4 math info booklet - metromomsevents.com · under both objective 2 and objective 6. in this case,...

MATHEMATICSGrade 4

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

January 2008

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.

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 4 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. Althoughsome student expectations are not tested, they are nonetheless critical for student understanding andmust be included in classroom instruction. For each strand of learning, the mathematics TEKSprovide more rigorous expectations as students master skills and progress through the curriculum. Itis important for educators to vertically align their instructional programs to reinforce the unifyingstrands of learning each year through grade-level-appropriate instruction. To understand how studentlearning progresses, educators are encouraged to become familiar with the curriculum at all gradelevels. Educators may find it helpful to examine sample items at each grade level to gain a greaterunderstanding of what students need to know and be able to do in mathematics as they move fromgrade 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 4

The fourth grade mathematics TEKS describe what students should know and be able to do in fourthgrade. 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 afterfourth grade will enable teachers to more effectively help their students develop mathematicsknowledge and skills.

TEST FORMAT

■ The fourth grade test includes a test booklet and a separate machine-scorable answer document.Enough room is left around each item in the booklet for students to work each problem.However, student responses must be recorded on the separate answer document.

■ 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 four-columngrid (with the last column designated as a fixed decimal point) will be provided on the answerdocument for students to record and bubble in their answers. Digits must be in the correctcolumn(s) with respect to the fixed decimal point. This griddable format is intended to allowstudents to work a problem and determine the correct answer without being influenced byanswer choices. An example of a blank grid is shown below.

0

9

1

2

3

4

5

6

7

8

0

9

1

2

3

4

5

6

7

8

0

9

1

2

3

4

5

6

7

8


MATHEMATICS CHART

■ For fourth 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 4 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

7

11

6

6

4

8

42

Number of Items

Objective 1: Numbers, Operations, and Quantitative Reasoning


Grade 4Mathematics Chart

10

23

45

67

89

1011

1213

1415

1617

1819

20

Cen

timet

ers

65

43

21

0Inches

LENGTH

Metric Customary

1 kilometer = 1000 meters 1 mile = 1760 yards

1 meter = 100 centimeters 1 mile = 5280 feet

1 centimeter = 10 millimeters 1 yard = 3 feet

1 foot = 12 inches

CAPACITY AND VOLUME

Metric Customary

1 liter = 1000 milliliters 1 gallon = 4 quarts

1 gallon = 128 fluid ounces

1 quart = 2 pints

1 pint = 2 cups

1 cup = 8 fluid ounces

MASS AND WEIGHT

Metric Customary

1 kilogram = 1000 grams 1 ton = 2000 pounds

1 gram = 1000 milligrams 1 pound = 16 ounces

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

(4.11) Measurement. The student applies measurement concepts. The student is expected toestimate and measure to solve problems involving length (including perimeter) and area. Thestudent uses measurement tools to measure capacity/volume and weight/mass. The student isexpected to

(C) use [concrete] models of standard cubic units to measure volume.

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 fourth grade mathematics. The number preceding the statement identifies the instructionallevel and the number 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

CB

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.


(4.10) (A) locate and name points on a number line using whole numbers, fractions such as halvesand fourths, and decimals such as tenths.

This student expectation lists fractions: such as halves and fourths; and decimals: such as tenths.Many other fractions and decimals exist on a number line.

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.


(4.5) (B) use strategies including rounding and compatible numbers to estimate solutions tomultiplication and division problems.

This student expectation lists two estimation strategies to include in instruction. Other strategies maybe taught in addition to those 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 4 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 and decimal parts of whole numbersand how this value relates to the value of the whole. From these basic concepts students move towardunderstanding specific combinations of numbers as solutions to problems. More abstract concepts andcomplicated numbers will be used as students work with and distinguish among the four basicoperations of addition, subtraction, multiplication, and division. Students should also be developing asense of the reasonableness of an expected answer. Quantitative reasoning is knowing when ananswer makes sense. Estimation strategies can be used when an exact answer is not required. Studentsshould be prepared to apply the basic concepts included in Objective 1 to other concepts in fourthgrade mathematics. In addition, the knowledge and skills in Objective 1 at fourth grade are closelyaligned with and provide the foundation for mastering the knowledge and skills in Objective 1 at fifthgrade.

