMorocco 24 q


Student Responses


Correct Response:

Incorrect Response:

ThenumberLiashouldaddto142toget369(continued)Item Number: M031130


Correct Response:






A


1279plus243bymistake

NuMbeR WholeNumbers reasoning

M031341

Juanita wanted to use her calculator to add 1,379 and 243. She entered

1,279 + 243 by mistake. Which of these could she do to correct the mistake?

a Add 100

b Add 1

c Subtract 1

d Subtract 100

Hungary 89 pNetherlands 88 pBelgium (Flemish) 88 pChinese Taipei 85 pHong Kong, SAR 84 pJapan 83 pRussian Federation 83 pSingapore 83 pEngland 82 pLatvia 79 pLithuania 77 pSlovenia 77 OAustralia 76 pUnited States 75 pScotland 74 OCyprus 73 OInternational average 72 OItaly 70 ONorway 70 OMoldova, Republic of 68 ONew Zealand 68 qArmenia 64 qPhilippines 47 qIran, Islamic Republic of 45 qTunisia 39 qMorocco 38 q


Correct Response:






D


Totalnumberofboysandgirls

NuMbeR WholeNumbers SolvingroutineProblems

M011002

In Toshi’s class there are twice as many girls as boys. There are 8 boys inthe class. What is the total number of boys and girls in the class?

a 12

b 16

c 20

d 24

Netherlands 82 pSingapore 81 pNew Zealand 64 pHungary 62 pJapan 62 pBelgium (Flemish) 62 pAustralia 60 pLithuania 60 pEngland 60 pCyprus 56 pUnited States 54 pLatvia 53 ORussian Federation 53 OItaly 51 OInternational average 51 OHong Kong, SAR 50 OSlovenia 50 ONorway 49 OScotland 48 OMoldova, Republic of 47 OArmenia 40 qChinese Taipei 29 qMorocco 24 qTunisia 24 qPhilippines 22 qIran, Islamic Republic of 20 q


Correct Response:






C



Totalnumberofpencils

M011003

There are 9 boxes of pencils. Each box has 125 pencils. What is the total

number of pencils?

a 1,025

b 1,100

c 1,125

d 1,220

e 1,225

Singapore 91 pChinese Taipei 83 pRussian Federation 79 pHong Kong, SAR 77 pCyprus 76 pUnited States 76 pJapan 74 pHungary 73 pLithuania 73 pLatvia 72 pItaly 70 pMoldova, Republic of 69 pArmenia 66 ONetherlands 64 OBelgium (Flemish) 63 OInternational average 63 OEngland 55 qScotland 51 qSlovenia 50 qIran, Islamic Republic of 49 qPhilippines 49 qAustralia 48 qNew Zealand 47 qTunisia 45 qMorocco 37 qNorway 34 q


Correct Response:






A


Howlongtowashwindows


M011011

It takes Chris 4 minutes to wash a window. He wants to know how manyminutes it will take him to wash 8 windows at this rate. He should

a multiply 4 × 8

b divide 8 by 4

c subtract 4 from 8

d add 8 and 4

Chinese Taipei 94 pSingapore 93 pNetherlands 92 pHong Kong, SAR 91 pJapan 91 pBelgium (Flemish) 89 pLithuania 88 pUnited States 88 pEngland 88 pCyprus 85 pHungary 84 pLatvia 83 pRussian Federation 83 pAustralia 81 pItaly 79 OScotland 79 OMoldova, Republic of 77 OInternational average 77 OArmenia 73 qNew Zealand 73 qSlovenia 69 qNorway 68 qPhilippines 56 qIran, Islamic Republic of 51 qMorocco 40 qTunisia 40 q


Correct Response:







estimatenumberofcabbages


C

M012117

Mark’s garden has 84 rows of cabbages. There are 57 cabbages in each row.

Which of these gives the BEST way to estimate how many cabbages there

are altogether?

a 100 × 50 = 5,000

b 90 × 60 = 5,400

c 80 × 60 = 4,800

d 80 × 50 = 4,000

Singapore 84 pHong Kong, SAR 71 pUnited States 70 pNetherlands 68 pBelgium (Flemish) 68 pHungary 66 pMoldova, Republic of 62 pChinese Taipei 61 pJapan 59 pCyprus 55 pEngland 51 OInternational average 50 OAustralia 48 OLithuania 46 qArmenia 45 qRussian Federation 45 OSlovenia 45 qScotland 42 qLatvia 40 qNew Zealand 36 qPhilippines 35 qItaly 34 qNorway 32 qTunisia 31 qIran, Islamic Republic of 30 qMorocco 26 q








• 920

Incorrect Response



Notebooksfor115students


M031011

Each student needs 8 notebooks for school. How many notebooks are neededfor 115 students?

