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    WASL Washington Assessment

    of Student Learning

    A Component of the Washington State Assessment Program

    Using Results to Improve

    Student Learning

    Mathematics

    Grade 10

    2002 Released Items

    Copyright ? 2002 by Washington Office of the Superintendent of Public Instruction. All rights reserved.

    Educational institutions within the State of Washington have permission to reproduce this document.

    All other individuals wishing to reproduce this document must contact OSPI.

    Table of Contents

    A Letter from the Superintendent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

9-18402 WA2 M Gr10 ADP 7-29-02 page ii

    How to Use this Released Item Booklet and the Item Analysis Report . . . . . . 3

    Introduction to Released Mathematics Items. . . . . . . . . . . . . . . . . . . . . . . . . . 4 2002 Released

    Items. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 August 1, 2002

    Dear Washington State Educators:

    I am delighted to offer this second annual released test item publication from the 2002 Washington Assessment of Student Learning (WASL). My staff worked hard to be able to release this material in time for your use in administration workshops and LID day trainings for all staff. This publication is designed to assist teachers and administrators in the analysis of the results of specific test items in order to identify patterns, trends, weaknesses, and strengths of student performance on the Essential Academic Learning Requirements (EALRs).

    In conjunction with the released test items, the writing prompts and annotations from the Spring 2002 WASL will be available electronically on the OSPI website, as will released science pilot items for grades 5, 8, and 10.

    As a teacher, or as a district or building administrator, you will be able to analyze the actual test items and the data that accompany them to learn more about students in your school and district. You will be able to compare the performance of your school to your district or the state. By analyzing the differences in the data and the relationship that each question has with the EALRs, you will be able to identify areas where performance is strong and areas for improvement in your school and district. I fervently hope opportunities will be provided prior to the start of the school year for principals and teachers to work with the item-specific scoring guides in listening, reading, mathematics, and science and the annotated student responses that illustrate each score point. This experience will help schools work more effectively with students and parents this fall and throughout the school year. OSPI hopes that you will use the information to begin a thoughtful, impassioned dialogue about what we expect our students to know and be able to do and how well they need to do it. We expect that this material will initiate conversations among administrators, faculty, students, and parents as to how this information can impact our teaching, our learning, and our communication. Plans to improve student learning should not be made based on these results alone. It is important to also include the results from other assessments used by the teacher, school, and/or district.

    In November, OSPI assessment staff will again conduct regional training on the effective use of these materials.

    Congratulations on our efforts to improve student learning in Washington. Have a great fall as we continue our work toward creating thoughtful, competent citizens in the 21st century. I encourage you to search our website for further resources (www.k12.wa.us).

    Sincerely,

Dr. Terry Bergeson

    State Superintendent of Public Instruction

    How to Use this Released Item Booklet and the Item Analysis

    Report

    Introduction:

    You should have two documents: one, this Released Item Booklet and two, the Item

    Analysis Report. These two documents should be used together to help administrators and

    teachers understand released WASL items that reflect content-specific learning strands and

    targets which are derived from the Essential Academic Learning Requirements.

    9-18402 WA2 M Gr10 ADP 7-29-02 page ii

    This Released Item Booklet includes the following information:

    •WASL items from the 2002 Operational Test

    •A table for each item where you can transfer the school-level, district-level, and

    state-level data information

    •Information to indicate the learning target and strand information for each item

    •Item-specific scoring guides, student work at representative score points, and

    annotated explanations for scores.

    The Item Analysis Report includes the following information:

    •A list of all released items referenced to learning strands and learning targets

    •Multiple-choice items include the percentage of students who responded to each

    possible answer. Correct answers have asterisks. Information is presented by the

    percentage of students responding to each possible answer by school, by district, and by

    state.

    •For constructed-response items, including short answers and extended response,

    information is presented by the percentage of students who scored at each score point by

    school, by district, and by state.

    How to Understand Your Data:

    •First, transfer your data from the Item Analysis Report to the Released Item

    Booklet. Transfer all the information for each item into each table. By transferring the

    data, you will have all the information in one place.

    •Second, examine the item types that represent the school’s or the district’s

    strengths or weaknesses. Does the school or district perform well on multiple- choice items?

    Constructed-response items? What percentage of students in a school or a district left

    constructed-response items blank or earned a zero?

    •Third, examine the learning strands and targets represented by each item.

    Group together targets that represent strengths or weaknesses for a school or a district.

    Do the targets all fit underneath one particular strand or do they belong to several strands?