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.

(4.1) Number, operation, and quantitative reasoning. The student uses place value to representwhole numbers and decimals. The student is expected to

(A) use place value to read, write, compare, and order whole numbers through 999,999,999;and

(B) use place value to read, write, compare, and order decimals involving tenths andhundredths, including money, using [concrete objects and] pictorial models.

(4.2) Number, operation, and quantitative reasoning. The student describes and comparesfractional parts of whole objects or sets of objects. The student is expected to

(A) use [concrete objects and] pictorial models to generate equivalent fractions;

(B) model fraction quantities greater than one using [concrete objects and] pictorial models;

(C) compare and order fractions using [concrete objects and] pictorial models; and


(D) relate decimals to fractions that name tenths and hundredths using [concrete objectsand] pictorial models.

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

(A) use addition and subtraction to solve problems involving whole numbers; and

(B) add and subtract decimals to the hundredths place using [concrete objects and] pictorialmodels.

(4.4) Number, operation, and quantitative reasoning. The student multiplies and divides tosolve meaningful problems involving whole numbers. The student is expected to

(A) model factors and products using arrays and area models;

(B) represent multiplication and division situations in picture, word, and number form;

(C) recall and apply multiplication facts through 12 × 12;

(D) use multiplication to solve problems (no more than two digits times two digits withouttechnology); and

(E) use division to solve problems (no more than one-digit divisors and three-digitdividends without technology).

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

(A) round whole numbers to the nearest ten, hundred, or thousand to approximatereasonable results in problem situations; and

(B) use strategies including rounding and compatible numbers to estimate solutions tomultiplication and division problems.


Objective 1—For Your Information

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

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

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

■ solve problems with fractions or decimals representing whole numbers, numbers greater thanone, or numbers less than one; 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.



Objective 1 Sample Items

1 The table below shows the number of tickets sold over a 4-month period at anamusement park.

Which list shows the months in order from least to greatest number of tickets sold?

A July, June, August, May

B May, August, June, July

C* July, June, May, August

D August, May, June, July

Amusement Park Tickets

Month Number ofTickets Sold

May

June

July

August

39,001

36,489

34,999

41,102



2 A car wash uses about 578 towels eachday. If 6 towels are used each time acar is washed, which is the bestestimate of the number of cars thatare washed each day?

A 3,000

B 6,000

C 200

D* 100

3 Which fraction represents the shadedmodel below?

A

B*

C

D 135

113

198

218

Note: In this item, it is appropriate touse compatible numbers to divide. Thenumber 578 is close to 600, which can beeasily divided by 6 to get 100.Considering the context of this problem,100 is the best estimate.

Note: Students should recognize thatfractions greater than 1 may beexpressed as an improper fraction or amixed number.



4 Alfred delivers 40 newspapers everyday. How many newspapers does hedeliver in two weeks?

Record your answer and fill in thebubbles on your answer document. Besure to use the correct place value.

0

9

1

2

3

4

5

6

7

8

0

9

1

2

3

4

5

6

7

8

0

9

1

2

3

4

5

6

7

8

5 6 0

Note: This item specifically asks for thenumber of newspapers. On griddableitems, students do not grid the labels,such as newspapers.



5 Which model below shows the answer to the problem 0.43 + 0.17?

A

B

C

D* + =

+ =

+ =

+ =



6 Each picture below shows an amount of money that could be written in dollars andcents. For which amount of money would the digit 7 represent seven cents?