Answer: _______________

Singapore 86 pChinese Taipei 85 pHong Kong, SAR 80 pRussian Federation 76 pLatvia 72 pHungary 69 pCyprus 68 pLithuania 67 pJapan 65 pMoldova, Republic of 65 pBelgium (Flemish) 63 pArmenia 58 pNetherlands 55 OItaly 54 OInternational average 52 OUnited States 51 OSlovenia 44 qIran, Islamic Republic of 38 qTunisia 35 qEngland 30 qAustralia 27 qNew Zealand 27 qPhilippines 26 qScotland 24 qMorocco 17 qNorway 12 q


Student Responses


Correct Response:

Incorrect Response:

Notebooksfor115students(continued)Item Number: M031011


Correct Response:







A204cmropecutinto4/calculation


D

M031310

A piece of rope 204 cm long is cut into 4 equal pieces. Which of these givesthe length of each piece in centimeters?

a 204 + 4

b 204 × 4

c 204 − 4

d 204 ÷ 4

Hong Kong, SAR 94 pSingapore 94 pChinese Taipei 90 pLatvia 90 pBelgium (Flemish) 90 pLithuania 88 pNetherlands 88 pJapan 87 pHungary 85 pRussian Federation 84 pArmenia 77 pEngland 76 pInternational average 73 OItaly 71 OMoldova, Republic of 70 OUnited States 70 OSlovenia 69 OAustralia 66 qScotland 65 qCyprus 64 qNorway 64 qNew Zealand 61 qIran, Islamic Republic of 55 qTunisia 46 qMorocco 40 qPhilippines 29 q








Numbertiles:largestnumber(+)


M031345_2

C. Use the tiles , , and . Write the numbers on the tiles in theboxes below to make the largest answer when you multiply.

End of Number Tiles section.

M031345_1

Finding the Largest Number Game

Using the number tiles, Joan and Herbert played a new game.They placed the numbers to make the largest answer.

A. Use the tiles , , and . Write the numbers on the tiles in theboxes below to make the largest answer when you add.

B. Use the tiles , , and . Write the numbers on the tiles in theboxes below to make the largest answer when you subtract.

This Number Tiles question continues on the next page.

M031345_1






Japan 74 pSingapore 71 pHong Kong, SAR 69 pEngland 68 pHungary 65 pNetherlands 65 pChinese Taipei 64 pCyprus 63 pLatvia 60 pLithuania 60 pScotland 60 pBelgium (Flemish) 57 OUnited States 56 OAustralia 56 OIran, Islamic Republic of 54 ONew Zealand 53 OInternational average 52 ORussian Federation 50 ONorway 47 OItaly 46 qSlovenia 45 qMorocco 35 qMoldova, Republic of 33 qArmenia 24 qTunisia 23 qPhilippines 11 q



Numbertiles:largestnumber(+)(continued)Item Number: M031345A


• 91+5or95+1

Incorrect Response

• Anyotherarrangementofdigits1,5,and9



Student Responses


Numbertiles:largestnumber(+)(continued)Item Number: M031345A

Correct Response:

Incorrect Response:








Numbertiles:largestnumber(-)


M031345_2



M031345_1






M031345_1






Japan 73 pSingapore 69 pHong Kong, SAR 67 pHungary 64 pNetherlands 64 pChinese Taipei 63 pLatvia 60 pEngland 59 pLithuania 57 pBelgium (Flemish) 56 pCyprus 55 pUnited States 53 ORussian Federation 52 OAustralia 52 OScotland 52 ONew Zealand 51 OInternational average 50 OIran, Islamic Republic of 49 ONorway 47 OItaly 46 OSlovenia 41 qMoldova, Republic of 39 qArmenia 23 qMorocco 21 qTunisia 19 qPhilippines 9 q



Numbertiles:largestnumber(-)(continued)Item Number: M031345B


• 73-2

Incorrect Response

• 72-3

• Anyotherarrangementofthedigits2,3,and7



Student Responses


Correct Response:

Incorrect Response:

Numbertiles:largestnumber(-)(continued)Item Number: M031345B








Numbertiles:largestnumber(X)


