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MATHEMATICSGrade 3

Revised Based on TEKS Refinements

Texas Assessmentof Knowledge and Skills

Information Booklet

Tex a s E d u c a t i o n A g e n c y • S t u d e n t A s s e s s m e n t D i v i s i o n

Copyright © 2008, Texas Education Agency. All rights reserved. Reproduction of all or portions of this work is prohibited without expresswritten permission from the Texas Education Agency.

January 2008

INTRODUCTION

The Texas Assessment of Knowledge and Skills (TAKS) is a completely reconceived testing program.It assesses more of the Texas Essential Knowledge and Skills (TEKS) than the Texas Assessment ofAcademic Skills (TAAS) did and asks questions in more authentic ways. TAKS has been developedto better reflect good instructional practice and more accurately measure student learning. We hopethat every teacher will see the connection between what we test on this state assessment and what ourstudents should know and be able to do to be academically successful. To provide you with a betterunderstanding of TAKS and its connection to the TEKS and to classroom teaching, the TexasEducation Agency (TEA) has developed this newly revised version of the TAKS information bookletbased on the TEKS refinements. The information booklets were originally published in January 2002,before the first TAKS field test. After several years of field tests and live administrations, theinformation booklets were revised in August 2004 to provide an even more comprehensive picture ofthe testing program. Since that time the TEKS for elementary mathematics have been refined. TheseTEKS refinements were approved by the State Board of Education in October 2005. In August 2006,the Student Assessment Division produced an online survey to obtain input as to which TEKS contentshould be eligible for assessment on TAKS mathematics tests at grades 3–5. The results of the surveyfrom about 1,500 groups composed of about 14,000 individuals were compiled and analyzed. Thenthe TEA math team from the Curriculum and Student Assessment Divisions, with input fromeducational service center math specialists, used the survey data to guide decisions on what contentshould be assessed on the elementary TAKS math tests. This content can be found in this newlyrevised information booklet. We hope this revised version of the TAKS information booklet will serveas a user-friendly resource to help you understand that the best preparation for TAKS is a coherent,TEKS-based instructional program that provides the level of support necessary for all students toreach their academic potential.

BACKGROUND INFORMATION

The development of the TAKS program included extensive public scrutiny and input from Texasteachers, administrators, parents, members of the business community, professional educationorganizations, faculty and staff at Texas colleges and universities, and national content-area experts.The agency involved as many stakeholders as possible because we believed that the development ofTAKS was a responsibility that had to be shared if this assessment was to be an equitable andaccurate measure of learning for all Texas public school students.

The three-year test-development process, which began in summer 1999, included a series of carefullyconceived activities. First, committees of Texas educators identified those TEKS student expectationsfor each grade and subject area assessed that should be tested on a statewide assessment. Then acommittee of TEA Student Assessment and Curriculum staff incorporated these selected TEKSstudent expectations, along with draft objectives for each subject area, into exit level surveys. Thesesurveys were sent to Texas educators at the middle school and secondary levels for their review.Based on input we received from more than 27,000 survey responses, we developed a second draft ofthe objectives and TEKS student expectations. In addition, we used this input during the developmentof draft objectives and student expectations for grades 3 through 10 to ensure that the TAKS program,like the TEKS curriculum, would be vertically aligned. This vertical alignment was a critical step inensuring that the TAKS tests would become more rigorous as students moved from grade to grade.

Grade 3 TAKS Mathematics Information Booklet 1

For example, the fifth grade tests would be more rigorous than the fourth grade tests, which would bemore rigorous than the third grade tests. Texas educators felt that this increase in rigor from grade tograde was both appropriate and logical since each subject-area test was closely aligned to the TEKScurriculum at that grade level.

In fall 2000 TEA distributed the second draft of the objectives and TEKS student expectations foreleventh grade exit level and the first draft of the objectives and student expectations for grades 3through 10 for review at the campus level. These documents were also posted on the StudentAssessment Division’s website to encourage input from the public. Each draft document focused ontwo central issues: first, whether the objectives included in the draft were essential to measure on astatewide assessment; and, second, whether students would have received enough instruction on theTEKS student expectations included under each objective to be adequately prepared to demonstratemastery of that objective in the spring of the school year. We received more than 57,000 campus-consensus survey responses. We used these responses, along with feedback from national experts, tofinalize the TAKS objectives and student expectations. Because the state assessment was necessarilylimited to a “snapshot” of student performance, broad-based input was important to ensure that TAKSassessed the parts of the TEKS curriculum most critical to students’ academic learning and progress.

In the thorough test-development process that we use for the TAKS program, we rely on educatorinput to develop items that are appropriate and valid measures of the objectives and TEKS studentexpectations the items are designed to assess. This input includes an annual educator review andrevision of all proposed test items before field-testing and a second annual educator review of dataand items after field-testing. In addition, each year panels of recognized experts in the fields ofEnglish language arts (ELA), mathematics, science, and social studies meet in Austin to criticallyreview the content of each of the high school–level TAKS assessments to be administered that year.This critical review is referred to as a content validation review and is one of the final activities in aseries of quality-control steps designed to ensure that each high school test is of the highest qualitypossible. A content validation review is considered necessary at the high school grades (9, 10, andexit level) because of the advanced level of content being assessed.