A

B

C

D*

YTR

EB I

L

199919991999

YTR

EB I

L

EW

DO

NI

TSU

RT

G

TR

BI

99

91

L

EY

EW

DO

NI

TSU

RT

G

TR

BI

99

91

L

EY

19991999LIBERTYLIBERTY

1999LIBERTY

EWDO

NI TSURTG

EWDO

NI TSURTG

UUEETTII

NNDD

EETTAATTSSSS

AA

C CIIRR

EEMM

A A

ooFF

M12550009M

11

11

11

11M12550009M

M

YTREBIL

9991

IN GOD WETRUST

YTREBIL

9991

UUEETTII

NNDD

EETTAATTSSSS

AA

CCIIRR

EEMM

A A

ooFF

M12550009M

11

11

11

11M12550009M

M

M12550009M

11

11

11

11M12550009M

M

YTR

EB I

L

199919991999

YTR

EB I

L

YTREBIL

9991

IN GOD WETRUST

YTREBIL

9991

15

15

15

15M21222490L

M21882356P

1963

YTR

EB I

L

199919991999

YTR

EB I

L

UN

ITE

D

STATESAM

ERIC

A

OF

Q

UARTER DOLLARQ

UARTER DOLLAR

UN

ITE

D

STATES OF AMER

ICA

UN

ITE

D

STATESAM

ERI C

A

OF

UN

ITE

D

STATES OF AMER

I CA

ONE DIME

DIMEO

NE

E PLUE PLU RIBRIB USUUSU NUMNUME PLU RIB USU NUM

15

15

15

15M21222490L

M21882356P

1963

YTR

EB I

L

199919991999

YTR

EB I

L

PPUUBBIIRRLL

SS

MM EE

EE

CCIITTNNOO LL LL OO AACCIIRREEMMAAFFOOSSEETTAATTSS

FF VVII EE NNEECC TT SSDDEETTII

NNUU

UUNNUU UU

MM

YTREBIL

9991

IN GOD WETRUST

YTREBIL

9991

M12550009M

11

11

11

11M12550009M

M

M12550009M

11

11

11

11M12550009M

M


Understanding patterns, relationships, and algebraic thinking is an integral component of thefoundation of algebra. Discovering patterns with whole numbers, recognizing numericalrelationships, making predictions, and solving problems help build the groundwork for learningmore-complex algebraic concepts. By using patterns, students are able to recognize that combinationsof numbers are interrelated. Fourth grade students need to understand the relationship between thepatterns generated by multiplication and division facts in order to solve problems. Students should beable to look at various sources of related data and describe how the data is related. These skills arecritical to the development of students' abilities to draw inferences from tables and other sources ofinformation. With an understanding of the basic concepts included in Objective 2, students should beprepared to continue learning more-advanced algebraic ideas. In addition, the knowledge and skills inObjective 2 at fourth grade are closely aligned with the knowledge and skills in Objective 2 at fifthgrade.

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.

(4.6) Patterns, relationships, and algebraic thinking. The student uses patterns in multiplicationand division. The student is expected to

(A) use patterns and relationships to develop strategies to remember basic multiplication anddivision facts (such as the patterns in related multiplication and division numbersentences (fact families) such as 9 × 9 = 81 and 81 ÷ 9 = 9); and

(B) use patterns to multiply by 10 and 100.

(4.7) Patterns, relationships, and algebraic thinking. The student uses organizational structuresto analyze and describe patterns and relationships. The student is expected to

(A) describe the relationship between two sets of related data such as ordered pairs in atable.




■ understand the difference between factors and multiples;

■ describe the relationship, in symbols or in words, between paired numbers in a set of relatednumber pairs; and

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




1 In which number sentence does 12 make the equation true?

A 80 ÷ = 8

B 88 ÷ = 8

C* 96 ÷ = 8

D 72 ÷ = 8

2 An office building has 16 floors. Thereare 100 offices on each floor. Howmany offices are in this building?

A* 1,600

B 160

C 16,000

D 116

3 The table below shows the number of feet Kristin travels on her skateboard indifferent numbers of seconds.

What is one way to find the number of feet Kristin travels on her skateboard in 1 second?

A Multiply the number of seconds by the number of feet

B* Divide the number of feet by the number of seconds

C Multiply the number of feet by 75

D Divide the number of seconds by 5

Number of Seconds

5 6 8 9

Number of Feet

75 90 120 135

Kristin’s Skateboarding Distance


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 identify and describe angles, lines, and two- and three-dimensional figures using specificgeometric terms (for example, obtuse, perpendicular, and vertices). Students should be able toconnect transformations to congruence and symmetry. These connections help students recognizecongruent and symmetrical shapes in such fields as art and science. Students should learn to plotpoints on a line using whole numbers, fractions, and decimals. This is essential for building spatialreasoning skills that help develop an understanding of distance and location. The knowledge andskills in Objective 3 will help students to understand the basic concepts of geometry as related to thereal world. In addition, the knowledge and skills in Objective 3 at fourth grade are closely alignedwith the knowledge and skills in Objective 3 at fifth 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.