M031345_2



M031345_1






M031345_1






Japan 35 pSingapore 26 pHong Kong, SAR 24 pCyprus 23 pChinese Taipei 22 pHungary 22 pEngland 19 OTunisia 18 OBelgium (Flemish) 18 OLatvia 17 OMorocco 17 OAustralia 16 OLithuania 16 OInternational average 16 OItaly 15 OScotland 15 ONetherlands 14 ONorway 14 OUnited States 14 qMoldova, Republic of 13 ONew Zealand 13 OIran, Islamic Republic of 12 qRussian Federation 12 qArmenia 7 qSlovenia 5 qPhilippines 3 q



Numbertiles:largestnumber(X)(continued)Item Number: M031345C


• 41x5

Incorrect Response

• 51x4

• Anyotherarrangementofthedigits1,4,and5



Student Responses


Correct Response:

Incorrect Response:

Numbertiles:largestnumber(X)(continued)Item Number: M031345C


Correct Response:






NuMbeR WholeNumbers usingConcepts

Numberrepresentedbysquares


b

M011004

Each small square ( ) is equal to 1. There are 10 small squares in eachstrip. There are 100 small squares in each large square.

What number is shown?

a 16

b 358

c 538

d 835

Chinese Taipei 98 pBelgium (Flemish) 92 pJapan 89 pSingapore 89 pUnited States 89 pAustralia 86 pNetherlands 86 pHong Kong, SAR 85 pEngland 84 pNew Zealand 82 pLithuania 80 pScotland 80 pLatvia 79 pCyprus 78 OMoldova, Republic of 78 OItaly 77 ONorway 76 OSlovenia 75 OInternational average 75 ORussian Federation 74 OHungary 68 qPhilippines 57 qIran, Islamic Republic of 56 qArmenia 39 qMorocco 38 qTunisia 34 q


Correct Response:







Whichhassamevalue


b

M011007

Which of these has the same value as 342?

a 3,000 + 400 + 2

b 300 + 40 + 2

c 30 + 4 + 2

d 3 + 4 + 2

Chinese Taipei 98 pBelgium (Flemish) 98 pHong Kong, SAR 97 pJapan 97 pLatvia 97 pNetherlands 97 pSingapore 97 pHungary 96 pRussian Federation 96 pLithuania 94 pUnited States 92 pEngland 91 pCyprus 89 OItaly 89 OMoldova, Republic of 89 OSlovenia 89 ONorway 88 OAustralia 87 OArmenia 87 OInternational average 87 ONew Zealand 82 qScotland 79 qMorocco 64 qTunisia 64 qPhilippines 62 qIran, Islamic Republic of 56 q


Correct Response:







Digitinhundredsplace


b

M011018

Which digit is in the hundreds place in 2,345?

a 2

b 3

c 4

d 5

Chinese Taipei 96 pSingapore 95 pJapan 94 pUnited States 92 pNetherlands 91 pBelgium (Flemish) 90 pEngland 87 pAustralia 83 pHungary 80 OLithuania 80 OMoldova, Republic of 80 OLatvia 79 OScotland 79 OCyprus 78 OItaly 77 OInternational average 77 ORussian Federation 75 OIran, Islamic Republic of 73 ONew Zealand 73 qHong Kong, SAR 70 qNorway 69 qArmenia 59 qPhilippines 59 qMorocco 57 qSlovenia 54 qTunisia 44 q


Correct Response:







Whichistrue


C

M011026

Which number sentence is true?

a 968 < 698

b 968 < 689

c 968 > 689

d 968 = 689

Chinese Taipei 90 pSingapore 84 pRussian Federation 82 pBelgium (Flemish) 81 pHong Kong, SAR 80 pHungary 80 pUnited States 80 pJapan 79 pMoldova, Republic of 78 pSlovenia 78 pLatvia 76 pLithuania 76 pItaly 75 pArmenia 71 pCyprus 68 OInternational average 66 ONorway 65 ONew Zealand 62 qEngland 59 qPhilippines 54 qNetherlands 53 qIran, Islamic Republic of 47 qAustralia 45 qMorocco 42 qTunisia 28 qScotland 28 q








Numbergoinginthenumberlinebox



• 7

Incorrect Response


M031162

On the number line above, what number goes in the box?