ORGANIZATION OF THE TAKS TESTS

TAKS is divided into test objectives. It is important to remember that the objective statements are notfound in the TEKS curriculum. Rather, the objectives are “umbrella statements” that serve asheadings under which student expectations from the TEKS can be meaningfully grouped. Objectivesare broad statements that “break up” knowledge and skills to be tested into meaningful subsets aroundwhich a test can be organized into reporting units. These reporting units help campuses, districts,parents, and the general public understand the performance of our students and schools. Testobjectives are not intended to be “translations” or “rewordings” of the TEKS. Instead, the objectivesare designed to be identical across grade levels rather than grade specific. Generally, the objectivesare the same for third grade through eighth grade (an elementary/middle school system) and for ninthgrade through exit level (a high school system). In addition, certain TEKS student expectations maylogically be grouped under more than one test objective; however, it is important for you tounderstand that this is not meaningless repetition—sometimes the organization of the objectivesrequires such groupings. For example, on the TAKS writing tests for fourth and seventh grades, someof the same student expectations addressing the conventions of standard English usage are listed


under both Objective 2 and Objective 6. In this case, the expectations listed under Objective 2 areassessed through the overall strength of a student’s use of language conventions on the writtencomposition portion of the test; these same expectations under Objective 6 are assessed throughmultiple-choice items attached to a series of revising and editing passages.

ORGANIZATION OF THE INFORMATION BOOKLETS

The purpose of the information booklets is to help Texas educators, students, parents, and otherstakeholders understand more about the TAKS tests. These booklets are not intended to replace theteaching of the TEKS curriculum, provide the basis for the isolated teaching of skills in the form ofnarrow test preparation, or serve as the single information source about every aspect of the TAKSprogram. However, we believe that the booklets provide helpful explanations as well as show enoughsample items, reading and writing selections, and prompts to give educators a good sense of theassessment.

Each grade within a subject area is presented as a separate booklet. However, it is still important thatteachers review the information booklets for the grades both above and below the grade they teach.For example, eighth grade mathematics teachers who review the seventh grade information booklet aswell as the ninth grade information booklet are able to develop a broader perspective of themathematics assessment than if they study only the eighth grade information booklet.

The information booklets for each subject area contain some information unique to that subject. Forexample, the mathematics chart that students use on TAKS is included for each grade at whichmathematics is assessed. However, all booklets include the following information, which we considercritical for every subject-area TAKS test:

■ an overview of the subject within the context of TAKS

■ a blueprint of the test—the number of items under each objective and the number of items on thetest as a whole

■ information that clarifies how to read the TEKS

■ the reasons each objective and its TEKS student expectations are critical to student learning andsuccess

■ the objectives and TEKS student expectations that are included on TAKS

■ additional information about each objective that helps educators understand how it is assessed onTAKS

■ sample items that show some of the ways objectives are assessed


TAKS MATHEMATICS

INFORMATION BOOKLET

GENERAL INTRODUCTION

Learning mathematics is essential in finding answers to real-life questions. The study of mathematicshelps students to think logically, solve problems, and understand spatial relationships. The conceptslearned in mathematics courses help students communicate clearly and use logical reasoning to makesense of their world. TEKS instruction in mathematics throughout elementary, middle, and highschool will build the foundation necessary for students to succeed in advanced math and sciencecourses and later in their careers.

The six strands identified in the mathematics curriculum for kindergarten through eighth grade are thefoundation skills necessary for high school–level mathematics courses. The TAKS assessmentobjectives are closely aligned with the six strands identified in the TEKS curriculum. For example, inTAKS Objective 1 students are to “demonstrate an understanding of numbers, operations, andquantitative reasoning”; in the TEKS curriculum the first strand identified is “number, operation, andquantitative reasoning.” This close alignment reflects the important link between TAKS and theTEKS curriculum. In fact, the TAKS mathematics tests are based on those TEKS student expectationsTexas educators have identified as the most critical to student achievement and progress inmathematics.

The TEKS were developed to provide educators with instructional goals at each grade level.Although some student expectations are not tested, they are nonetheless critical for studentunderstanding and must be included in classroom instruction. For each strand of learning, themathematics TEKS provide more rigorous expectations as students master skills and progress throughthe curriculum. It is important for educators to vertically align their instructional programs toreinforce the unifying strands of learning each year through grade-level-appropriate instruction. Tounderstand how student learning progresses, educators are encouraged to become familiar with thecurriculum at all grade levels. Educators may find it helpful to examine sample items at each gradelevel to gain a greater understanding of what students need to know and be able to do in mathematicsas they move from grade to grade.