(4.8) Geometry and spatial reasoning. The student identifies and describes attributes ofgeometric figures using formal geometric language. The student is expected to

(A) identify and describe right, acute, and obtuse angles;

(B) identify and describe parallel and intersecting (including perpendicular) lines using[concrete objects and] pictorial models; and

(C) use essential attributes to define two- and three-dimensional geometric figures.

(4.9) Geometry and spatial reasoning. The student connects transformations to congruence andsymmetry. The student is expected to

(B) use translations, reflections, and rotations to verify that two shapes are congruent; and

(C) use reflections to verify that a shape has symmetry.

(4.10) Geometry and spatial reasoning. The student recognizes the connection between numbersand points on a number line. The student is expected to

(A) locate and name points on a number line using whole numbers, fractions such as halvesand fourths, and decimals such as tenths.




■ describe two- and three-dimensional figures and/or identify critical attributes with or without art;

■ match the name of a transformation with its pictorial representation;

■ work with symmetrical figures on which lines of symmetry may not be 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 single transformation isrepresented in the drawing below?

A Translation

B* Reflection

C Rotation

D Not here

2 Which point best represents 36.7 on the number line below?

A Point W

B Point X

C* Point Y

D Point Z

36 37 37.3

W YX Z



3 Look at the rectangle below.

Which statement about the line segments in this rectangle is true?

A* Line segments KQ and MS are parallel.

B Line segments MK and PS are parallel.

C Line segments NQ and LR are perpendicular.

D Line segments SQ and LK are perpendicular.

P

R

N Q

M

K

S

L

4 Look at the angle made by the back of the arrow shown below.

What type of angle does ∠T appear to be?

A Right

B* Obtuse

C Acute

D Straight

T



5 Which of these drawings has exactly 1 line of symmetry?

A

B

C

D*

Note: In this item, students shouldrecognize that the drawings in answerchoices A, B, and C have more than oneline of symmetry. Answer choice D is theonly drawing that has exactly one line ofsymmetry.

6 Which statement is true about thefollowing figure?

A* It has an equal number of verticesand faces.

B It has more faces than vertices.

C It has an equal number of verticesand edges.

D It has more faces than edges.


Understanding the concepts and uses of measurement provides a basis for developing geometryskills. Students need to know how to reasonably estimate and accurately measure length, area,capacity, and weight/mass using both SI (metric) and customary units. Students need to usemeasurement concepts to solve real-life problems, including those involving length, perimeter, area,time, and temperature. With the basic concepts included in Objective 4, students will be prepared toapply measurement skills in various situations. In addition, the knowledge and skills in Objective 4 atfourth grade are closely aligned with the knowledge and skills in Objective 4 at fifth 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.

(4.11) Measurement. The student applies measurement concepts. The student is expected toestimate and measure to solve problems involving length (including perimeter) and area. Thestudent uses measurement tools to measure capacity/volume and weight/mass. The student isexpected to

(A) estimate and use measurement tools to determine length (including perimeter), area,capacity, and weight/mass using standard units SI (metric) and customary;

(B) perform simple conversions between different units of length, between different units ofcapacity, and between different units of weight within the customary measurementsystem; and

(C) use [concrete] models of standard cubic units to measure volume.

(4.12) Measurement. The student applies measurement concepts. The student measures time andtemperature (in degrees Fahrenheit and Celsius). The student is expected to

(A) use a thermometer to measure temperature and changes in temperature.




■ utilize the conversions on the Mathematics Chart to solve problems;

■ 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;

■ match a measurement of weight, mass, volume, or capacity with an ordinary or familiar objectusing standard units;

■ determine the area of a figure using models that represent the dimensions of the figure; and

■ determine the volume of a figure by counting models of cubic units.

14




1 A rectangular prism made of 1-unitcubes is shown below.

What is the volume of this rectangularprism?

