mathematics concepts 4 mathematics items mathematics concepts and mathematics items book contains...

4 &MATHEMATICS CONCEPTSMATHEMATICS ITEMS

MATHEMATICS CONCEPTSMATHEMATICS ITEMS

The Mathematics Concepts and Mathematics Items book contains the released TIMSS mathematics assessment items. These are the released items from the 1995 and 2003 assessments (as distinct from the secure items, which are kept confidential so that they may be used in subsequent cycles to monitor trends).

Guide to Using the Mathematics Concepts and Mathematics Items Materials

The materials contained in this book can be used in a number of ways as a tool to assist teachers in making a formative assessment of student knowledge and skills. Some of these ways include the following:

Teacher-designed formative assessments. A teacher might, for example, decide to examine how well his or her class knows facts and procedures. In such a case, the first step would be to review 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 can print these items or present them to students on an overhead. Student responses can be scored by referring to the appropriate page in Mathematics Concepts and Mathematics Items. Teachers can also compare the overall percentage of students responding correctly to the international benchmark for that item.

Feedback on teaching. To the extent that the items coincide with concepts taught, the teacher might 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 incorrect or partially correct responses of the class for insight into any general misunderstandings, with a view to re-teaching a particular topic or skill.

Identifying individual difficulties. In the same way, the teacher might use the items to identify particular difficulties experienced by individual students, as the basis for some remedial teaching or focused practice.

18675.0206 33

Guide to the Content and Layout of This Book

This book contains the released items from both TIMSS 1995 and 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.

1995 Content Domains:• Whole numbers• Fractions and proportionality• Measurement, estimation, and number sense• Data representation, analysis, and probability• Geometry • Patterns, relations, and functions

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

1995 Cognitive Domains:• Knowing• Performing routine procedures• Using complex procedures• Solving problems

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

Take a look at Which number is it, the name given to the first 1995 item in this book. As specified in boxes at the top of the page, the content domain for this item is whole numbers and the cognitive domain is using complex procedures. Looking at Symbolic linear equation of magazines, the first item from TIMSS 2003 (page 73), 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. Which number is it provides an example of the letter code type—the correct answer is D.

• Scoring guide. This form is used to assist in scoring write-in responses. Complete number sentence (S2) further along in the Whole Numbers domain (page 13), provides an example of the scoring guide approach, indicating the general nature of correct and incorrect 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 TIMSS 2003 extended response items. An example of an actual U.S. fourth-grade student’s response is provided for each scoring category. See Item M031249 on page 76.

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.

TIMSS 1995 4th-Grade Mathematics Concepts and Mathematics Items

Content Domain Cognitive Domain

Overall Percent Correct

3

When you subtract one of the numbers below from 900, theanswer is greater than 300. Which number is it?

A. 823

B. 712

C. 667

D. 579

Country average vs. International average:

Higher ▲

Not different OLower ▼

Correct Response: D

Whole Numbers Using Complex Procedures

Which number is it

Item Number: I3

Korea 82 ▲

Czech Republic 74 ▲

Hong Kong 74 ▲

Hungary 74 ▲

Slovenia 72 ▲

Japan 71 ▲

Netherlands 70 ▲

Austria 65 OIreland 62 OSingapore 62 OLatvia (LSS) 61 OInternational average 57United States 57 OScotland 56 OThailand 54 OCanada 53 OCyprus 52 OGreece 52 OIsrael 52 OAustralia 51 OEngland 48 ▼

Iceland 47 ONew Zealand 47 ONorway 43 ▼

Portugal 40 ▼

Iran, Islamic Rep. 39 ▼

Kuwait 34 ▼

Correct Response: C


4


What is 3 times 23

Item Number: I4


Higher ▲


Netherlands 98 ▲


Hungary 96 ▲

Japan 96 ▲

Hong Kong 95 ▲

Latvia (LSS) 95 ▲

Slovenia 95 ▲

Austria 94 ▲

Singapore 93 ▲

United States 90 ▲

England 89 OIreland 87 OAustralia 86 OGreece 86 OKorea 86 OCanada 85 OScotland 85 OInternational average 84Cyprus 82 ONorway 82 OIceland 80 OIsrael 80 OPortugal 80 ONew Zealand 78 OIran, Islamic Rep. 73 ▼

Thailand 54 ▼

Kuwait 12 ▼

What is 3 times 23?

A. 323

B. 233

C. 69

D. 26


Whole Numbers Performing Routine Procedures




Correct Response: C


5

Korea 93 ▲

Austria 92 ▲

Hungary 91 ▲

Singapore 91 ▲

Hong Kong 89 ▲

Japan 89 ▲

Netherlands 86 ▲

Slovenia 86 ▲


Greece 82 ▲

Ireland 82 ▲

Latvia (LSS) 80 ▲

Cyprus 79 ▲

Portugal 77 OInternational average 71Israel 71 OUnited States 71 OThailand 65 OIran, Islamic Rep. 62 OCanada 61 ▼

Norway 60 OScotland 55 ▼

Australia 47 ▼

Iceland 47 ▼

Kuwait 46 ▼

England 36 ▼

New Zealand 30 ▼

Subtraction of 4 digit numbers

Item Number: I9

Subtract: 6,000–2,369

A. 4,369

B. 3,742

C. 3,631

D. 3,531


Higher ▲





Correct Response: B


6

Korea 80 ▲

Singapore 73 ▲

Hong Kong 63 ▲

Netherlands 60 ▲

Japan 59 ▲

Austria 58 ▲

Hungary 52 OIreland 51 OSlovenia 51 OCzech Republic 50 OIsrael 47 OUnited States 46 OInternational average 45Latvia (LSS) 42 OAustralia 41 OCanada 41 OCyprus 38 ONorway 38 OPortugal 38 OEngland 37 OScotland 37 OIceland 33 ▼

Thailand 33 ▼

Greece 29 ▼

New Zealand 28 ▼


Kuwait 19 ▼

What is the increase in product

Item Number: J4

25 ✕ 18 is more than 24 ✕ 18. How much more?

A. 1

B. 18

C. 24

D. 25


Higher ▲


Here is part of a wall chart that lists numbers from 1 to 100.

Below is part of the same wall chart. What number shouldbe in the box with the question mark inside?

A. 34

B. 44

C. 54

D. 64

43

53

?


Correct Response: D


7



Netherlands 92 ▲

Korea 91 ▲

Japan 90 ▲

Australia 85 ▲

Canada 84 ▲

Hong Kong 84 ▲

Singapore 84 ▲

England 83 ▲

Ireland 83 ▲


Austria 81 OScotland 80 OHungary 77 OSlovenia 77 OCzech Republic 75 OInternational average 73New Zealand 73 OCyprus 72 OIsrael 72 ONorway 68 OLatvia (LSS) 66 OPortugal 62 ▼

Iceland 60 ▼

Greece 59 ▼

Thailand 50 ▼


Kuwait 38 ▼

Number in box

Item Number: J9


Higher ▲


Content Domain

Correct Response: C


8



Korea 96 ▲

Singapore 94 ▲

Cyprus 93 ▲


Japan 93 ▲

Ireland 92 ▲

Austria 91 ▲

Slovenia 91 ▲

Thailand 91 ▲

Hong Kong 90 ▲

Netherlands 90 ▲

Canada 87 OHungary 86 OPortugal 86 OUnited States 86 OIsrael 85 OLatvia (LSS) 85 OInternational average 84Greece 81 OIran, Islamic Rep. 80 OIceland 79 OAustralia 76 ▼

Norway 76 OScotland 73 ▼

Kuwait 72 ▼

New Zealand 69 ▼

England 60 ▼

Addition of four digit numbers

Item Number: K2

Add: 6,971+5,291

A. 11,162

B. 12,162

C. 12,262

D. 1,211,162


Higher ▲


Cognitive Domain

In which pair of numbers is the second number 100 morethan the first number?

A. 199 and 209

B. 4,236 and 4,246

C. 9,635 and 9,735

D. 51,863 and 52,863


Correct Response: C




9

Korea 80 ▲

Japan 73 ▲

Hong Kong 70 ▲

Austria 68 ▲


Netherlands 65 ▲

Slovenia 63 ▲

Hungary 62 ▲

Singapore 61 ▲

Israel 56 OCyprus 53 OLatvia (LSS) 52 OInternational average 49Australia 45 OUnited States 45 OIreland 44 OScotland 43 OCanada 42 OGreece 42 OThailand 36 ▼

Norway 35 ▼

England 34 ▼

New Zealand 33 ▼

Portugal 31 ▼

Iceland 28 ▼

Kuwait 24 ▼


Which pair different by 100

Item Number: L7


Higher ▲




Whole Numbers Knowing

Correct Response: A


10

Which operation equivalent

Item Number: M3


Higher ▲


Japan 89 ▲

Korea 82 ▲

Israel 78 ▲

Singapore 78 ▲

Hong Kong 75 ▲


Australia 69 OHungary 69 OCyprus 67 ONetherlands 66 OAustria 65 ONorway 64 OInternational average 63England 61 OLatvia (LSS) 61 OCanada 60 OIreland 60 ONew Zealand 59 OScotland 58 OSlovenia 57 OIran, Islamic Rep. 56 OThailand 55 OGreece 54 OIceland 54 OPortugal 51 ▼

Czech Republic 41 ▼

Kuwait 41 ▼

stands for a number. 7 ✕ will always give the sameanswer as

A. ✕ 7

B. + 7

C. – 7

D. 7 +

E. ÷ 7

John wanted to use his calculator to add 1,463 and 319. He entered 1,263 + 319 by mistake. What could he do to correct his mistake?

A. Add 200.

B. Add 2.

C. Subtract 2.

D. Subtract 200.


Correct Response: A



11

Japan 88 ▲

Korea 87 ▲

Hungary 84 ▲

Netherlands 84 ▲


Hong Kong 82 ▲

Singapore 81 ▲

Slovenia 80 ▲

Australia 78 ▲

Latvia (LSS) 78 OIsrael 77 ▲

Cyprus 73 OIreland 72 OCanada 71 OEngland 70 OInternational average 70United States 69 ONorway 68 OScotland 66 ONew Zealand 65 OAustria 60 OGreece 60 ▼

Iceland 59 OThailand 53 ▼

Portugal 48 ▼


Kuwait 38 ▼

What to do to correct mistake

Item Number: M6


Higher ▲


Whole Numbers Solving Problems




Correct Response: D


12

Korea 97 ▲

Austria 95 ▲

Hong Kong 95 ▲

Japan 94 ▲


Netherlands 93 ▲

Slovenia 92 ▲

Australia 91 ▲

Hungary 91 ▲

Israel 91 OSingapore 91 ▲

United States 89 OCanada 88 OIreland 88 OLatvia (LSS) 88 OGreece 87 ONorway 87 OInternational average 86Scotland 85 OEngland 83 ONew Zealand 83 OCyprus 82 OThailand 81 OIceland 80 OPortugal 80 OIran, Islamic Rep. 63 ▼

Kuwait 47 ▼

Choose largest number

Item Number: M8


Higher ▲


Which of these is the largest number?