A system of support has been designed to ensure that all students master the TEKS. The StudentSuccess Initiative (SSI) requires that students meet the standard on TAKS to be eligible for promotionto the next grade level as specified below:

■ the reading test at Grade 3, beginning in the 2002–2003 school year;

■ the reading and mathematics tests at Grade 5, beginning in the 2004–2005 school year; and

■ the reading and mathematics tests at Grade 8, beginning in the 2007–2008 school year.

To prepare students for the SSI requirements and to promote vertical alignment, it is essential thatteachers collaborate and coordinate across grade levels.


TAKS MATHEMATICSINFORMATION BOOKLET

GRADE 3

The third grade mathematics TEKS describe what students should know and be able to do in thirdgrade. However, teachers need to be aware of the “big picture”—an understanding of the TEKScurriculum for both the lower and the higher grades. This awareness of what comes before and afterthird grade will enable teachers to more effectively help their students develop mathematicsknowledge and skills.

TEST FORMAT

■ The third grade test booklet is a machine-scorable booklet designed to allow third graders tomark their answers directly in the booklet. Enough room is left around each item in the bookletfor students to work each problem.

■ Any item may include application context and extraneous information.

■ Most items will be in a multiple-choice format with four answer choices.

■ Not here or a variation of this phrase may be used as the fourth answer choice when appropriate.

■ There will be a limited number of open-ended griddable items. For these items a two-columngrid will be provided for students to record and bubble in their answers. This griddable format isintended to allow students to work a problem and determine the correct answer without beinginfluenced by answer choices. An example of a blank grid is shown below.

\\\\\

\

\1

\0

\2

\4

3

5

6

7

8

9 \\\\\

\

\1

\0

\2

\4

3

5

6

7

8

9



MATHEMATICS CHART

■ For third grade the Mathematics Chart (found on page 8) will have measurement conversions.

■ A metric ruler and a customary ruler will be provided on the front of the separate MathematicsChart.

■ Items that require students to measure with a ruler from the Mathematics Chart may be found inany objective as appropriate.

TEXAS ASSESSMENT OF KNOWLEDGE AND SKILLS (TAKS)

BLUEPRINT FOR GRADE 3 MATHEMATICS

TAKS Objectives

Objective 2: Patterns, Relationships, and Algebraic Reasoning

Objective 3: Geometry and Spatial Reasoning

Objective 4: Measurement

Objective 5: Probability and Statistics

Objective 6: Mathematical Processes and Tools

Total number of items

6

10

6

6

4

8

40

Number of Items

Objective 1: Numbers, Operations, and Quantitative Reasoning



10

23

45

67

89

1011

1213

1415

1617

1819

20

Cen

timet

ers

65

43

21

0InchesGrade 3

Mathematics Chart

LENGTH

Metric Customary

1 meter = 100 centimeters 1 yard = 3 feet

1 centimeter = 10 millimeters 1 foot = 12 inches

TIME

1 year = 365 days

1 year = 12 months

1 year = 52 weeks

1 week = 7 days

1 day = 24 hours

1 hour = 60 minutes

1 minute = 60 seconds

Texas Assessmentof Knowledge and Skills

A Key to Understanding the TEKS Included on TAKS

Example from Objective 4

(3.11) Measurement. The student directly compares the attributes of length, area, weight/mass, andcapacity, and uses comparative language to solve problems and answer questions. The studentselects and uses standard units to describe length, area, capacity/volume, and weight/mass.The student is expected to

(C) use [concrete and] pictorial models of square units to determine the area of two-dimensionalsurfaces.

KEY

NOTE: The full TEKS curriculum can be found at http://www.tea.state.tx.us/teks/.

A. Knowledge and Skills Statement

This broad statement describes what students should know and be able to do for third grademathematics. The number preceding the statement identifies the instructional level and thenumber of the knowledge and skills statement.

B. Student Expectation

This specific statement describes what students should be able to do to demonstrateproficiency in what is described in the knowledge and skills statement. Students will betested on skills outlined in the student expectation statement.

C. [bracketed text]

Although the entire student expectation has been provided for reference, text in bracketsindicates that this portion of the student expectation will not specifically be tested onTAKS.


A

C

B

http://www.tea.state.tx.us/teks

TEKS STUDENT EXPECTATIONS—IMPORTANT VOCABULARY

For every subject area and grade level, two terms—such as and including—are used to help make theTEKS student expectations more concrete for teachers. However, these terms function in differentways. To help you understand the effect each of the terms has on specific student expectations, we areproviding the following:

■ a short definition of each term;

■ an example from a specific student expectation for this subject area; and

■ a short explanation of how this term affects this student expectation.

Such as

The term such as is used when the specific examples that follow it function only as representativeillustrations that help define the expectation for teachers. These examples are just that—examples.Teachers may choose to use them when teaching the student expectation, but there is no requirementto use them. Other examples can be used in addition to those listed or as replacements for those listed.


(3.6) (C) identify patterns in related multiplication and division sentences (fact families) such as 2 × 3 = 6, 3 × 2 = 6, 6 ÷ 2 = 3, 6 ÷ 3 = 2.