    •Fourth, look for trends. Does a school perform markedly lower on a particular

    item in comparison to the district or the state? Does a school or a district perform

    markedly higher on a particular item in comparison to the state?

    3

    Introduction to Released Mathematics Items

    Welcome to the Released Item Booklet for the WASL 2002 mathematics items. In this booklet you will find 11 items that were part of the spring 2002 WASL test for mathematics. There are four types of test items:

    •multiple-choice items where students earn one point by selecting the right answer

    from a few options

    •extended multiple-choice items where students can earn up to two points by first

    selecting the right answer from options and then explaining something about

    their choice

    •short-answer items where students earn up to two points by writing an answer,

    9-18402 WA2 M Gr10 ADP 7-29-02 page ii

    explaining their thinking, drawing a picture or diagram, or showing steps used to solve a

    problem

    •extended-response items where students can earn up to four points by

    constructing a response that asks for more details (graphs, tables, written summaries) or

    more thinking.

    Please note that in releasing 11 items from the 2002 WASL test for mathematics, OSPI is releasing approximately 36% of the mathematics WASL. The items that were not

    released this year will be used on future WASLs. However, these released items also provide invaluable opportunities for teachers and administrators to become familiar with the types of mathematics items derived from the mathematics EALRs while also becoming experienced with the item-specific scoring guides and annotated samples of student responses. You may want to become familiar with the WASL test and item specifications (located on our websitewww.k12.wa.us) as you

    study the items, your school or district’s data, and the annotated student responses contained in this Released Item Booklet. Each item in

    this booklet represents a “learning target,” which is a mathematics skill derived from the EALRs

    that can be captured in a paper and pencil assessment. These targets are subsets of the nine content and process mathematics strands. As you begin to analyze your data, think about what would account for the performance of students on particular items. Although many of the items can represent strength and weaknesses across schools, districts, and the state, attempt to maintain the whole picture in your analysis. Staff at OSPI recommends that you examine the items themselves closely and ask yourselves, “What do we expect our students to know and be able to do in order to be successful on this item?” Along with classroom performance information, results from other tests, and these test items, informed curriculum decisions can be made. In order to assist you in your efforts in understanding and using the Released Item Test

    Booklet, please do not hesitate to search our website for further resources or call our offices in Olympia for further information.

    4

    Mathematics

    1 Audrey is given the following problem to solve.

    a ba + ab

    a 77

    Audrey has to solve for a and b.W hich of the following is not possible?

    \\

    A.b is odd and greater than a.

    \\

    B.a is even and smaller than 5.

    \\

    C.a and b are both odd numbers.

    \\

    9-18402 WA2 M Gr10 ADP 7-29-02 page ii

    D.a and b are both prime numbers.

    Item Information:

    Correct Answer: C

    Strand: Number Sense

    Learning Target: NS02: Demonstrate an understanding of the properties of

    rational numbers, powers, and roots; demonstrate an understanding

    of concepts and processes involving prime and composite numbers,

    factors and multiples, and divisibility (Mathematics EALR 1.1.1, 1.1.3)

    Performance Data (Use this space to fill in student performance information for your

    school, district, and the state.):

    Percent Distribution

    School District State Responses (* = correct response)

    A

    B

    C*

    D

    NR

    5

    Mathematics

    22 Which term is a factor of 3a12a?

    \\

    A.3a

    \\

    B.4a

    \\

    2 C.3a

    \\

    2 D.4a

    Item Information:

    Correct Answer: A

    Strand: Number Sense

    9-18402 WA2 M Gr10 ADP 7-29-02 page ii

    Learning Target: NS02: Demonstrate an understanding of the properties of

    rational numbers, powers, and roots; demonstrate an understanding

    of concepts and processes involving prime and composite numbers,

    factors and multiples, and divisibility (Mathematics EALR 1.1.1,

    1.1.3)

    Performance Data(Use this space to fill in student performance information for your

    school, district, and the state.):

    Percent Distribution

    School District State Responses (* = correct response)

    A*

    B

    C

    D

    NR

    6

    s3 Grand Coulee Dam is made of about 10,585,000 cubic yards of

    tconcrete.

    aWhich of the following would give the total amount of concrete tin cubic feet? e

    \\ .