A. 2,735

B. 2,537

C. 2,573

D. 2,753

Here is a number sentence.

2,000 + + 30 + 9 = 2,739

What number goes where the is to make this sentencetrue?

Answer: ______________________________




13

Complete number sentence

Item Number: S2

Singapore 92 ▲

Korea 91 ▲

Japan 86 ▲

Netherlands 83 ▲

Hong Kong 82 ▲

Slovenia 81 ▲


Hungary 76 ▲

Israel 71 ▲

Canada 65 OLatvia (LSS) 63 OInternational average 63Ireland 62 OAustralia 61 OAustria 61 OCyprus 61 OPortugal 60 OThailand 59 OUnited States 58 OGreece 52 ▼

England 49 ▼

New Zealand 49 ▼

Scotland 47 ▼

Iceland 45 ▼

Norway 45 ▼

Kuwait 27 ▼



Higher ▲


SCORINGCorrect Response• 700 or written out as "seven hundred."

Incorrect Response• 7• 43• 70• Gives other numbers made by digits in 2,739 such as 73, 30, 9, 39, 739, 2,739,...• Other incorrect.





14

Korea 92 ▲

Singapore 72 ▲

Australia 66 ▲

Hong Kong 66 ▲

Hungary 58 ▲

Iran, Islamic Rep. 55 ▲

Japan 53 ▲


Canada 49 OIreland 49 OInternational average 43Netherlands 43 OAustria 41 OCzech Republic 40 ONew Zealand 39 OScotland 39 OLatvia (LSS) 38 OEngland 35 ▼

Cyprus 33 ▼

Israel 33 ▼

Greece 31 ▼

Portugal 31 ▼

Slovenia 30 ▼

Norway 29 ▼

Iceland 27 ▼

Thailand 19 ▼

Kuwait 10 ▼

Make smallest whole number

Item Number: T2


Higher ▲


SCORINGCorrect Response• 1,349

Incorrect Response• 1,3,4,9• 1• 4• 17• Any four-digit number with digits 4,3,9 and 1, other than 1,349• 13 OR "1 and 3" OR "3 and 1"• Other incorrect.


What is the smallest whole number that you can make usingthe digits 4, 3, 9 and 1? Use each digit only once.

Answer: ______________________________




15

Addition/multiplication task

Item Number: U5

Hong Kong 95 ▲

Korea 94 ▲

Japan 92 ▲

Singapore 90 ▲

Ireland 86 ▲

Israel 86 ▲

Slovenia 86 ▲

Netherlands 85 ▲


Cyprus 83 ▲


Austria 82 OLatvia (LSS) 81 OHungary 80 OGreece 79 OInternational average 77Canada 76 OIran, Islamic Rep. 73 OAustralia 71 ▼

New Zealand 67 ▼

Norway 66 ▼

Scotland 66 ▼

Portugal 65 ▼

Thailand 65 ▼

Iceland 63 ▼

England 53 ▼

Kuwait 42 ▼


Higher ▲


SCORING


Correct Response• 5x4=20• 4x5=20• Other correct

Incorrect Response• 4x4=16• 4x4=20• 10x2=20 OR 2x10=20• Other incorrect

Write this addition fact as a multiplication fact.

_____ ✕ _____ = _____




16

Korea 85 ▲

Singapore 83 ▲

Japan 75 ▲


Slovenia 70 ▲

Hong Kong 60 ▲

Austria 59 ▲


Netherlands 55 OHungary 53 OIreland 53 OAustralia 51 OLatvia (LSS) 50 OInternational average 49Canada 47 OCyprus 45 ONorway 45 OGreece 41 ▼

England 36 ▼

Israel 36 ▼

Scotland 35 ▼

New Zealand 32 ▼

Portugal 32 ▼

Thailand 32 ▼

Iceland 27 ▼


Kuwait 13 ▼

Number larger than 56,821

Item Number: V2


Higher ▲


SCORINGCorrect Response• 57,821

Incorrect Response• 66,821• Any number except 66,821 where one or more digits in 56,821 have been increased by 1.

Example: 56,921, 66,932, 57,921• Other incorrect.


Write the number that is 1,000 more than 56,821.

Answer: ______________________________




17

What is 5 less than 203

Item Number: V3

Korea 89 ▲

Austria 84 ▲

Singapore 82 ▲

Japan 81 ▲

Slovenia 79 ▲

Hungary 78 ▲


Ireland 75 ▲

Hong Kong 74 ▲

Australia 71 ▲

Netherlands 67 OScotland 67 ▲

Norway 64 OUnited States 64 OInternational average 62England 61 OCanada 60 OLatvia (LSS) 59 OCyprus 57 OIsrael 56 ONew Zealand 51 ▼

Iceland 50 ▼

Greece 48 ▼

Thailand 39 ▼

Portugal 34 ▼


Kuwait 10 ▼


Higher ▲


SCORINGCorrect Response

• 198

Incorrect Response• 98 OR 298• 5• 208• Other incorrect


What is 5 less than 203?

Answer: ___________________




18

Korea 63 ▲

Slovenia 45 ▲

Hungary 41 ▲

Israel 41 ▲

Canada 38 ▲

Japan 36 ▲

Portugal 32 ▲

Singapore 29 ▲

Cyprus 27 OGreece 27 OInternational average 24Austria 23 OUnited States 23 OAustralia 22 OCzech Republic 22 ONetherlands 22 OHong Kong 21 OIceland 21 OIreland 20 OIran, Islamic Rep. 17 ▼

New Zealand 13 ▼

Scotland 12 ▼

England 11 ▼

Latvia (LSS) 11 ▼

Norway 6 ▼

Kuwait 1 ▼

Thailand 0 ▼

Game with cards: who won? Explain

Item Number: V4A


Higher ▲


SCORINGScoring for Part aCorrect Response• Mysong. 64 and 55 are shown (or 9, which is the difference between 64 and 55) with a

correct verbal explanation.

Partially Correct• Mysong. 64 and 55 are shown (or 43 - 31 > 24 - 21) with an unsatisfactory explanation.• Mysong. 64 and 55 are shown (or 43 - 31 > 24 - 21) without any further explanation.• Mysong. The response given is a verbal explanation. Either 64 or 55 is shown but not both.• Mysong. The response gives no verbal or numeric explanation.• Other responses containing Mysong. For example, “because Mysong had the largest answer.”

Incorrect Response• Neither Mysong nor Naoki win.• Naoki. There may or may not be an explanation.• Other incorrect, including “both won.”


In a game, Mysong and Naoki are making problems. Theyeach have four cards like these.

The winner of the game is the person who can make theproblem with the largest answer.

Who won this game? ______________________How do you know? ________________________________________________________________________________

Write numbers in the squares below to show how you wouldplace the cards to beat both Mysong and Naoki.




19

Game with cards: winning numbers

Item Number: V4B

Hong Kong 82 ▲

Japan 81 ▲

Singapore 70 ▲

Korea 66 ▲

Netherlands 62 ▲

Hungary 59 ▲

Slovenia 57 ▲


Canada 55 OAustralia 54 ▲

Austria 53 OIsrael 53 OEngland 50 OScotland 48 OInternational average 48Greece 46 OIreland 46 OCzech Republic 43 ONew Zealand 42 ONorway 41 OLatvia (LSS) 39 ▼

Iceland 35 ▼

Cyprus 34 ▼

Portugal 29 ▼


Thailand 18 ▼

Kuwait 5 ▼


Higher ▲


SCORINGScoring for Part bCorrect Response• One of the following: 42+31; 41+32; 31+42; or 32+41

Incorrect Response• Combinations of the numbers 1, 2, 3 and 4. Every number is used only once.• Combinations of the numbers 1, 2, 3 and 4. One or more numbers are used more than once.• Combinations containing one or more numbers other than 1, 2, 3 and 4• Other incorrect


In a game, Mysong and Naoki are making problems. Theyeach have four cards like these.

The winner of the game is the person who can make theproblem with the largest answer.

Who won this game? ______________________How do you know? ________________________________________________________________________________

Write numbers in the squares below to show how you wouldplace the cards to beat both Mysong and Naoki.




20

Portugal 90 ▲

Singapore 90 ▲

Hong Kong 78 ▲

Japan 73 ▲

Korea 70 ▲

Cyprus 61 ▲

Ireland 55 ▲

Iran, Islamic Rep. 54 ▲

Australia 49 ▲

United States 40 OInternational average 39Canada 31 OHungary 31 OGreece 29 ▼

Netherlands 29 OScotland 28 ▼

Thailand 26 ▼

Austria 24 ▼


Kuwait 22 ▼

England 20 ▼

New Zealand 20 ▼

Israel 18 ▼

Latvia (LSS) 17 ▼

Slovenia 16 ▼

Norway 14 ▼

Iceland 9 ▼

0.4 is the same as

Item Number: I2


Higher ▲


Correct Response: B

0.4 is the same as

A. four

B. four tenths

C. four hundredths

D. one-fourth

Fractions and Proportionality Knowing

Mario uses 5 tomatoes to make half a liter of tomato sauce.How much sauce can he make from 15 tomatoes?