This student expectation lists only one fact family: such as 2 × 3 = 6, 3 × 2 = 6, 6 ÷ 2 = 3, 6 ÷ 3 = 2.However, there are many other fact families students may use to identify patterns in multiplicationand division sentences.

Including

The term including is used when the specific examples that follow it must be taught. However, otherexamples may also be used in conjunction with those listed.


(3.14) (C) select or develop an appropriate problem-solving plan or strategy, including drawing apicture, looking for a pattern, systematic guessing and checking, acting it out, making atable, working a simpler problem, or working backwards to solve a problem.

This student expectation lists several problem-solving strategies to include in instruction. Otherproblem-solving strategies may be taught in addition to the strategies listed.


Remember

■ Any example preceded by the term such as in a particular student expectation may or may notprovide the basis for an item assessing that expectation. Because these examples do notnecessarily have to be used to teach the student expectation, it is equally likely that otherexamples may be used in assessment items. The rule here is that an example will be used only ifit is central to the knowledge, concept, or skill the item assesses.

■ It is more likely that some of the examples preceded by the term including in a particular studentexpectation will provide the basis for items assessing that expectation, since these examples mustbe taught. However, it is important to remember that the examples that follow the term includingdo not represent all the examples possible, so other examples may also provide the basis for anassessment item. Again, the rule here is that an example will be used only if it is central to theknowledge, concept, or skill the item assesses.


Grade 3 TAKS Mathematics—Objective 1

Knowledge of numbers, operations, and quantitative reasoning is critical for the development ofmathematical skills. Students need to understand numbers as digits, words, and models. They need tounderstand the value of each digit based on its position in a number in order to read and work withnumbers. It is also important that students understand fractional parts of whole numbers and how thevalue of the fractional part relates to the value of the whole. From these basic concepts students movetoward understanding specific combinations of numbers as solutions to problems. As students learn towork with and distinguish among the four basic operations of addition, subtraction, multiplication,and division, they should also be developing a sense of the reasonableness of an expected answer.Quantitative reasoning is knowing when an answer makes sense. Estimation strategies can be usedwhen an exact answer is not required. Students should be prepared to apply the basic conceptsincluded in Objective 1 to other concepts in third grade mathematics. In addition, the knowledge andskills in Objective 1 at third grade provide the foundation for mastering the knowledge and skills inObjective 1 at fourth grade.

Objective 1 groups together the basic building blocks within the TEKS—numbers, operations, andquantitative reasoning—from which all mathematical understanding stems.

TAKS Objectives and TEKS Student Expectations

Objective 1

The student will demonstrate an understanding of numbers, operations, and quantitativereasoning.

(3.1) Number, operation, and quantitative reasoning. The student uses place value tocommunicate about increasingly large whole numbers in verbal and written form, includingmoney. The student is expected to

(A) use place value to read, write (in symbols and words), and describe the value of wholenumbers through 999,999;

(B) use place value to compare and order whole numbers through 9,999; and

(C) determine the value of a collection of coins and bills.

(3.2) Number, operation, and quantitative reasoning. The student uses fraction names andsymbols (with denominators of 12 or less) to describe fractional parts of whole objects orsets of objects. The student is expected to

(B) compare fractional parts of whole objects or sets of objects in a problem situation using[concrete] models; and


(C) use fraction names and symbols to describe fractional parts of whole objects or sets ofobjects.

(3.3) Number, operation, and quantitative reasoning. The student adds and subtracts to solvemeaningful problems involving whole numbers. The student is expected to

(A) model addition and subtraction using pictures, words, and numbers; and

(B) select addition or subtraction and use the operation to solve problems involving wholenumbers through 999.

(3.4) Number, operation, and quantitative reasoning. The student recognizes and solvesproblems in multiplication and division situations. The student is expected to

(B) solve and record multiplication problems (up to two digits times one digit); and

(C) use models to solve division problems and use number sentences to record the solutions.

(3.5) Number, operation, and quantitative reasoning. The student estimates to determinereasonable results. The student is expected to

(A) round whole numbers to the nearest ten or hundred to approximate reasonable results inproblem situations; and

(B) use strategies including rounding and compatible numbers to estimate solutions toaddition and subtraction problems.


Objective 1—For Your Information

The following list provides additional information for some of the student expectations tested inObjective 1. At third grade, students should be able to

■ sequence numbers or the words associated with numbers (for example, listing the names of citiesin order from greatest to least based on their populations);

■ recognize U.S. currency in the dollars-and-cents form ($1.53, $0.45) and the cents-only form(82¢);

■ determine the value of a group of coins that may total more than $1.00;

■ match fractions with models or models with fractions;

■ recognize fractions written in different forms (for example, , two-thirds, or 2 out of 3);

■ work with comparisons using pictorial models, word phrases (is less than, is equal to, etc.), orsymbols (>, <, =); and

■ use a variety of strategies (including rounding and compatible numbers) to estimate,approximate, and determine a reasonable solution based on the context of the problem.

23



Objective 1 Sample Items

1 Devan paid for a package of pens with a five-dollar bill. The change she received isshown below. How much change did Devan receive? Mark your answer.