    A. 10,585,000 27 )

    :

    \\

    Percent Distribution B. 10,585,000 27

    School District State Responses (* = correct response)

    \\ A*

    C. 10,585,0009 B

    C \\ D

    D. 10,585,0009 NR

    Mathematics

    Item Information: 7

    Correct Answer: A

    Strand: Measurement

    Learning Target: ME02: Measure objects and events directly and use indirect

    methods; calculate rate and other derived

    and indirect

    measurements (Mathematics EALR 1.2.2,

    1.2.3)

    Performance Data(Use this space to fill in student

    performance information for your school, district, and the

    9-18402 WA2 M Gr10 ADP 7-29-02 page

    Mathematics

    4Terry is designing a flyer to advertise storage boxes that he sells.

    He wants to show the boxes from least to greatest volume. What is the correct order?

    \\

    A.BACD

    \\

    B. ABCD

    \\

    C. DCBA

    \\

    D. DCAB

    8

    Mathematics 4 (continued)

    Item Information:

    Correct Answer: D

    Strand: Measurement

    Learning Target: ME02: Measure objects and events directly and use indirect

    methods; calculate rate and other derived and indirect

    measurements (Mathematics EALR 1.2.2, 1.2.3)

    Performance Data (Use this space to fill in student performance information for your

    school, district, and the state.):

    Percent Distribution

    School District State Responses (* = correct response)

    A

    B

    C

    D*

    NR

    9

    Mathematics

    9-18402 WA2 M Gr10 ADP 7-29-02 page

    5 Each letter in the diagram below represents an angle. x

    wyz

    Which of the following statements is true?

    A.xzyz

    \\

    B.wxyz

    \\

    C.wxyyz

    \\

    D.wxyyz

    \\

    Item Information:

    Correct Answer: C

    Strand: Geometric Sense

    Learning Target: GS01: Use geometric properties and relationships to describe,

    compare, contrast, and classify 2- and 3-dimensional geometric

    figures; draw geometric models and scale drawings using tools as

    appropriate (Mathematics EALR 1.3.1, 1.3.2)

    Performance Data (Use this space to fill in student performance information for your

    school, district, and the state.):

    Percent Distribution

    School District State Responses (* = correct response)

    A

    B

    C*

    D

    NR

    10

    \6 In a certain carnival game, a player gets to spin each of the

    \ following

    Aspinners once. What is the probability of getting two numbers . that have a 4sum of 7?

    1

    \1

    9-18402 WA2 M Gr10 ADP 7-29-02 page

    \ Mathematics

    B. 11 6

    5 2

    \\

    C.

    1

    7D.24

    \\

    Mathematics

    6 (continued)

    Item Information:

    Correct Answer: B

    Strand: Probability and Statistics

    Learning Target: PS01: Demonstrate an understanding of the properties of

    dependent and independent events; demonstrate an understanding of

    and use appropriate counting procedures to determine probabilities;

    use both experimental and theoretical methods to determine

    probabilities (Mathematics EALR 1.4.1, 1.4.2, 1.4.3)

    Performance Data(Use this space to fill in student performance information for your

    school, district, and the state.):

    Percent Distribution

    School District State Responses (* = correct response)

    A

    B*

    C

    D

    NR

    12

    K7Kesha is planning to rent a van for her trip to Mt. Rainier. Two of

    esher

    hfriends each rented the same type of van from the same car a rental company last week. This is what they told her: plJohn: “The cost of my rental was $240. The company acharged me a certain amount per day and a certain amount ns per mile. I had the rental for five days and I drove it 200 to miles.” ge

    t Katie: “The cost of my rental was only $100. I drove it for

    th100 miles and had it for two days.”

    9-18402 WA2 M Gr10 ADP 7-29-02 page

    e same type of van that John and Katie had from the same car Mathematics

    rental company. Kesha estimated her trip would be 250 miles, 13 and she would have the vehicle for four days. Which of the

    following equations could Kesha use to figure out how much her

    rental would cost?

    LetC = cost, M = miles, and D = days

    \\

    A.C = 40.00M 0.20D

    \\

    B.C = 40.00D 0.20M

    \\

    C.C = 20.00M 0.40D

    \\

    D.C = 20.00D 0.40M

    Mathematics

    7 (continued)

    Item Information:

    Correct Answer: B

    Strand: Algebraic Sense

    Learning Target: AS03: Simplify and evaluate expressions and formulas; solve

    equations and inequalities (Mathematics EALR 1.5.5, 1.5.6)

    Performance Data(Use this space to fill in student performance information for your

    school, district, and the state.):

    Percent Distribution

    School District State Responses (* = correct response)

    A

    B*

    C

    D

    NR

    14

    Mathematics

    8 The school playground, a 36 m square, is going to lose part of one corner

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