A. A liter and a half

B. Two liters

C. Two liters and a half

D. Three liters

Fractions and Proportionality Using Complex Procedures



Correct Response: A


21

Hong Kong 73 ▲

Korea 67 ▲

Netherlands 67 ▲


Slovenia 61 OHungary 60 OIsrael 60 OSingapore 60 ▲

Australia 59 OThailand 57 OIreland 56 OLatvia (LSS) 53 OInternational average 53Austria 51 OCyprus 51 OEngland 51 ONorway 51 OGreece 50 ONew Zealand 48 OScotland 46 OJapan 45 OIceland 44 OIran, Islamic Rep. 44 ▼

United States 43 ▼

Portugal 42 ▼

Canada 41 ▼

Kuwait 23 ▼

Sauce from 15 tomatoes

Item Number: I5


Higher ▲






22

Singapore 72 ▲

Austria 71 ▲

Iceland 69 ▲

Hong Kong 67 ▲

Slovenia 64 ▲

Netherlands 59 OJapan 58 OEngland 57 OKorea 57 OCyprus 56 ONorway 55 OInternational average 54Israel 53 OLatvia (LSS) 53 OCanada 52 OUnited States 52 OHungary 51 OIreland 51 OGreece 50 ONew Zealand 50 OCzech Republic 47 OScotland 46 OAustralia 44 ▼

Thailand 43 OPortugal 42 ▼


Kuwait 38 ▼

Which 2 figures represent same fraction

Item Number: I8


Higher ▲


Correct Response: A

Each figure represents a fraction.

Which two figures represent the same fraction?

A. 1 and 2

B. 1 and 4

C. 2 and 3

D. 3 and 4


Part of the figure is shaded.

What fraction of the figure is shaded?

A.

B.

C.

D.

54

45

69

59

Fractions and Proportionality Solving Problems


Correct Response: D


23

Hong Kong 96 ▲

Singapore 94 ▲

Korea 92 ▲

Japan 89 ▲


Canada 79 ▲

Ireland 79 ▲

Cyprus 75 ▲

Thailand 75 ▲

Australia 72 ▲

Netherlands 70 ▲

Iran, Islamic Rep. 68 OScotland 66 OIsrael 62 OInternational average 61Greece 58 OHungary 58 ONew Zealand 50 OEngland 48 ▼

Latvia (LSS) 48 ▼

Slovenia 47 ▼

Austria 45 ▼


Norway 25 ▼

Kuwait 21 ▼

Iceland 20 ▼

Portugal 16 ▼

Fraction of figure shaded

Item Number: J7


Higher ▲






24

Singapore 76 ▲


Austria 59 ▲

Korea 54 ▲

Netherlands 51 ▲

Japan 49 ▲

Hong Kong 47 ▲

Slovenia 47 OLatvia (LSS) 45 OHungary 44 OIreland 44 OAustralia 38 OInternational average 38United States 36 OEngland 35 OIsrael 34 ONew Zealand 33 OScotland 33 OCanada 29 ▼

Portugal 26 ▼

Thailand 25 ▼

Cyprus 23 ▼

Greece 23 ▼

Kuwait 20 ▼

Iceland 19 ▼


Norway 12 ▼

How many marbles in two bags

Item Number: K9


Higher ▲


Correct Response: B

There are 54 marbles, and they are put into 6 bags, so thatthe same number of marbles is in each bag. How many mar-bles would 2 bags contain?

A. 108 marbles

B. 18 marbles

C. 15 marbles

D. 12 marbles

E. 9 marbles

Which number represents the shaded part of the figure?

A. 2.8

B. 0.5

C. 0.2

D. 0.02




Correct Response: C


25

Singapore 81 ▲

Hong Kong 73 ▲

Japan 71 ▲

Portugal 71 ▲

Korea 67 ▲

Ireland 48 OCyprus 41 OInternational average 40Australia 40 OCanada 40 OIran, Islamic Rep. 35 OThailand 35 OAustria 34 OEngland 34 OScotland 34 OKuwait 32 ONetherlands 32 OUnited States 32 ▼


Hungary 31 ▼

Greece 30 ▼

Latvia (LSS) 30 ▼

Slovenia 29 ▼

Israel 28 ▼

New Zealand 25 ▼

Iceland 23 ▼

Norway 19 ▼

Decimal representing shaded part of figure

Item Number: M5


Higher ▲




26

Singapore 61 ▲

Korea 53 ▲

Japan 40 ▲


Slovenia 33 OHong Kong 32 OThailand 32 OUnited States 32 ▲

Austria 31 OIreland 29 ONetherlands 28 OScotland 27 OInternational average 26Canada 25 OIsrael 25 OAustralia 23 OEngland 22 OGreece 21 ONorway 19 ▼

Latvia (LSS) 18 ▼

Cyprus 16 ▼

Portugal 15 ▼

Hungary 13 ▼

New Zealand 13 ▼


Iceland 6 ▼

Kuwait 5 ▼

Longest box on shelf

Item Number: S3

Julie put a box on a shelf that is 96.4 centimeters long. Thebox is 33.2 centimeters long. What is the longest box shecould put on the rest of the shelf?Show all your work.

Answer: ______________________________


Higher ▲


SCORINGNote: There is no distinction made between responses with and without units.

Correct Response• 63.2. The calculation will be "96.4 - 33.2" or its equivalent.

Partially Correct • 63.2. No acceptable description or calculation is shown.• The calculation "96.4 - 33.2," or equivalent, is shown but the answer is incorrect.• Other partial.

Incorrect Response• Any incorrect numerical answers (answers not equal to 63.2). No acceptable description or cal-

culation is shown.• Other incorrect.






27

How many pupils in class

Item Number: S4

A teacher marks 10 of her pupils’ tests every half hour. Ittakes her one and one-half hours to mark all her pupils’ tests.How many pupils are in her class?

Answer: ______________________________

Netherlands 73 ▲

Japan 70 ▲

Korea 69 ▲

Singapore 63 ▲

Ireland 58 ▲


Israel 57 ▲

Australia 56 ▲

Hong Kong 55 ▲

Austria 53 OEngland 53 ▲

Scotland 52 OSlovenia 51 ONew Zealand 47 OInternational average 46Latvia (LSS) 46 OUnited States 45 OCanada 44 OHungary 42 OCyprus 37 ▼

Iceland 37 ▼

Greece 31 ▼

Norway 27 ▼

Thailand 26 ▼

Portugal 25 ▼


Kuwait 11 ▼


Higher ▲


SCORINGCorrect Response• 30

Incorrect Response• 10• 15• 20• 21• 25• 40• Other incorrect.





28

Korea 43 ▲

Singapore 41 ▲

Netherlands 38 ▲

Australia 34 ▲

England 30 ▲

Japan 30 ▲

Ireland 26 OScotland 26 OCzech Republic 25 ONew Zealand 25 OUnited States 25 ONorway 24 OSlovenia 24 OCanada 22 OInternational average 21Cyprus 21 OIsrael 19 OAustria 13 ▼

Greece 11 ▼

Hong Kong 11 ▼

Latvia (LSS) 9 ▼

Portugal 9 ▼


Kuwait 7 ▼

Iceland 5 ▼

Thailand 4 ▼

Girl/boy ratio: is Juanita right

Item Number: T4A

There are 10 girls and 20 boys in Juanita’s class. Juanita said that there is one girl for every two boys. Her friendAmanda said that means 1 of all the students in the classare girls.

How many students are there in Juanita’s class? Answer: ________________

Is Juanita right? Answer: _________________Use words or pictures to explain why.

Is Amanda right? Answer: _________________Use words and pictures to explain why.


Higher ▲


SCORINGScoring for Part aCorrect Response• YES. The response expresses verbally, symbolically or pictorially that 20 is twice as much as

10, or that 10 is half of 20.• Other correct. (Includes satisfactory explanations when neither a “yes” or “no” answer is

given).

Incorrect Response• NO. An explanation is given but is not satisfactory.• NO. No explanation is given.• YES. An explanation is given but is not satisfactory.• YES. No explanation is given.• Other incorrect.





29

Girl/boy ratio: is Amanda right

Item Number: T4B

There are 10 girls and 20 boys in Juanita’s class. Juanita said that there is one girl for every two boys. Her friendAmanda said that means 1 of all the students in the classare girls.

How many students are there in Juanita’s class? Answer: ________________

Is Juanita right? Answer: _________________Use words or pictures to explain why.

Is Amanda right? Answer: _________________Use words and pictures to explain why.

Singapore 37 ▲

Korea 32 ▲

Japan 30 ▲

Ireland 25 ▲

Netherlands 24 ▲

Australia 21 ▲

England 20 ▲

Czech Republic 18 OUnited States 17 OIsrael 16 OScotland 16 ONew Zealand 15 ONorway 15 OInternational average 15Hong Kong 13 OCanada 12 OCyprus 12 OSlovenia 12 OGreece 8 ▼

Latvia (LSS) 6 ▼

Austria 5 ▼

Iceland 5 ▼

Kuwait 4 ▼

Thailand 4 ▼

Portugal 3 ▼



Higher ▲


SCORINGScoring for Part bCorrect Response• NO. The response expresses verbally, symbolically or pictorially that 10 is not half of 30.• Other correct. (Includes satisfactory explanations when neither a “yes” or “no” answer is

given).

Incorrect Response• YES. An explanation is given but it is not satisfactory.• YES. No explanation is given.• NO. An explanation is given but it is not satisfactory.• NO. No explanation is given.• Other incorrect.




30

Korea 90 ▲

Hong Kong 84 ▲

Japan 78 ▲

Singapore 76 ▲

Ireland 74 ▲

Thailand 73 ▲

Cyprus 69 ▲


Israel 65 OHungary 63 OCanada 62 OCzech Republic 60 OAustralia 59 OInternational average 57Greece 56 OAustria 55 OEngland 55 OScotland 54 ONew Zealand 51 ONetherlands 50 ▼

Latvia (LSS) 45 ▼


Slovenia 39 ▼

Norway 38 ▼

Kuwait 30 ▼

Portugal 28 ▼

Iceland 27 ▼

Fraction larger than 2/7

Item Number: U2

Write a fraction that is larger than

Answer: __________________________________


Higher ▲


SCORINGCorrect Response• A fraction with numerator greater than 2 and denominator equal to 7• A fraction with numerator equal to 2 and denominator less than 7• 3/8• 1/2. (Other fractions with numeric value equal 1/2 should be scored as correct.)• Other correct fraction.

Incorrect Response• 1/7• 4/14• 2/8• Other incorrect





31

Bicycle ride: how long, Maria

Item Number: U3A

Maria and her sister Louisa leave home at the same time andride their bicycles to school 9 kilometers away.

Maria rides at a rate of 3 kilometers in 10 minutes. How longwill it take her to get to school?

Answer: ______________________________ minutes

Louisa rides at a rate of 1 kilometer in 3 minutes. How longwill it take her to get to school?

Answer: ______________________________ minutes

Who arrives at school first?