77¢

* $0.87

92¢

$1.37

YTREBIL

9891

IN GOD WETRUST

YTREBIL

9891

UN

ITE

D

STATESAM

ERIC

A

OF

UN

ITE

D

STATES OF AMER

ICA

ONE DIME

DIMEO

NE

E PLUE PLU RIBRIB USUUSU NUMNUME PLU RIB USU NUM 19891989LIBERTYLIBERTY

1989LIBERTY

EWDO

NI TSURTG

EWDO

NI TSURTG

O

NE

O

NE CE NT

UN

ITED

CE NT

UN

ITED

STATES oFAMERIC

A

STATES oFAMERIC

A

E PLURIBUSE PLURIBUSUNUMUNUM

E PLURIBUSUNUM

UN

ITE

D

STATESAM

ERIC

A

OF

Q

UART ER DOLLARQ

UART ER DOLLAR

UN

ITE

D

STATES OF AMER

ICA

YTR

EB I

L

198919891989

YTR

EB I

L

EW

DO

NI

TSU

RT

G

TR

BI

98

91

L

EY

EW

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NI

TSU

RT

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BI

98

91

L

EY

E

IPLUR BUS UNUM

UNUM

IPLUR BUS

E

UN

ITEDSTATES OF AMER

ICAU

NITED

STATES OF AMERIC

A

F IVE CENTSF IVE CENTS

M O N T I C E L L OM O N T I C E L L OM O N T I C E L L O

EW

DO

NI

TSU

RT

G

TR

BI

98

91

L

EY

EW

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TSU

RT

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98

91

L

EY



3 Tom has 121 football cards and 167 baseball cards in his collection.Which is the best estimate of the totalnumber of football and baseball cardsin Tom’s collection? Mark youranswer.

200

* 290

360

400

2 Tracy reads 14 pages of a book eachday. How many pages will she read in6 days?

Record your answer in the boxesbelow. Then fill in the bubbles. Besure to use the correct place value.

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\1

\0

\2

\4

3

5

6

7

8

9 \\\\\

\

\1

\0

\2

\4

3

5

6

7

8

9

8 4

Note: This item specifically asks for thenumber of pages. On griddable items,students do not grid the labels, such aspages.

Note: In this item, the numbers couldbe rounded to the nearest ten or nearesthundred. If rounded correctly, eithermethod could give a reasonableestimate.



4 Franco earned stickers for doing

chores. Franco’s sticker chart was less

than full of stickers. Which could

show Franco’s sticker chart? Mark

your answer.

*

59

5 Rita makes puppets. She has 16 buttons. She puts 2 buttons oneach puppet for eyes.

Which number sentence can be usedto find the number of puppets onwhich Rita can put eyes? Mark youranswer.

16 × 2 = 32

16 − 2 = 14

16 + 2 = 18

* 16 ÷ 2 = 8

Note: Students should be able torecognize that fractions can name partof a whole or part of a set.


Understanding patterns, relationships, and algebraic thinking is an integral component of thefoundation of algebra. Solving problems and making predictions by discovering and extendingwhole-number and geometric patterns help build the groundwork for learning more-complexalgebraic concepts. With this knowledge students will be able to see that combinations of numbers areinterrelated. Third grade students need to understand the relationship between the patterns generatedby multiplication and division facts. By looking at fact families, students will be able to see how thebasic concepts of addition, subtraction, multiplication, and division are related. For example, studentsshould know that division is the opposite of multiplication. By using tables that represent real-lifesituations, students will identify patterns in related number pairs and be able to extend these patternsto solve problems. Students should be able to look at a table of related numbers and realize how thenumbers are related. This skill is critical to the development of students’ abilities to draw inferencesfrom tables. With an understanding of the basic concepts included in Objective 2, students should beprepared to continue learning more-advanced algebraic ideas. In addition, mastering the knowledgeand skills in Objective 2 at third grade will help students master the knowledge and skills in Objective 2 at fourth grade.

Objective 2 combines the basic algebra concepts within the TEKS—patterns, relationships, andalgebraic thinking.


Objective 2

The student will demonstrate an understanding of patterns, relationships, and algebraicreasoning.

(3.6) Patterns, relationships, and algebraic thinking. The student uses patterns to solveproblems. The student is expected to

(A) identify and extend whole-number and geometric patterns to make predictions and solveproblems;

(B) identify patterns in multiplication facts using [concrete objects,] pictorial models[, ortechnology]; and

(C) identify patterns in related multiplication and division sentences (fact families) such as 2 × 3 = 6, 3 × 2 = 6, 6 ÷ 2 = 3, 6 ÷ 3 = 2.


(3.7) Patterns, relationships, and algebraic thinking. The student uses lists, tables, and charts toexpress patterns and relationships. The student is expected to

(A) generate a table of paired numbers based on a real-life situation such as insects and legs;and

(B) identify and describe patterns in a table of related number pairs based on a meaningfulproblem and extend the table.