Number in C = _______________

30

Japan 88 pBelgium (Flemish) 88 pSingapore 87 pHungary 86 pChinese Taipei 85 pNetherlands 85 pEngland 80 pLatvia 76 pItaly 74 pHong Kong, SAR 72 pLithuania 72 pSlovenia 71 pNew Zealand 66 OUnited States 66 OInternational average 66 OAustralia 64 OCyprus 60 qRussian Federation 60 qScotland 60 qMoldova, Republic of 56 qIran, Islamic Republic of 55 qNorway 54 qArmenia 45 qPhilippines 36 qMorocco 30 qTunisia 28 q


Student Responses


Numbergoinginthenumberlinebox(continued)Item Number: M031162

Correct Response:

Incorrect Response:









Numbertiles:getto20using2,7,9

RULES

Each player draws three number tiles.

Each player places the three tiles to make an addition problemwith the sum total closest to 20.

For example, here are four ways a player who draws , , and could

place the tiles:

+

+ + + +

55 46 19 10

This player should choose to show the addition problem

15+419

because 19 is

the total closest to 20.

M031344_2

Joan and Herbert played the game “Get to 20.”

Joan picked , , and . Herbert picked , , and .

A. What is the addition problem that Joan could make with her numbertiles that gives a total closest to 20? Be sure to include the total.

B. What is the addition problem that Herbert could make with his numbertiles that gives a total closest to 20? Be sure to include the total.

C. Herbert said, “If I pick , , and , I can make 20 two differentways.”

Show two ways Herbert could make 20 with , , and .

First way:

Second way:

Questions for Number Tiles continue.

M031344_2







First way:

Second way:


M031344_2







First way:

Second way:


M031344_2







First way:

Second way:


Chinese Taipei 69 pJapan 65 pHong Kong, SAR 61 pHungary 53 pItaly 53 pLithuania 51 pCyprus 50 pSingapore 49 pRussian Federation 47 OBelgium (Flemish) 47 pLatvia 45 OMoldova, Republic of 44 OUnited States 43 ONew Zealand 41 OInternational average 41 ONetherlands 40 OSlovenia 40 OEngland 40 OAustralia 38 ONorway 36 OScotland 36 OTunisia 24 qIran, Islamic Republic of 22 qPhilippines 13 qMorocco 9 qArmenia 5 q



Numbertiles:getto20using2,7,9(continued)Item Number: M031344A


• 2+7+9=18

• 18withoutadditionstatementshown

Incorrect Response

• 2+7+9but18notshown



Student Responses


Correct Response:

Incorrect Response:

Numbertiles:getto20using2,7,9(continued)Item Number: M031344A










RULES




place the tiles:

+

+ + + +

55 46 19 10


15+419

because 19 is


M031344_2







First way:

Second way:


M031344_2







First way:

Second way:


M031344_2







First way:

Second way:


M031344_2







First way:

Second way:


Chinese Taipei 65 pHungary 64 pJapan 61 pSingapore 57 pBelgium (Flemish) 57 pLatvia 55 pHong Kong, SAR 51 pLithuania 51 pEngland 50 pCyprus 49 pItaly 49 pUnited States 48 pRussian Federation 46 ONetherlands 43 ONew Zealand 43 OSlovenia 41 OInternational average 41 OAustralia 39 OScotland 37 OMoldova, Republic of 36 ONorway 35 qIran, Islamic Republic of 13 qPhilippines 13 qArmenia 6 qTunisia 6 qMorocco 4 q



Numbertiles:getto20using1,3,6(continued)Item Number: M031344B


• 13+6=19OR16+3=19

• 19withoutadditionstatementshown

Incorrect Response

• 13+6OR16+3but19notshown



Student Responses


Correct Response:

Incorrect Response:

Numbertiles:getto20using1,3,6(continued)Item Number: M031344B










RULES




place the tiles:

+

+ + + +

55 46 19 10


15+419

because 19 is


M031344_2







First way:

Second way:


M031344_2







First way:

Second way:


M031344_2







First way:

Second way:


M031344_2







First way:

Second way:


Chinese Taipei 66 pSingapore 65 pHungary 59 pEngland 59 pJapan 58 pUnited States 58 pLatvia 57 pHong Kong, SAR 56 pBelgium (Flemish) 56 pItaly 55 pCyprus 53 pNew Zealand 53 pRussian Federation 53 pNetherlands 51 OScotland 51 pLithuania 47 OSlovenia 47 OAustralia 47 OInternational average 44 ONorway 39 OMoldova, Republic of 36 qPhilippines 12 qIran, Islamic Republic of 11 qArmenia 7 qTunisia 4 qMorocco 0 q