Answer: ________________________________

Netherlands 81 ▲

Hong Kong 79 ▲

Japan 76 ▲

Korea 76 ▲


Singapore 74 ▲

Slovenia 68 ▲

Australia 67 ▲

Austria 67 OIreland 67 OHungary 63 OUnited States 62 OInternational average 61Canada 61 OCyprus 61 ONorway 61 OEngland 60 OIsrael 60 OLatvia (LSS) 60 ONew Zealand 60 OIceland 58 OScotland 57 OThailand 54 OGreece 53 OPortugal 46 ▼


Kuwait 17 ▼


Higher ▲


SCORINGScoring for Part aCorrect Response• 30

Incorrect Response• 10• Other incorrect.





32

Hong Kong 70 ▲

Singapore 69 ▲

Korea 64 ▲


Netherlands 62 ▲

Austria 61 ▲

Japan 61 ▲

Slovenia 61 ▲

Australia 49 OHungary 49 OIreland 47 OLatvia (LSS) 47 OScotland 45 OInternational average 45United States 44 OIsrael 43 ONorway 43 OCanada 42 OEngland 40 ONew Zealand 36 ▼

Iceland 33 OThailand 32 ▼

Cyprus 29 ▼

Greece 29 ▼

Portugal 25 ▼


Kuwait 7 ▼

Bicycle ride: how long, Louisa

Item Number: U3B

Maria and her sister Louisa leave home at the same time andride their bicycles to school 9 kilometers away.


Answer: ______________________________ minutes


Answer: ______________________________ minutes


Answer: ________________________________


Higher ▲


SCORINGScoring for Part bCorrect Response• 27Incorrect Response• Any other multiple of 3.• Other incorrect.





33

Bicycle ride: who arrived first

Item Number: U3C

Maria and her sister Louisa leave home at the same and ridetheir bicycles to school 9 kilometers away.


Answer: ______________________________ minutes


Answer: ______________________________ minutes


Answer: ________________________________

Netherlands 90 ▲

Singapore 86 ▲

Japan 85 ▲


Ireland 83 ▲

Slovenia 82 ▲


Austria 81 ▲

Hong Kong 81 ▲

Scotland 80 ▲

Australia 79 ▲

Canada 79 ▲

Hungary 79 ▲

Korea 76 OEngland 75 ONew Zealand 75 ONorway 73 OInternational average 73Israel 71 OCyprus 70 OIceland 66 OLatvia (LSS) 66 OThailand 66 OGreece 63 ▼

Portugal 62 ▼


Kuwait 28 ▼


Higher ▲


SCORINGScoring for Part cCorrect Response• Louisa• Maria (or other responses), in cases where the response is consistent with (a) and (b).

Incorrect Response• Inconsistent with part (a) or (b) or both.• Other incorrect





34

Singapore 58 ▲

Netherlands 56 ▲

Hong Kong 47 ▲

Japan 41 ▲

Korea 41 ▲

Israel 39 ▲

Hungary 33 OCzech Republic 31 OIreland 30 OAustria 27 OUnited States 27 OInternational average 26Slovenia 26 OAustralia 24 OLatvia (LSS) 24 OIceland 22 OCanada 20 OCyprus 20 ▼

England 20 ▼

Scotland 20 ▼

New Zealand 16 ▼

Norway 16 ▼

Greece 14 ▼

Thailand 14 ▼

Kuwait 6 ▼

Portugal 6 ▼


Fractions of pie

Item Number: V1

Sam said that of a pie is less than of the same pie.

Is Sam correct? ________________

Use the circles below to show why this is so.


Higher ▲


SCORINGNote: The partition of circles has priority over shading. This is reflected in the scoring guide below.

Correct Response• NO. Both circles are correctly partitioned.

Partially Correct • NO. No partitioning is shown.• NO. Only one of the circles correctly partitioned.• NO. Other incorrect ways of partitioning.• YES, or there is no conclusion stated. Both circles are correctly partitioned.• Other partial.

Incorrect Response• YES. No partitioning is shown.• YES. The part representing 1/3 is made consistently smaller than the part representing 1/4.• YES. Other responses where one or both of the circles partitioned into 3 and/or 4 parts.• Other incorrect.





Measurement, Estimation, and Number Sense Solving Problems

Correct Response: A


35

Japan 94 ▲

Netherlands 92 ▲

Hungary 91 ▲

Korea 90 ▲

Austria 89 ▲

Hong Kong 89 ▲

Slovenia 89 ▲


Portugal 79 ▲

Latvia (LSS) 77 OSingapore 76 ONorway 74 OAustralia 73 OThailand 73 OInternational average 72Greece 71 OIceland 71 OCanada 68 OKuwait 67 OEngland 62 ▼


New Zealand 58 ▼

Ireland 56 ▼

Scotland 55 ▼


Israel 50 ▼

Cyprus 21 ▼

Choose largest mass

Item Number: J6

Which of these is largest?

A. 1 kilogram

B. 1 centigram

C. 1 milligram

D. 1 gram


Higher ▲




Measurement, Estimation, and Number Sense Knowing


36

Singapore 80 ▲

Korea 78 ▲

Japan 75 ▲

Hong Kong 72 ▲


Israel 66 ▲

Netherlands 66 ▲

Canada 65 ▲

Austria 61 OCzech Republic 61 ▲

Hungary 60 ▲

Australia 58 OIreland 58 OInternational average 52Scotland 47 OEngland 46 OSlovenia 45 ONew Zealand 42 ONorway 40 ▼

Latvia (LSS) 39 ▼

Cyprus 38 ▼

Iceland 35 ▼

Portugal 34 ▼

Greece 32 ▼

Thailand 28 ▼


Kuwait 20 ▼

Which is best estimate of hours

Item Number: J8


Higher ▲


Correct Response: C

Elena worked 57 hours in March, 62 hours in April, and 59hours in May. Which of these is the BEST estimate of thetotal number of hours she worked for the three months?

A. 50 + 50 + 50

B. 55 + 55 + 55

C. 60 + 60 + 60

D. 65 + 65 + 65

About how long is this picture of a pencil?

A. 5 cm

B. 10 cm

C. 20 cm

D. 30 cm



Measurement, Estimation, and Number Sense Using Complex Procedures

Correct Response: B


37


Hong Kong 91 ▲

Singapore 91 ▲

Austria 89 ▲

Japan 88 ▲

Cyprus 86 ▲

Korea 85 ▲

Latvia (LSS) 85 OSlovenia 84 OThailand 84 OIreland 79 ONorway 79 OHungary 78 OAustralia 77 ONetherlands 77 OInternational average 77Canada 72 ONew Zealand 71 OScotland 69 OEngland 68 OIceland 68 OKuwait 67 ▼


Israel 66 ▼

Portugal 66 ▼

Greece 63 OUnited States 55 ▼

Estimate pencil length

Item Number: K5


Higher ▲




Measurement, Estimation, and Number Sense Performing Routine Procedures


38

Singapore 46 ▲

Korea 38 ▲

Netherlands 35 ▲

Japan 32 ▲

England 29 OHong Kong 29 OCyprus 28 OLatvia (LSS) 24 OScotland 24 OInternational average 23Australia 23 OAustria 23 OCanada 23 ONew Zealand 23 OUnited States 23 OKuwait 22 OIreland 20 OSlovenia 20 ONorway 19 OPortugal 18 OIsrael 17 OCzech Republic 16 ▼

Greece 16 OIran, Islamic Rep. 16 ▼

Hungary 15 ▼

Thailand 15 ▼

Iceland 12 ▼

Length of rectangle

Item Number: K7


Higher ▲


A thin wire 20 centimeters long is formed into a rectangle. Ifthe width of this rectangle is 4 centimeters, what is itslength?

A. 5 centimeters

B. 6 centimeters

C. 12 centimeters

D. 16 centimeters

Correct Response: B

The weight (mass) of a clothespin is 9.2 g. Which of these isthe best estimate of the total weight (mass) of 1,000 clothes-pins?

A. 900 g

B. 9,000 g

C. 90,000 g

D. 900,000 g




Correct Response: B


39

Best estimate of clothespin mass

Item Number: L6


Higher ▲



Hong Kong 71 ▲

Hungary 71 ▲

Netherlands 71 ▲

Slovenia 71 ▲

Korea 67 ▲

Austria 65 ▲

Israel 62 OSingapore 59 OLatvia (LSS) 57 OInternational average 55Greece 55 OAustralia 53 OIreland 52 OUnited States 52 OCanada 50 OScotland 50 OThailand 50 ONorway 49 OEngland 47 OKuwait 45 ▼

Cyprus 44 ▼

Iceland 44 ▼

Portugal 43 ▼

New Zealand 42 ▼






40

Korea 65 ▲

Netherlands 61 ▲

Austria 55 ▲

Slovenia 54 ▲

Latvia (LSS) 48 ▲


Japan 45 ▲

Hong Kong 42 ▲

Ireland 39 OIceland 35 ONorway 35 OInternational average 32England 27 OHungary 27 OIsrael 27 OPortugal 27 OGreece 25 OSingapore 25 ▼

Scotland 23 ▼

Australia 21 ▼

Cyprus 21 ▼

New Zealand 21 ▼

Canada 19 ▼

Thailand 15 ▼



Kuwait 8 ▼

Who had the longest pace

Item Number: L8


Higher ▲


Correct Response: D

Four children measured the width of a room by countinghow many paces it took them to cross it. The chart showstheir measurements.

Who had the longest pace?

A. Stephen

B. Erlane

C. Ana

D. Carlos




Correct Response: A


41

Japan 75 ▲

Hong Kong 73 ▲

Hungary 55 ▲

Austria 51 ▲

Australia 45 ▲

Portugal 45 OSingapore 45 ▲

Slovenia 45 OIreland 44 OLatvia (LSS) 42 OUnited States 38 OInternational average 38England 37 ONew Zealand 35 OScotland 35 OCzech Republic 32 OCanada 31 OKorea 31 OIceland 29 OIsrael 28 OGreece 27 aNetherlands 27 ▼


Norway 24 ▼

Thailand 22 ▼

Cyprus 20 ▼

Kuwait 15 ▼

Substance measured in milliliters

Item Number: M7


Higher ▲


Which of these would most likely be measured in milliliters?