■ recognize and extend patterns with whole numbers or geometric shapes presented in lists, tables,or pictorial models;

■ understand the difference between factors and multiples;

■ identify patterns in tables based on the relationship between paired numbers; and

■ work with tables of related number pairs that may not begin with 1 and/or may not be sequential.




1 Whales add a layer of blubber to their bodies each year. The blubber helps keep thewhales warm. The table below shows the amount of blubber a whale produces overseveral years.

Based on the table above, how much blubber will the whale produce in 7 years? Markyour answer.

72 in.

48 in.

* 56 in.

88 in.

Number of Years Blubber(inches)

2

4

5

7

16

32

40

Whale Blubber

2 Ravi has a jar of coins.

If he counts his coins in groups of 5,which list shows only numbers hecould have named? Mark your answer.

15, 18, 21, 24

* 15, 20, 25, 30

15, 16, 17, 18

15, 17, 19, 21

3 Marcie started the number patternbelow.

479, 476, 473, 470, ___, ___, ___

Which number could NOT be part ofMarcie’s pattern? Mark your answer.

464

467

* 466

461

Note: Students should be able to find the relationship betweenthe pairs of numbers given in a table and apply that samerelationship in order to find a missing number.


Knowledge of geometry and spatial reasoning is important because the structure of the world isbased on geometric properties. For example, Earth is a sphere. With this knowledge students shouldbe able to recognize and name geometric figures and describe them using formal geometric languageas related to everyday applications. Students should be able to identify two-dimensional and three-dimensional figures in terms of congruence and symmetry because congruent and symmetrical figuresare found both in art and in nature. It is essential that students begin to plot points on a line to buildspatial reasoning skills that help develop an understanding of distance and location. The knowledgeand skills in Objective 3 will help students understand the basic concepts of geometry as related to thereal world. In addition, the knowledge and skills in Objective 3 at third grade are closely aligned withthe knowledge and skills in Objective 3 at fourth grade.

Objective 3 combines the fundamental concepts of size and shape found within the TEKS—geometry and spatial reasoning—from which all geometric understanding is built.


Objective 3

The student will demonstrate an understanding of geometry and spatial reasoning.

(3.8) Geometry and spatial reasoning. The student uses formal geometric vocabulary. Thestudent is expected to

(A) identify, classify, and describe two- and three-dimensional geometric figures by theirattributes. The student compares two-dimensional figures, three-dimensional figures, orboth by their attributes using formal geometry vocabulary.

(3.9) Geometry and spatial reasoning. The student recognizes congruence and symmetry. Thestudent is expected to

(A) identify congruent two-dimensional figures; and

(C) identify lines of symmetry in two-dimensional geometric figures.

(3.10) Geometry and spatial reasoning. The student recognizes that a line can be used torepresent numbers and fractions and their properties and relationships. The student isexpected to

(A) locate and name points on a number line using whole numbers and fractions, includinghalves and fourths.




■ recognize the relationship between pictures, descriptions, and/or formal geometric terms, whichinclude two-dimensional and three-dimensional figures (for example, a quadrilateral has fourvertices);

■ work with two-dimensional figures on which lines of symmetry are drawn; and

■ work with number lines that may or may not show the location of zero but will have at least twopoints numbered to indicate the interval being used.




1 Which shape has exactly 1 more sidethan a quadrilateral? Mark youranswer.

* Pentagon

Triangle

Rectangle

Hexagon

2 Look at the 3 figures shown below.

Which statement about these 3 figuresis true? Mark your answer.

* They are all prisms.

They each have the samenumber of faces.

They are all pyramids.

They each have at least 4rectangular faces.

Note: Art of geometric figures may ormay not be provided.



3 Which number on the number line does point V best represent? Mark your answer.

5

6

6

* 6 14

34

34

7

V

5 5 124 1

4



4 Which figure below shows a line ofsymmetry? Mark your answer.

*


Understanding the concepts and uses of measurement provides a foundation for real-lifemathematics and the development of geometry skills. Students need to know how to reasonablyestimate size and then accurately measure using appropriate SI (metric) and customary units oflength. These skills allow students to solve geometric problems, including those involving perimeterand area. Time and temperature are concepts that students should be able to understand and apply inorder to function in everyday society. Understanding the basic concepts included in Objective 4 willprepare students to apply measurement skills in various situations. In addition, the knowledge andskills in Objective 4 at third grade are closely aligned with the knowledge and skills in Objective 4 atfourth grade.

Objective 4 includes the concepts within the TEKS from which an understanding of measurement isdeveloped.


Objective 4

The student will demonstrate an understanding of the concepts and uses of measurement.

(3.11) Measurement. The student directly compares the attributes of length, area, weight/mass, andcapacity, and uses comparative language to solve problems and answer questions. Thestudent selects and uses standard units to describe length, area, capacity/volume, andweight/mass. The student is expected to

(A) use linear measurement tools to estimate and measure lengths using standard units;

(B) use standard units to find the perimeter of a shape; and

(C) use [concrete and] pictorial models of square units to determine the area of two-dimensional surfaces.