Numbertiles:getto20using1,4,6(continued)Item Number: M031344C


• Bothwayscorrect16+4AND14+6


• Onlyonewaycorrect16+4OR14+6

Incorrect Response



Correct Response:

Partially Correct Response:

Student Responses




Incorrect Response:

Student Responses (continued)




Content Domain Page

Patterns and Relationships

M012048 Symboliclinearequationofmagazines 3

M031220 Robsoldsomeofhisapples 4

M031249 Thevalueof37timesboxplus6 5

M011027 Completenumberpattern 7

M031023 Thenumbertogointhecenterofthetable 8

M031051 Thedailystarttimesforamovie 9

M031190 Outputofthenumbermachine 10

Data

M012126 Heightsoffourgirlsongraph 11

M011009 Bargraph:whichshows45bottles 12

M011012 Bargraph:whichtwoshow80bottles 13

M012078 Highesttemperatureonchart 14

M031264 Colorsofstudents’haironthegraph 15

M031265 Howmanymorepencilsthanrulerssold 17

M031333 Highandlowtemperaturesforaweek 19

M031315 Thefavoriteicecreamsof30students 20

Geometry

M011014 Congruentfigures 21

M031267 Shadeintwotrianglesofdifferentsizes 22

M031327 DrawalineonthegridparalleltolineL 24

M012069 Rotated3-dimensionalfigure 26

M011006 Whichhasflatandcurvedsurface 27

M011022 Statementsabouttriangle 28

M031269 Indicatesgeometricshapesinthepicture 29

M031347AGeometrytiles:blacktriangle 33

M031347BGeometrytiles:blacksquare 35

M031347CGeometrytiles:fractionshaded 37

M031272ADrawlineonrectangle/2triangles 39

M031272BDrawlineonrectangle/2rectangles 41

M031272CDrawlineonrectangle/1rectangle,2triangles 43

Measurement

M011023 Weightofanadult 45

M012023 Unitstomeasuremassofegg 46

M031338 Whichcouldequal150milliliters 47

M011005 Whichhaslargestarea 48

M031008 Thelengthofthefilms 49

M011013 Howmuchdidtemperaturerise 50

M031322 DrawatrianglewithABasthebase 51

M012065 Distanceonmap 53

M031298 Completethefigurewithanareaof13cm2 54

M011017 WhenisMary’strip 56

M011025 Perimeterofrectangle 57

M031097 Betty’saveragedrivingspeed 58

M031178 Georgepracticedsoccer6daysaweek 59

M011010 Volumeofstackofcubes 60

Content Domain Page

Number

M011008 Sumoftwonumberswithdecimals 61

M011015 Subtractionwithdecimals 62

M011020 Fractiontodecimal 63

M031348AGeometryTiles:1/2black 64

M031348BGeometryTiles:5/8black 66

M012119 Fractionofcakeleft 68

M031065 1/3of600ballsinabox 69

M031216 WhatfractionofcakeJohnate 71

M011001 Whichfigurehasone-halfblackdots 72

M011016 3of4squaresshaded 73

M012044 Figureshowingfractionofshadedsquare 74

M031108 Mariacollectedsoftdrinkbottles 75

M011019 Numberroundedto600 76

M011021 Whichnumberisit 77

M011024 Expressnumberinwords 78

M011028 Whichnumberisequal 79

M031305 15times9 80

M031306 204dividedby4 82

M031130 ThenumberLiashouldaddto142toget369 84

M031341 1279plus243bymistake 86

M011002 Totalnumberofboysandgirls 87

M011003 Totalnumberofpencils 88

M011011 Howlongtowashwindows 89

M012117 Estimatenumberofcabbages 90

M031011 Notebooksfor115students 91

M031310 A204cmropecutinto4/calculation 93

M031345ANumbertiles:largestnumber(+) 94

M031345BNumbertiles:largestnumber(-) 97

M031345CNumbertiles:largestnumber(X) 100

M011004 Numberrepresentedbysquares 103

M011007 Whichhassamevalue 104

M011018 Digitinhundredsplace 105

M011026 Whichistrue 106

M031162 Numbergoinginthenumberlinebox 107

M031344ANumbertiles:getto20using2,7,9 109

M031344BNumbertiles:getto20using1,3,6 112

M031344CNumbertiles:getto20using1,4,6 115

Item Index 2003

released 4 mathematics items

Documents