A. The amount of liquid in a teaspoon

B. The weight (mass) of a pin

C. The amount of gasoline in a tank

D. The thickness of 10 sheets of paper



42

Japan 68 ▲

Korea 67 ▲

Austria 65 ▲

Netherlands 61 ▲

Ireland 60 ▲

Norway 60 ▲

Australia 58 ▲

England 58 ▲

Hungary 57 ▲

Scotland 57 ▲


Canada 54 ▲


Hong Kong 52 OInternational average 48Singapore 47 OIceland 46 ONew Zealand 45 OSlovenia 43 OCyprus 37 ▼

Latvia (LSS) 37 ▼

Greece 36 ▼

Israel 35 ▼

Thailand 33 ▼

Portugal 29 ▼


Kuwait 14 ▼

How many paper clip lengths

Item Number: S5


Higher ▲


SCORINGCorrect Response• 4.• 5.• Within the interval 4<X<5.5.

Incorrect Response• Less than 3.• Within the interval 3<X<4.• Within the interval 5.5<X<6.5.• Within the interval 6.5<X<8.• Other incorrect.


Measurement, Estimation, and Number Sense Using Complex Procedures

Here is a paper clip.

About how many lengths of the paper clip is the same as thelength of this line?

Answer: ______________________________



43

When did Mr. Brown start walk

Item Number: T3

Korea 74 ▲

Netherlands 72 ▲

Austria 64 ▲


Australia 62 ▲

Japan 60 ▲

Norway 60 ▲

Latvia (LSS) 59 ▲

Slovenia 59 ▲

Ireland 57 ▲

Scotland 54 ▲

Hungary 53 OSingapore 51 OEngland 49 OUnited States 49 OInternational average 47Israel 46 OCanada 45 ONew Zealand 45 OIceland 43 OCyprus 41 OHong Kong 32 ▼

Greece 29 ▼

Portugal 16 ▼

Thailand 13 ▼


Kuwait 6 ▼


Higher ▲


SCORINGCorrect Response• 05:30 OR 5:30• The answer expressed informally.

Example: "half past five"

Incorrect Response• 04:30, 4:30, or equivalent informal expression.• 06:00, 6:00, or equivalent informal expression.• 06:30, 6:30, or equivalent informal expression.• 08:30, 8:30, or equivalent informal expression.• Other incorrect.


Measurement, Estimation, and Number Sense Performing Routine Procedures

Mr. Brown goes for a walk and returns to where he startedat 07:00. If his walk took 1 hour and 30 minutes, at whattime did he start his walk?

Answer:______________________________



44

Japan 77 ▲

Netherlands 76 ▲

Korea 74 ▲

Austria 73 ▲

Hungary 69 ▲

Singapore 66 ▲

Hong Kong 63 ▲


Slovenia 53 ONorway 52 OScotland 52 OInternational average 50Australia 49 OCanada 49 OIceland 46 OIsrael 46 OUnited States 46 OCyprus 44 OPortugal 43 ▼

Greece 41 ▼


Latvia (LSS) 40 ▼

England 38 ▼

New Zealand 37 ▼

Ireland 36 ▼

Thailand 22 ▼

Kuwait 15 ▼

Triangles in figure

Item Number: U1


Higher ▲


SCORINGCorrect Response• 14. Figure is correctly partitioned.

Partial Response• 14. Partition includes errors.• 14. Partition is not shown.• The figure is correctly partitioned. Triangles are miscounted. (Count does not equal 14.)

Incorrect Response• Neither partition nor number of triangles is correct.• Other incorrect.



The triangle represents one tile in the shape of a triangle.

How many tiles will it take to cover the figure below?

Number of tiles: _______________________

Use the figure above to show how you worked out youranswer.



45

Millimeters in a meter

Item Number: V5


Hong Kong 72 ▲

Slovenia 70 ▲

Austria 67 ▲

Hungary 67 ▲

Latvia (LSS) 65 ▲

Japan 62 ▲

Australia 57 ▲

Netherlands 57 OPortugal 54 OGreece 53 OKorea 52 OInternational average 49Ireland 46 OEngland 44 ONew Zealand 43 ONorway 43 OSingapore 43 OCanada 41 OCyprus 41 ▼

Israel 41 OIran, Islamic Rep. 38 ▼

Scotland 37 ▼

Thailand 34 ▼

Iceland 29 ▼


Kuwait 17 ▼


Higher ▲


SCORINGCorrect Response• 1,000• Thousand or "one thousand."

Incorrect Response• 10• 60• 100• 10,000• Other incorrect



How many millimeters are in a meter?

Answer: ______________________________



Data Representation,Analysis and Probability Using Complex Procedures


46

Korea 96 ▲

Singapore 90 ▲

Austria 88 ▲

Netherlands 88 ▲

Hong Kong 86 ▲

Ireland 84 ▲

Slovenia 82 OAustralia 81 ▲

Norway 80 OCzech Republic 78 OUnited States 78 OCanada 75 OEngland 75 OIceland 75 OInternational average 75Scotland 74 OThailand 74 OHungary 73 ONew Zealand 73 OLatvia (LSS) 70 OPortugal 70 OIsrael 68 OGreece 65 OCyprus 63 ▼

Kuwait 43 ▼


What % of time in play and homework

Item Number: J3


Higher ▲


Correct Response: D

The figure shows how Mary spent her time one day.

What percent of time altogether did she spend playing anddoing homework?

A. 10%

B. 15%

C. 20%

D. 25%

E. 30%

Kyle and Bob are playing a game. The object of the game isto get the highest total of points. This chart shows howmany points they each scored.

Who won, and by how many points?

A. Bob won by 25 points.

B. Bob won by 100 points.

C. Kyle won by 25 points.

D. Kyle won by 175 points.




Correct Response: A


47

Singapore 71 ▲


Netherlands 70 ▲

Ireland 69 ▲

Austria 66 ▲

Japan 65 ▲

Slovenia 63 ▲

Hong Kong 62 ▲

Israel 57 OAustralia 55 OKorea 53 OScotland 53 OUnited States 53 OInternational average 50New Zealand 49 OCanada 47 OEngland 45 OLatvia (LSS) 43 OGreece 39 ONorway 38 ▼

Hungary 37 ▼

Iceland 36 OPortugal 34 ▼

Thailand 28 ▼

Cyprus 25 ▼

Kuwait 10 ▼

Who won and by how many points

Item Number: K4


Higher ▲




48

Japan 90 ▲

Hong Kong 83 ▲

Singapore 75 ▲


Korea 63 ▲

Netherlands 63 ▲

Ireland 62 ▲

Scotland 56 OIceland 54 OAustralia 51 OCzech Republic 51 OIsrael 51 OCyprus 50 OInternational average 49Canada 49 OEngland 49 OThailand 48 OAustria 45 ONew Zealand 45 OHungary 44 OSlovenia 44 ONorway 40 OLatvia (LSS) 31 ▼

Greece 25 ▼

Portugal 22 ▼


Kuwait 7 ▼

Pictograph of trees

Item Number: L1


Higher ▲


SCORINGCorrect Response• 100.

Incorrect Response• One of the following: 1, 5, 6, 6 1/2, 7, or 650.• Other incorrect.


Data Representation,Analysis and Probability Knowing

The graph shows 500 cedar trees and 150 hemlock trees.

How many trees does each represent?

Answer: ______________________________



Data Representation,Analysis and Probability Solving Problems

Correct Response: A


49

Netherlands 74 ▲

Japan 70 ▲

Hong Kong 69 ▲


Canada 63 ▲

Hungary 61 ▲

Singapore 61 ▲

Australia 59 ▲

Norway 58 OCzech Republic 56 OEngland 55 ONew Zealand 55 OScotland 55 OAustria 54 OIreland 52 OIsrael 51 OInternational average 51Slovenia 49 OIceland 47 OLatvia (LSS) 42 OKorea 39 ▼

Thailand 39 ▼

Cyprus 32 ▼

Kuwait 31 ▼

Greece 30 ▼

Portugal 30 ▼


Chance of picking red marble

Item Number: L2


Higher ▲


There is only one red marble in each of these bags.

Without looking in the bags, you are to pick a marble out ofone of the bags. Which bag would give you the greatestchance of picking the red marble?

A. The bag with 10 marbles.

B. The bag with 100 marbles.

C. The bag with 1,000 marbles.

D. All bags would give the same chance.

1,000 Marbles 100 Marbles 10 Marbles





50

Japan 89 ▲

Netherlands 86 ▲

Norway 86 ▲

Israel 85 OGreece 84 OHong Kong 84 ▲

Korea 84 OSlovenia 84 OCanada 83 OUnited States 83 ▲

Czech Republic 82 OAustria 81 OAustralia 80 OLatvia (LSS) 79 OEngland 78 OThailand 78 OInternational average 78Hungary 76 OIceland 76 ONew Zealand 74 OScotland 73 OIreland 72 OIran, Islamic Rep. 70 OSingapore 70 ▼

Cyprus 68 ▼

Portugal 62 ▼

Kuwait 58 ▼

Chance of hitting shaded region

Item Number: M1


Higher ▲


Correct Response: B

Samantha drops a stone onto each of these targets. Thestone has the best chance of landing on a shaded space inwhich target?

A team is selling raffle tickets. The table shows how manytickets they have sold so far.

They need to sell 60 tickets altogether. How many more tick-ets must they sell?

Answer:______________________________



51

How many raffle tickets

Item Number: M2

Korea 83 ▲

Austria 75 ▲

Singapore 73 ▲


Hungary 71 ▲

Netherlands 69 ▲

Japan 68 ▲

Ireland 65 ▲

Slovenia 65 ▲

Latvia (LSS) 59 OHong Kong 57 OAustralia 56 OIsrael 56 OInternational average 55Canada 54 OScotland 54 OUnited States 53 OGreece 51 OCyprus 50 OEngland 49 ONorway 48 OPortugal 47 OIceland 45 ▼

Thailand 44 ▼

New Zealand 38 ▼


Kuwait 8 ▼


Higher ▲


SCORINGCorrect Response• 24

Incorrect Response• 30• 34• 36• Other incorrect.





52

Korea 83 ▲

Japan 78 ▲

Hong Kong 75 ▲

Singapore 74 ▲


Australia 50 ▲

England 49 ▲

New Zealand 48 OCanada 46 OScotland 45 ONetherlands 42 OInternational average 41Austria 39 OThailand 38 OIsrael 37 OIceland 36 OIreland 34 ▼


Slovenia 32 ▼

Hungary 31 ▼

Latvia (LSS) 31 ▼

Cyprus 30 ▼

Greece 28 ▼

Norway 26 ▼

Portugal 13 ▼

Kuwait 8 ▼


Bar graphs of boys and girls

Item Number: S1


Higher ▲


SCORINGCorrect Response• All 4 bars correct for height, placement, and shading.• All 4 bars of correct height; either bars misplaced or bars shaded incorrectly in no more than

one set (i.e., for age 9 or age 10).