(3.12) Measurement. The student reads and writes time and measures temperature in degreesFahrenheit to solve problems. The student is expected to

(A) use a thermometer to measure temperature; and

(B) tell and write time shown on analog and digital clocks.





■ measure with the ruler on the Mathematics Chart only if the item specifically instructs studentsto use the ruler;

■ measure to the nearest centimeter or inch;

■ use the dimensions of a figure to solve a problem;

■ recognize abbreviations of measurement units;

■ use standard units in the SI (metric) and/or customary systems to measure or estimate length;

■ use pictorial models of a square unit to determine the area of a figure. Grid lines will be showninside the figure. Partial squares will be limited to halves;

■ identify the time shown on a clock or select the clock that represents a given time; and

■ read a thermometer with temperatures given in degrees Fahrenheit (°F).

12



1 Use the ruler on the Mathematics Chart to measure the length of the craft stick to thenearest half inch. About how long is the craft stick below? Mark your answer.

9 in.

8 in.

4 in.

* 3 in.12

12

Note: This item specifically instructs students to measure the length of the stick tothe nearest half inch. Students need to use the correct ruler on the Mathematics Chartbased on the unit of measure stated in the problem.



2 Jonathan leaves his house to catch the school bus at the time shown on the digitalclock.

Which clock below shows the same time? Mark your answer.

*

121110

9

87 6 5

4

32

1

121110

9

87 6 5

4

32

1

121110

9

87 6 5

4

32

1

121110

9

87 6 5

4

32

1

7:557:55



3 Noriko ran around her block. A diagram of the block Noriko lives on is shown below.

What is the perimeter of her block in yards? Mark your answer.

320 yd

360 yd

* 400 yd

440 yd

120 yd

40 yd

80 yd

40 yd

80 yd

40 yd


Understanding probability and statistics will help students become informed consumers of data andinformation. It is important for students to correctly display information in graphical formats tocommunicate that information effectively. Learning to interpret various graphs and developing anunderstanding of the significance of the displayed information will allow students to applymathematical data to real-world situations. By interpreting data, students should be able to determinethe likelihood that an event will occur. The knowledge and skills contained in Objective 5 areessential for processing everyday information. In addition, mastering the knowledge and skills in Objective 5 at third grade provides the foundation for mastering the knowledge and skills inObjective 5 at fourth grade.

Objective 5 includes the concepts within the TEKS that form the groundwork for an understanding ofprobability and statistics.


Objective 5

The student will demonstrate an understanding of probability and statistics.

(3.13) Probability and statistics. The student solves problems by collecting, organizing,displaying, and interpreting sets of data. The student is expected to

(A) collect, organize, record, and display data in pictographs and bar graphs where eachpicture or cell might represent more than one piece of data;

(B) interpret information from pictographs and bar graphs; and

(C) use data to describe events as more likely than, less likely than, or equally likely as.



■ identify the graph that fits a given set of data or the information that would complete a portion ofthe graph;

■ read information directly from a graph to answer a question or interpret a graph by combining orseparating some of the information from the graph;

■ read graphs that are oriented either vertically or horizontally; and

■ use the information presented in written or graphic form to make a decision about the likelihoodof an event. The terms impossible or certain may be used to describe that likelihood.




1 The table below shows the number of different types of pets brought into an animalclinic during one week.

Which pictograph best represents the information given in the table? Mark youranswer.

*

Pets in the Animal Clinic

Each means 5 pets.

Dog

Cat

Bird


Each means 4 pets.

Dog

Cat

Bird


Each means 3 pets.

Dog

Cat

Bird


Each means 2 pets.

Dog

Cat

Bird


Type of Pet Number Broughtinto Clinic

Dog

Cat

Bird

14

18

10

Note: In the answer choices, the key for each pictograph may represent differentamounts.



2 The table below shows the differentcolors of small plastic cups inJeannette’s cabinet.

If Jeannette takes 1 cup out of thecabinet at random, which statement istrue? Mark your answer.

She is least likely to get a bluecup.

* She is equally likely to get agreen or a blue cup.

She is most likely to get a redcup.

She is certain to get a yellowcup.

Color Numberof Cups

Red

Green

Yellow

Blue

3

4

8

4

Plastic Cups

3 Bonnie is making a graph to show thenumber of photos taken by each offour students at the school picnic.

Dexter took 6 more pictures thanTimo took. Which bar can be used tocomplete the graph for Dexter? Markyour answer.

*

4 8 12 16 20 24 280

Dexter

4 8 12 16 20 24 280

Dexter

4 8 12 16 20 24 280

Dexter

4 8 12 16 20 24 280

Dexter

School Picnic Photos

Number of Photos4

Oliver

8 12 16 20 24 280

Timo

Georgia

Dexter

Note: Students should understand thata random event occurs when a selectionis made without looking.



4 The graph below shows informationabout the number of hotel rooms thatwere filled on several different days.

Which days show between 40 and 70hotel rooms filled? Mark your answer.