A 16 cubic units

B* 24 cubic units

C 12 cubic units

D 28 cubic units

2 Sara has a ribbon that is 48 inches inlength. What is the length in feet ofSara’s ribbon?

A* 4 feet

B 60 feet

C 16 feet

D 576 feet

Note: In this item, students can countthe number of 1-unit cubes in the toplayer of the model. Then they canmultiply this number by the number oflayers to determine the volume of thisrectangular prism. Finding volumeusing this procedure helps develop thevolume formula used at higher grades.



3 Use the ruler on the Mathematics Chart to measure the dimensions of the squareshown below to the nearest centimeter.

Which is closest to the perimeter of this square?

A 6 centimeters

B* 24 centimeters

C 12 centimeters

D 36 centimeters

Note: Students can determine the perimeter of this figure by adding the length of eachside together. Finding perimeter using this procedure helps develop the perimeterformulas used at higher grades.

This item specifically instructs students to measure the dimensions of the square incentimeters. Students need to use the correct ruler on the Mathematics Chart based onthe unit of measure stated in the problem.



Understanding probability and statistics will help students become informed consumers of data andinformation. It is important for students to organize information in order to see all possiblecombinations of a set of data. Students will learn to interpret various bar graphs and understand thesignificance of the displayed information so that it can be applied to real-world situations. Theknowledge and skills contained in Objective 5 are essential for processing everyday information. Inaddition, the knowledge and skills in Objective 5 at fourth grade are closely aligned with theknowledge and skills in Objective 5 at fifth 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.

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

(A) use [concrete objects or] pictures to make generalizations about determining all possiblecombinations of a given set of data or of objects in a problem situation; and

(B) interpret bar graphs.



■ determine the total number of possible combinations when given pictures;

■ read information directly from a bar graph to answer a question or interpret a bar graph bycombining or separating some of the information from the graph; and

■ read bar graphs that are oriented either vertically or horizontally.



1 The picture below shows the fish and the fish tanks for sale at a pet store.

If Jacob chooses 1 fish and 1 fish tank, how many combinations are possible?

A 9

B 16

C* 20

D 25

Fish Fish Tanks



2 The graph shows the number of sack lunches brought by students in Mrs. Johnson’sand Mr. Peña’s classes on four days this week.

According to the graph, how many more sack lunches were brought by Mr. Peña’sclass than by Mrs. Johnson’s class during these four days?

A 1

B 40

C 21

D* 2

Number of Sack Lunches

Sack Lunches

Monday

0 862 4

Tuesday

Wednesday

Thursday

Day

Mrs. Johnson

Mr. Peña


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 fourthgrade are closely aligned with the knowledge and skills in Objective 6 at fifth 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.

(4.14) Underlying processes and mathematical tools. The student applies Grade 4 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.

(4.15) Underlying processes and mathematical tools. The student communicates about Grade 4mathematics using informal language. The student is expected to

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


(4.16) 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.




1 Megan saw this poster in a store.

Megan had $4 when she went to thestore to buy soda and candy. Whatinformation is needed in order to findthe amount of change Megan shouldreceive?

A The price of 1 candy bar

B The price of 4 sodas

C The amount of money the store had

D* The amount Megan spent

2 Sodas for $1

2 Candy Bars for 75¢

SALE

2 José bought some tokens to play videogames at the mall. Then he found 2 tokens on the floor. He used 8 tokensto play video games. If José had 6 tokens when he went home, howmany tokens did he buy?

A* 12

B 14

C 16

D 10



3 Kellie calls these designs marbos.

These are not marbos.

Which figure below is a marbo?

A C

B* D

Note: Marbos is a nonsensical (made-up) word used to label this set of examples.



4 Jin bought four books. The least shepaid for a book was $3, and the mostshe paid for a book was $7. Which ofthe following is NOT a reasonableamount for the total cost of the fourbooks?

A* $12

B $24

C $18

D $17

5 Kirk has 2 dogs named Fido and Lady.Fido eats twice as much dog food asLady eats. If Lady eats 3 cups of food,which of the following can Kirk use tofind how many cups of food in all Fidoand Lady eat?

A Multiply 2 by 3

B Add 2 to 3

C* Multiply 2 by 3 and then add 3

D Add 3 to 3 and then subtract 2

4 math info booklet - metromomsevents.com · under both objective 2 and objective 6. in this case,...

Documents