Partially Correct• Placement, shading, and height all correct for one, two, or three bars. (At least one bar com-

pletely correct).• All 4 bars of correct height, but two or more errors involving placement or shading.

Incorrect Response• Work is shown, but no bars are drawn. For example: only numbers are shown on the graph.• Other incorrect.



This table shows the ages of the girls and boys in a club.

Use the information in the table to complete the graph forages 9 and 10.



53

Bar graph: cartons sold Monday

Item Number: T1A

Korea 96 ▲

Singapore 95 ▲

Japan 94 ▲

Netherlands 94 ▲

Canada 93 ▲


Australia 87 ▲

Ireland 87 ▲


Scotland 83 ▲

Thailand 82 ▲

Cyprus 79 ONorway 79 OAustria 78 OIceland 77 ONew Zealand 77 OIsrael 76 OInternational average 75Hong Kong 74 OSlovenia 73 OHungary 70 OLatvia (LSS) 63 ▼

Greece 62 ▼

Portugal 57 ▼

Kuwait 17 ▼



Higher ▲


SCORINGScoring for Part aCorrect Response• 25

Incorrect Response• 5• Other incorrect.



The graph shows the number of cartons of milk sold eachday of a week at a school.

How many cartons of milk did the school sell on Monday?

Answer: ______________________________

How many cartons of milk did the school sell that week?Show your work.

Answer: ______________________________



54

Singapore 80 ▲

Korea 73 ▲


Netherlands 56 ▲


Ireland 48 ▲

Slovenia 48 ▲

Canada 46 ▲

Scotland 43 OIsrael 40 OAustria 38 OHong Kong 38 OInternational average 37Australia 34 OGreece 33 OLatvia (LSS) 33 OJapan 32 ONew Zealand 30 OHungary 28 ▼

Norway 28 ▼

Portugal 26 ▼

Thailand 23 ▼

Iceland 20 ▼

Cyprus 18 ▼


Kuwait 3 ▼

Bar graph: cartons sold for week

Item Number: T1B


Higher ▲


SCORINGScoring for Part bCorrect Response• 125. Calculation is shown.• 125. Verbal explanation of correct procedure.• Other correct.

Partially Correct• The addition task is shown, but a calculation error was made and answer is incorrect but is

other than 115 or 135.• 125. No work shown.• Other partial.

Incorrect Response• 115 OR 135. Note: If correct addition task is shown, score as partially correct.• 25• Other incorrect.



The graph shows the number of cartons of milk sold eachday of a week at a school.

How many cartons of milk did the school sell on Monday?

Answer: ______________________________

How many cartons of milk did the school sell that week?Show your work.

Answer: ______________________________



Geometry Using Complex Procedures

Correct Response: B


55

Japan 77 ▲

Austria 70 ▲


Korea 68 ▲

Hong Kong 66 ▲

England 64 ▲

Latvia (LSS) 63 ONetherlands 63 OSlovenia 63 ▲


Scotland 61 ONorway 60 OAustralia 59 OCanada 59 OHungary 59 OIreland 54 OIsrael 54 OInternational average 54New Zealand 52 OIceland 48 OSingapore 48 OCyprus 41 ▼

Greece 36 ▼

Portugal 34 ▼

Kuwait 24 ▼

Thailand 24 ▼


Map of city blocks

Item Number: I1


Higher ▲


This map shows city blocks with a delivery truck at one corner.

The driver of the delivery truck starts at corner X. He goes 3blocks east and 2 blocks north to get to the school. On what corner is the school located?

A. AB. BC. CD. DE. E



Geometry Knowing


56

Japan 90 ▲

Hong Kong 89 ▲

Latvia (LSS) 88 ▲

Netherlands 88 ▲

Australia 86 ▲

Slovenia 85 ▲

Hungary 84 ▲


Korea 83 ▲

England 82 ▲

Canada 81 ▲

New Zealand 81 ▲

Norway 81 ▲

United States 75 OAustria 74 OSingapore 74 OScotland 73 OInternational average 72Israel 72 OThailand 72 OIreland 71 OIceland 70 OCyprus 46 ▼

Greece 41 ▼

Portugal 41 ▼

Kuwait 37 ▼


Which figure made with straight sides

Item Number: I6


Higher ▲


Correct Response: D

Which of these is made with straight sides only?

Here is a hexagon.

The hexagon is divided into six

A. triangles

B. squares

C. pentagons

D. rectangles



Geometry Knowing

Correct Response: A


57


Hong Kong 97 ▲

Scotland 95 ▲

Slovenia 95 ▲

Australia 94 ▲

Netherlands 94 ▲

Canada 93 ▲

New Zealand 93 OSingapore 92 ▲

England 91 OIceland 91 OUnited States 91 OGreece 90 OIsrael 90 OJapan 90 OAustria 89 OLatvia (LSS) 89 OInternational average 88Cyprus 88 OIreland 87 OPortugal 84 OHungary 82 ▼

Korea 81 ▼

Norway 78 ▼


Kuwait 75 ▼

Thailand 71 ▼

Shapes in hexagon

Item Number: J1


Higher ▲




Geometry Knowing


58

Singapore 93 ▲

Scotland 90 ▲

Hong Kong 89 ▲

Korea 87 ▲

England 84 ▲

Australia 76 ▲

Austria 74 ▲



Canada 72 ▲

Hungary 70 OIsrael 68 OIran, Islamic Rep. 66 OThailand 66 OCyprus 65 OInternational average 64Slovenia 63 OIreland 62 OLatvia (LSS) 62 ONew Zealand 58 OIceland 52 ▼

Japan 52 ▼

Greece 41 ▼

Netherlands 40 ▼

Portugal 37 ▼

Norway 29 ▼

Kuwait 21 ▼

Which does not show symmetry

Item Number: J2


Higher ▲


Correct Response: C

Which of these does NOT show a line of symmetry?

Which number in square but not in triangle

Here is a figure.

Which number is in the square and the circle but is NOT inthe triangle?

A. 2

B. 3

C. 4

D. 5



Geometry Knowing

Correct Response: A


59


Hungary 83 ▲

Canada 78 ▲

Australia 76 ▲

England 74 ▲


Slovenia 72 OHong Kong 70 ONetherlands 70 ONew Zealand 70 OIreland 69 OScotland 69 OAustria 68 OIsrael 66 OInternational average 65Singapore 64 OCyprus 60 OIceland 59 OIran, Islamic Rep. 59 ONorway 59 OPortugal 58 OJapan 56 ▼

Latvia (LSS) 56 OGreece 54 OThailand 50 ▼

Kuwait 49 ▼

Korea 38 ▼

Item Number: K1


Higher ▲




Geometry Knowing


60

Korea 90 ▲

Netherlands 89 ▲

Japan 86 ▲

Singapore 85 ▲

Australia 84 ▲

Austria 83 ▲

Ireland 83 ▲



Canada 78 OHong Kong 78 OHungary 78 OSlovenia 78 OScotland 77 OEngland 75 OIceland 75 OLatvia (LSS) 75 OInternational average 73Israel 72 OThailand 71 ONew Zealand 69 OCyprus 66 ONorway 63 ▼

Greece 52 ▼

Portugal 49 ▼


Kuwait 35 ▼

Rectangle divided into four parts

Item Number: K8


Higher ▲


Correct Response: D

Which rectangle is NOT divided into 4 equal parts?

Objects on game board grid

This is a game board.

Which object is located at (2, D)?

A. The plane

B. The truck

C. The bus

D. The boat



Geometry Knowing

Correct Response: A


61

Netherlands 97 ▲



Scotland 95 ▲

Australia 94 ▲

England 94 ▲

Canada 93 OHong Kong 93 ▲

Iceland 93 ONew Zealand 93 ▲

Slovenia 93 OIreland 92 OSingapore 92 ▲

Korea 91 OAustria 90 OHungary 88 ONorway 88 OInternational average 88Greece 86 OLatvia (LSS) 85 OCyprus 83 OIsrael 80 OThailand 80 OIran, Islamic Rep. 70 ▼

Portugal 69 ▼

Kuwait 61 ▼

Item Number: L3


Higher ▲




Geometry Knowing


62

Hong Kong 72 ▲

Portugal 62 ▲

Slovenia 60 ▲

Canada 59 ▲

Japan 59 ▲

Netherlands 55 ▲

Australia 54 ▲

Austria 50 OCzech Republic 47 OScotland 44 OSingapore 44 OIreland 43 OHungary 42 OInternational average 40England 39 OUnited States 35 OGreece 33 OIsrael 32 OLatvia (LSS) 32 ONew Zealand 32 OThailand 32 OKorea 31 ▼

Cyprus 25 ▼

Iceland 25 ▼


Kuwait 17 ▼

Norway 8 ▼

Edges of cube

Item Number: L5


Higher ▲


Correct Response: C

This picture shows a cube with one edge marked. How manyedges does the cube have altogether?

A. 6

B. 8

C. 12

D. 24

Coordinates of dot on grid

On this grid, find the dot with the circle around it. We candescribe where this dot is by saying it is at First Number 1,Second Number 3

Now find the dot with the triangle around it. Describe where thedot is on the grid in the same way. Fill in the numbers we woulduse:

First Number _____________ Second Number _____________



63

Item Number: M4

England 68 ▲

Japan 61 ▲

Australia 56 ▲

Singapore 56 ▲


Scotland 55 ▲

Korea 52 ▲

Canada 51 ONetherlands 50 OIsrael 49 OIceland 47 OSlovenia 46 OIreland 45 ONew Zealand 45 OHong Kong 43 OLatvia (LSS) 42 OInternational average 42Norway 41 OAustria 37 OCzech Republic 37 OGreece 30 ▼

Hungary 30 ▼

Cyprus 22 ▼

Thailand 19 ▼

Portugal 17 ▼


Kuwait 14 ▼


Higher ▲


SCORINGCorrect Response• 3 and 2, in this order.

Incorrect Response• 2 and 3, in this order.• Other incorrect.