* Monday and Thursday

Wednesday and Friday

Monday and Friday

Wednesday and Thursday

Roo

ms

Fill

ed

Hotel Rooms Filled

Day

Mon

day

Tues

day

Wed

nesd

ay

Thurs

day

Frida

y

80

70

60

50

40

30

20

10

0


Knowledge and understanding of underlying processes and mathematical tools are critical forstudents to be able to apply mathematics in their everyday lives. Problems found in everyday lifeoften require the use of multiple concepts and skills. Students should be able to recognizemathematics as it occurs in real-life problem situations, generalize from mathematical patterns andsets of examples, select an appropriate approach to solving a problem, solve the problem, and thendetermine whether the answer is reasonable. Expressing problem situations in mathematical languageand symbols is essential for finding solutions to real-life questions. These concepts allow students tocommunicate clearly and use logical reasoning to make sense of their world. Students can thenconnect the concepts they have learned in mathematics to other disciplines and to highermathematics. Through understanding the basic ideas found in Objective 6, students will be able toanalyze and solve real-world problems. In addition, the knowledge and skills in Objective 6 at thirdgrade vertically align with the knowledge and skills in Objective 6 at fourth grade.

Objective 6 incorporates the underlying processes and mathematical tools within the TEKS that areused to find mathematical solutions to real-world problems.


Objective 6

The student will demonstrate an understanding of the mathematical processes and tools used inproblem solving.

(3.14) Underlying processes and mathematical tools. The student applies Grade 3 mathematics tosolve problems connected to everyday experiences and activities in and outside of school.The student is expected to

(A) identify the mathematics in everyday situations;

(B) solve problems that incorporate understanding the problem, making a plan, carrying outthe plan, and evaluating the solution for reasonableness; and

(C) select or develop an appropriate problem-solving plan or strategy, including drawing apicture, looking for a pattern, systematic guessing and checking, acting it out, making atable, working a simpler problem, or working backwards to solve a problem.

(3.15) Underlying processes and mathematical tools. The student communicates about Grade 3mathematics using informal language. The student is expected to

(B) relate informal language to mathematical language and symbols.


(3.16) Underlying processes and mathematical tools. The student uses logical reasoning. Thestudent is expected to

(A) make generalizations from patterns or sets of examples and nonexamples.



■ select the description of a mathematical situation when provided with a written or pictorialprompt;

■ identify the information that is needed to solve a problem;

■ select or describe the next step or a missing step in a problem-solving situation;

■ match informal language to mathematical language or symbols;

■ identify the question that is being asked or answered;

■ identify the common characteristic among examples;

■ select an example or a nonexample based on a common characteristic. A nonexample proves ageneral statement to be false; and

■ understand that nonsensical words may be used to label sets of examples and/or nonexamples.




2 Melissa had some money in her pursewhen she went to the mall with hermother. She spent $5 on a book. Thenher mother gave her $10. AfterMelissa spent $2 on a snack, she had$23 in her purse. How much moneydid Melissa have in her purse whenshe first went to the mall? Mark youranswer.

$26

$17

* $20

$6

1 Mrs. Maldonado needs enough ribbonto go across the top of her bulletinboard. She has 5 pieces of ribbon.Their lengths are shown in the tablebelow.

The top of the bulletin board is 30 inches long. Which pieces of ribbonmeasure 30 inches together? Markyour answer.

P and Q

* P, R, and S

P, Q, and T

P, Q, R, and S

Mrs. Maldonado’s Ribbon

Piece Length(inches)

P

Q

R

S

T

17

10

8

5

2



3 Mateo had a set of cards with the numbers 1 through 25 written on them. He putsome of the cards in groups of 3 according to a rule.

Which group of cards fits Mateo’s rule? Mark your answer.

* 2311 12

1411 12

1712 15

1614 15

31 2

188 10

94 5

136 7

Note: Students should look for a rule that fits each of the examples given at the top.Students should then apply that rule to the answer choices to find the one that fits.



4 The school soccer team played 5 games. The team scored 7 goals ineach of the first 3 games. The teamscored 6 goals in each of the last 2 games. Which shows one way offinding the total number of goals theteam scored in the 5 games? Markyour answer.

Add 7, 3, 6, and 2.

Multiply 7 by 3 by 6 by 2.

Add 7 and 3. Add 6 and 2. Thenmultiply the two sums.

* Multiply 7 by 3. Multiply 6 by 2.Then add the two products.

5 Amy, Evan, Nadja, Joe, and Carmellaare in line to buy movie tickets.Carmella is not the first or the lastperson in line. Amy is third in line.Evan and Joe are in line after Amy.Joe is not the last person in line. Whatis the order of the children from firstto last? Mark your answer.

Evan, Joe, Amy, Carmella, Nadja

* Nadja, Carmella, Amy, Joe, Evan

Nadja, Carmella, Amy, Evan, Joe

Joe, Evan, Amy, Carmella, Nadja

Note: This problem requires students toexpress a mathematical process inwords. Problems may involve more thanone step.

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