Geometry Solving Problems



64

Japan 88 ▲

Singapore 87 ▲

Korea 84 ▲

Hong Kong 81 ▲

England 76 ▲

Scotland 76 ▲

Australia 72 ▲

Netherlands 71 ▲

Canada 68 ▲

Slovenia 68 ▲

Austria 66 ▲


New Zealand 64 OCzech Republic 63 OHungary 62 OLatvia (LSS) 60 OInternational average 59Iceland 57 OIreland 57 OIsrael 55 OThailand 46 ▼

Norway 43 ▼

Cyprus 35 ▼

Greece 28 ▼

Portugal 26 ▼


Kuwait 7 ▼

Cut-out shape

Item Number: T5


Higher ▲


SCORING

Note: See the examples above. The accuracy in drawing is not important, nor is the size ofthe figure.

Correct Response• The drawing of the cut-out shape corresponds to figure A.• The drawing of the remaining piece of paper corresponds to figure B.• Other correct.

Incorrect Response• Drawing corresponds to figure C.• Drawing corresponds to figure D.• Drawings correspond to figures E or F or G.• Other incorrect.

A B C D

GFE


Geometry Knowing

Craig folded a piece of paper in half and cut out a shape.

Draw a picture to show what the cut-out shape will look likewhen it is opened up and flattened out.



Patterns, Relations,and Functions Solving Problems

Correct Response: D


65

Japan 88 ▲

Korea 86 ▲

Austria 83 ▲


Hungary 78 ▲

Hong Kong 75 ▲

Netherlands 75 ▲

Singapore 74 ▲

Latvia (LSS) 72 ▲


Slovenia 67 OCanada 63 OInternational average 62Israel 61 OIreland 60 OAustralia 59 OCyprus 57 OThailand 54 OGreece 50 ▼

Iceland 49 ▼

Norway 49 ▼

New Zealand 48 ▼


Portugal 47 ▼

Scotland 47 ▼

England 43 ▼

Kuwait 25 ▼

Number sentence for pages

Item Number: I7


Higher ▲


Tanya has read the first 78 pages in a book that is 130 pageslong. Which number sentence could Tanya use to find the number of pages she must read to finish the book?

A. 130 + 78 =

B. - 78 = 130

C. 130 ÷ 78 =

D. 130 - 78 =





66

Operation to get B from A

Item Number: J5


Higher ▲


Correct Response: D

What do you have to do to each number in Column A to getthe number next to it in Column B?

A. Add 8 to the number in Column A.

B. Subtract 8 from the number in Column A.

C. Multiply the number in Column A by 5.

D. Divide the number in Column A by 5.

Korea 70 ▲


Hungary 56 ▲

Singapore 54 ▲

Latvia (LSS) 53 ▲

Japan 50 ▲

Slovenia 47 OIsrael 45 OAustria 41 ONetherlands 41 OInternational average 39Canada 38 OIreland 38 OAustralia 37 OThailand 37 OEngland 35 OPortugal 32 OUnited States 32 OScotland 31 ONorway 30 OCyprus 29 ▼


New Zealand 27 ▼

Greece 24 ▼

Iceland 24 ▼

Kuwait 20 ▼

Which pair of numbers follows the rule “Multiply the first number by 5 to get the second number”?

A. 15 ➝ 3

B. 6 ➝ 11

C. 11 ➝ 6

D. 3 ➝ 15



Patterns, Relations,and Functions Knowing

Correct Response: D


67

Korea 80 ▲

Japan 73 ▲

Hong Kong 71 ▲

Hungary 68 ▲

Singapore 66 ▲


Ireland 62 ▲

Slovenia 61 OIsrael 59 OCzech Republic 56 OAustralia 54 OLatvia (LSS) 53 OInternational average 53Canada 50 OIceland 50 OScotland 49 OCyprus 48 OAustria 47 ONorway 46 OThailand 44 OEngland 42 ▼

New Zealand 42 OGreece 41 ▼

Portugal 40 ▼


Netherlands 36 ▼

Kuwait 31 ▼

Multiply by five

Item Number: K3


Higher ▲






68

Korea 87 ▲

Japan 86 ▲

Netherlands 83 ▲

Hong Kong 76 ▲

Singapore 75 ▲


Latvia (LSS) 72 OSlovenia 72 ▲

Austria 68 OIreland 68 OAustralia 65 OHungary 65 OInternational average 63Scotland 61 OCanada 60 OThailand 59 OUnited States 59 OCyprus 56 OIsrael 56 OPortugal 56 OEngland 54 ▼

Iceland 52 OGreece 50 ONew Zealand 49 ▼

Norway 49 ▼

Kuwait 41 ▼


How many tiles in next figure

Item Number: K6


Higher ▲


Correct Response: C

Here is the beginning of a pattern of tiles.

If the pattern continues, how many tiles will be in Figure 6?

A. 12

B. 15

C. 18

D. 21

These shapes are arranged in a pattern.

Which set of shapes is arranged in the same pattern?

A.

B.

C.

D.




Correct Response: C


69

Korea 93 ▲

Japan 91 ▲

Austria 85 ▲

Singapore 85 ▲

Netherlands 84 ▲

Hong Kong 82 ▲

Latvia (LSS) 82 ▲


Hungary 80 ▲


Australia 78 OCanada 78 OEngland 75 OIreland 75 OSlovenia 75 OScotland 73 OInternational average 72New Zealand 71 OIsrael 69 OIceland 67 ONorway 65 OPortugal 58 ▼

Thailand 55 ▼


Cyprus 52 ▼

Greece 51 ▼

Kuwait 44 ▼

Shapes in a pattern

Item Number: L4


Higher ▲






70

Korea 86 ▲

Hong Kong 74 ▲

Japan 73 ▲


Singapore 72 ▲

Slovenia 72 OAustralia 70 ▲

Canada 68 OIsrael 68 OEngland 66 OIreland 66 ONetherlands 66 ONorway 66 OScotland 65 OHungary 64 ONew Zealand 64 OInternational average 63Czech Republic 62 OIceland 61 OAustria 57 OCyprus 56 OGreece 54 OPortugal 54 ▼

Latvia (LSS) 50 ▼

Thailand 47 ▼

Kuwait 43 ▼


True statement of ages

Item Number: L9


Higher ▲


Correct Response: A

Henry is older than Bill, and Bill is older than Peter. Whichstatement must be true?

A. Henry is older than Peter.

B. Henry is younger than Peter.

C. Henry is the same age as Peter.

D. We cannot tell who is oldest from the information.

Here is a number sentence.

4 ✕ < 17

Which number could go in the to make the sentence true?

A. 4

B. 5

C. 12

D. 13



Patterns, Relations,and Functions Performing Routine Procedures

Correct Response: A


71

Korea 93 ▲

Japan 89 ▲

Singapore 87 ▲

Slovenia 86 ▲

Hong Kong 83 ▲

Hungary 79 ▲

Latvia (LSS) 79 OIsrael 77 OAustria 74 OCzech Republic 72 OUnited States 71 ONetherlands 70 OInternational average 70Canada 69 OCyprus 67 OIceland 67 OGreece 66 OAustralia 65 OIreland 65 OPortugal 65 ONorway 63 OIran, Islamic Rep. 62 OScotland 59 ▼

New Zealand 57 ▼

England 56 ▼

Thailand 56 ▼

Kuwait 43 ▼

Make number sentence true

Item Number: M9


Higher ▲




72

Hungary 79 ▲

Singapore 79 ▲

Netherlands 77 ▲

Ireland 74 ▲

Korea 74 ▲

Australia 72 ▲

Latvia (LSS) 70 ▲

Slovenia 68 ▲

Cyprus 67 ▲


Hong Kong 65 ▲

Austria 64 OScotland 63 OUnited States 61 OJapan 58 OCanada 57 OEngland 57 OInternational average 57New Zealand 48 ▼

Israel 46 ▼

Norway 46 ▼

Greece 42 ▼

Portugal 30 ▼

Iceland 27 ▼


Kuwait 12 ▼

Next number in pattern

Item Number: U4


Higher ▲


SCORINGCorrect Response• “The number decreases by 4”.• 30 OR 30,26,22,. . .• Other correct.

Incorrect Response• Indicates an increase by 4.• Focuses on the number 4. No indication of increase or decrease.• Other incorrect, includes decreases by 4 that are wrong numbers in the pattern.



These numbers are part of a pattern.

50 , 46 , 42 , 38 , 34 , ...

What do you have to do to get the next number?

Answer: ______________________________

Correct Response:

73

Main TopicContent Domain Cognitive Domain



Higher pNotdifferent OLower q


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

Correct Response:

74







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

75







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

76

student Responses


Thevalueof37timesboxplus6(continued)Item Number: M031249

Correct Response:

Incorrect Response:

Correct Response:

77







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:

78







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:

79







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:

80







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:

81






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:

82






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:

83







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:

84






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

85


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

86

student Responses

TitleNamePulledfromItemHere(continued)Item Number: M022002A


Colorsofstudents’haironthegraph(continued)Item Number: M031264

Correct Response:

Incorrect Response:

87






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

88

student Responses

TitleNamePulledfromItemHere(continued)Item Number: M022002A


Correct Response:

Incorrect Response:

Howmanymorepencilsthanrulerssold(continued)Item Number: M031265

Correct Response:

89






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:

90






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:

91






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

92






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

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

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

93

student Responses


Shadeintwotrianglesofdifferentsizes(continued)Item Number: M031267

Correct Response:

Incorrect Response:

94






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

95

student Responses


DrawalineonthegridparalleltolineL(continued)Item Number: M031327

Correct Response:

Incorrect Response:

Correct Response:

96






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:

97






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

98






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

99








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

100

student Responses


Indicatesgeometricshapesinthepicture(continued)Item Number: M031269

Fully Correct Response:

101



student Responses (continued)

Partially Correct Response:

102



student Responses (continued)

Incorrect Response:

103






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

104

student Responses


Geometrytiles:blacktriangle(continued)Item Number: M031347A

Correct Response:

Incorrect Response:

105






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

106

student Responses


Geometrytiles:blacksquare(continued)Item Number: M031347B

Correct Response:

Incorrect Response:

107






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

108

student Responses


Geometrytiles:fractionshaded(continued)Item Number: M031347C

Correct Response:

Incorrect Response:

109







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

110

student Responses


Drawlineonrectangle/2triangles(continued)Item Number: M031272A

Correct Response:

Incorrect Response:

111








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

112

student Responses


Correct Response:

Incorrect Response:

Drawlineonrectangle/2rectangles(continued)Item Number: M031272B

113








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

114

student Responses


Correct Response:

Incorrect Response:

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

Correct Response:

115






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:

116







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

117







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:

118






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:

119







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:

120






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

121






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

122

student Responses


Correct Response:

Incorrect Response:

DrawatrianglewithABasthebase(continued)Item Number: M031322

Correct Response:

123






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

124






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

125

student Responses


Correct Response:

Incorrect Response:

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

Correct Response:

126







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:

127








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:

128








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:

129








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:

130







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:

131






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:

132







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:

133







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

134






A. NuMbeR Fractions and Decimals Knowing Facts and Procedures

B.NumBer FractionsandDecimals reasoning

GeometryTiles:½black



• 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

135

Student Responses


GeometryTiles:½black(continued)Item Number: M031348A

Correct Response:

Incorrect Response:

136






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

137

Student Responses


GeometryTiles:½black(continued)Item Number: M031348B

Correct Response:

Incorrect Response:

85

Correct Response:

138







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

139






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

140

Student Responses


Correct Response:

Incorrect Response:

½of600ballsinabox(continued)Item Number: M031065

3

Correct Response:

141






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:

142






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:

143






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:

144







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:

145






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:

146






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:

147







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:

148






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:

149







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

150







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

151

Student Responses


Correct Response:

Incorrect Response:

15times9(continued)Item Number: M031305

152







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

153

Student Responses


Correct Response:

Incorrect Response:

204dividedby4(continued)Item Number: M031306

154








• 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

155

Student Responses


Correct Response:

Incorrect Response:

ThenumberLiashouldaddto142toget369(continued)Item Number: M031130

Correct Response:

156






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:

157






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:

158






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:

159






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:

160







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

161







• 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

162

Student Responses


Correct Response:

Incorrect Response:

Notebooksfor115students(continued)Item Number: M031011

Correct Response:

163







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

164







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

165


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


• 91+5or95+1

Incorrect Response

• Anyotherarrangementofdigits1,5,and9


166

Student Responses


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

Correct Response:

Incorrect Response:

167







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

168


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


• 73-2

Incorrect Response

• 72-3

• Anyotherarrangementofthedigits2,3,and7


169

Student Responses


Correct Response:

Incorrect Response:

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

170







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

171


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


• 41x5

Incorrect Response

• 51x4

• Anyotherarrangementofthedigits1,4,and5


172

Student Responses


Correct Response:

Incorrect Response:

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

Correct Response:

173






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:

174







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:

175







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:

176







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

177







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

178

Student Responses


Numbergoinginthenumberlinebox(continued)Item Number: M031162

Correct Response:

Incorrect Response:

179








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

180


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


• 2+7+9=18

• 18withoutadditionstatementshown

Incorrect Response

• 2+7+9but18notshown


181

Student Responses


Correct Response:

Incorrect Response:

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

182









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

183


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


• 13+6=19OR16+3=19

• 19withoutadditionstatementshown

Incorrect Response

• 13+6OR16+3but19notshown


184

Student Responses


Correct Response:

Incorrect Response:

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

185









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

186


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


• Bothwayscorrect16+4AND14+6


• Onlyonewaycorrect16+4OR14+6

Incorrect Response


187

Correct Response:

Partially Correct Response:

Student Responses



188

Incorrect Response:

Student Responses (continued)



Item Index 1995Content Domain Page

Whole Numbers

I3 Whichnumberisit 3

I4 Whatis3times23 4

I9 Subtractionof4digitnumbers 5

J4 Whatistheincreaseinproduct 6

J9 Numberinbox 7

K2 Additionoffourdigitnumbers 8

L7 Whichpairdifferentby100 9

M3 Whichoperationequivalent 10

M6 Whattodotocorrectmistake 11

M8 Chooselargestnumber 12

S2 Completenumbersentence 13

T2 Makesmallestwholenumber 14

U5 Addition/multiplicationtask 15

V2 Numberlargerthan56,821 16

V3 Whatis5lessthan203 17

V4A Gamewithcards:whowon?Explain 18

V4B Gamewithcards:winningnumbers 19

Fractions and Proportionality

I2 0.4isthesameas 20

I5 Saucefrom15tomatoes 21

I8 Which2figuresrepresentsamefraction 22

J7 Fractionoffigureshaded 23

K9 Howmanymarblesintwobags 24

M5 Decimalrepresentingshadedpartoffigure 25

S3 Longestboxonshelf 26

S4 Howmanypupilsinclass 27

T4A Girl/boyratio:isJuanitaright 28

T4B Girl/boyratio:isAmandaright 29

U2 Fractionlargerthan2/7 30

U3A Bicycleride:howlong,Maria 31

U3B Bicycleride:howlong,Louisa 32

U3C Bicycleride:whoarrivedfirst 33

V1 Fractionsofpie. 34

Content Domain Page

Measurement, Estimation, and Number Sense

J6 Chooselargestmass 35

J8 Whichisbestestimateofhours 36

K5 Estimatepencillength 37

K7 Lengthofrectangle 38

L6 Bestestimateofclothespinmass 39

L8 Whohadthelongestpace 40

M7 Substancemeasuredinmilliliters 41

S5 Howmanypapercliplengths 42

T3 WhendidMr.Brownstartwalk 43

U1 Trianglesinfigure 44

V5 Millimetersinameter 45

Data Representation, Analysis, and Probability

J3 What%oftimeinplayandhomework 46

K4 Whowonandbyhowmanypoints 47

L1 Pictographoftrees 48

L2 Chanceofpickingredmarble 49

M1 Chanceofhittingshadedregion 50

M2 Howmanyraffletickets 51

S1 Bargraphsofboysandgirls 52

T1A Bargraph:cartonssoldMonday 53

T1B Bargraph:cartonssoldforweek 54

Geometry

I1 Mapofcityblocks 55

I6 Whichfiguremadewithstraightsides 56

J1 Shapesinhexagon 57

J2 Whichdoesnotshowsymmetry 58

K1 Whichnumberinsquarebutnotintriangle 59

K8 Rectangledividedintofourparts 60

L3 Objectsongameboardgrid 61

L5 Edgesofcube 62

M4 Coordinatesofdotongrid 63

T5 Cut-outshape 64

Patterns, Relations, and Functions

I7 Numbersentenceforpages 65

J5 OperationtogetBfromA 66

K3 Multiplybyfive 67

K6 Howmanytilesinnextfigure 68

L4 Shapesinapattern 69

L9 Truestatementofages 70

M9 Makenumbersentencetrue 71

U4 Nextnumberinpattern 72

Content Domain Page

Patterns and Relationships

M012048 Symboliclinearequationofmagazines 73

M031220 Robsoldsomeofhisapples 74

M031249 Thevalueof37timesboxplus6 75

M011027 Completenumberpattern 77

M031023 Thenumbertogointhecenterofthetable 78

M031051 Thedailystarttimesforamovie 79

M031190 Outputofthenumbermachine 80

Data

M012126 Heightsoffourgirlsongraph 81

M011009 Bargraph:whichshows45bottles 82

M011012 Bargraph:whichtwoshow80bottles 83

M012078 Highesttemperatureonchart 84

M031264 Colorsofstudents’haironthegraph 85

M031265 Howmanymorepencilsthanrulerssold 87

M031333 Highandlowtemperaturesforaweek 89

M031315 Thefavoriteicecreamsof30students 90

Geometry

M011014 Congruentfigures 91

M031267 Shadeintwotrianglesofdifferentsizes 92

M031327 DrawalineonthegridparalleltolineL 94

M012069 Rotated3-dimensionalfigure 96

M011006 Whichhasflatandcurvedsurface 97

M011022 Statementsabouttriangle 98

M031269 Indicatesgeometricshapesinthepicture 99

M031347AGeometrytiles:blacktriangle 103

M031347BGeometrytiles:blacksquare 105

M031347CGeometrytiles:fractionshaded 107

M031272ADrawlineonrectangle/2triangles 109

M031272BDrawlineonrectangle/2rectangles 111

M031272CDrawlineonrectangle/1rectangle,2triangles 113

Measurement

M011023 Weightofanadult 115

M012023 Unitstomeasuremassofegg 116

M031338 Whichcouldequal150milliliters 117

M011005 Whichhaslargestarea 118

M031008 Thelengthofthefilms 119

M011013 Howmuchdidtemperaturerise 120

M031322 DrawatrianglewithABasthebase 121

M012065 Distanceonmap 123

M031298 Completethefigurewithanareaof13cm2 124

M011017 WhenisMary’strip 126

M011025 Perimeterofrectangle 127

M031097 Betty’saveragedrivingspeed 128

M031178 Georgepracticedsoccer6daysaweek 129

M011010 Volumeofstackofcubes 130

Content Domain Page

Number

M011008 Sumoftwonumberswithdecimals 131

M011015 Subtractionwithdecimals 132

M011020 Fractiontodecimal 133

M031348AGeometryTiles:1/2black 134

M031348BGeometryTiles:5/8black 136

M012119 Fractionofcakeleft 138

M031065 1/3of600ballsinabox 139

M031216 WhatfractionofcakeJohnate 141

M011001 Whichfigurehasone-halfblackdots 142

M011016 3of4squaresshaded 143

M012044 Figureshowingfractionofshadedsquare 144

M031108 Mariacollectedsoftdrinkbottles 145

M011019 Numberroundedto600 146

M011021 Whichnumberisit 147

M011024 Expressnumberinwords 148

M011028 Whichnumberisequal 149

M031305 15times9 150

M031306 204dividedby4 152

M031130 ThenumberLiashouldaddto142toget369 154

M031341 1279plus243bymistake 156

M011002 Totalnumberofboysandgirls 157

M011003 Totalnumberofpencils 158

M011011 Howlongtowashwindows 159

M012117 Estimatenumberofcabbages 160

M031011 Notebooksfor115students 161

M031310 A204cmropecutinto4/calculation 163

M031345ANumbertiles:largestnumber(+) 164

M031345BNumbertiles:largestnumber(-) 167

M031345CNumbertiles:largestnumber(X) 170

M011004 Numberrepresentedbysquares 173

M011007 Whichhassamevalue 174

M011018 Digitinhundredsplace 175

M011026 Whichistrue 176

M031162 Numbergoinginthenumberlinebox 177

M031344ANumbertiles:getto20using2,7,9 179

M031344BNumbertiles:getto20using1,3,6 182

M031344CNumbertiles:getto20using1,4,6 185

Item Index 2003

mathematics concepts 4 mathematics items mathematics concepts and mathematics items book contains...

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