Blueprint Algebra I Test

Transcription

1 Blueprint Algebra I Test Spring 2003

2 2003 by te Commonwealt of Virginia Department of Education, James Monroe Building, 101 N. 14t Street, Ricmond, Virginia, All rigts reserved. Except as permitted by law, tis material may not be reproduced or used in any form or by any means, electronic or mecanical, including potocopying or recording, or by any information storage or retrieval system, witout written permission from te copyrigt owner. Please contact te Commonwealt of Virginia Department of Education at (804) , Division of Assessment and Reporting, to request written permission.

3 Algebra I Blueprint Table of Contents Standards of Learning (SOL) Test Blueprint Introduction... 1 Algebra I Test Development Guidelines...3 Algebra I Blueprint Summary Table...4 Expanded Blueprint...5 Algebra I Formula Seet...8 ii

4 Standards of Learning (SOL) Test Blueprint Introduction Wat is a test blueprint? A test blueprint is a guide for test construction and use. Te Standards of Learning (SOL) test blueprints serve a number of purposes. One, tey serve as a guide to test developers as tey write test questions and construct te SOL tests. Two, tey serve as a guide to educators, parents, and students in tat tey sow (a) te SOL covered by te test and wic, if any, ave been excluded; (b) wic SOL are assigned to eac reporting category; (c) te number of test items in eac reporting category and on te total test; (d) general information about ow te test questions were constructed; and (e) te materials tat students are allowed to use wile taking te test. How is te test blueprint organized? Tere is a blueprint for eac test (e.g., grade 3 Englis, grade 5 matematics, grade 8 science, U.S. History). Eac blueprint contains te following information: 1. Test Development Guidelines: guidelines used by te testing contractor and te members of te Content Review Committees in developing te SOL tests. Tis section contains tree parts: A. General Considerations lists general considerations tat are used in developing te test as well as considerations specific to a particular content area. B. Item Format lists information on ow items for te test are constructed. C. Ancillary Materials lists any materials (e.g., calculators, rulers, protractors, compasses, dictionaries) tat students are allowed to use wile taking eac test. 2. Blueprint Summary Table: a summary of te blueprint wic displays te following information: reporting categories for eac test; number of test items in eac reporting category; Standards of Learning (SOL) included in eac reporting category. SOL are identified by numbers and letters tat correspond to te original SOL document; SOL wic are excluded from te SOL test; number of operational items on te test; number of field-test items on te test; and total number of items (operational and field-test items) on te test. 3. Expanded Blueprint: provides te same information as te Blueprint Summary Table except tat te full text of eac SOL is included. In addition, SOL tat are excluded from te test are categorized by te reason tey are not included. 1

5 Wat is a reporting category? Eac test covers a number of SOL. In te test blueprint, SOL are grouped into categories tat address related content or skills. Tese categories are labeled Reporting Categories. For example, a Reporting Category for te Grade 5 Matematics test is Computation and Estimation. Eac of te SOL in tis reporting category addresses computation using addition, subtraction, multiplication, or division or requires te student to estimate te answer to a problem. Wen te results of te SOL tests are reported, te scores will be presented in terms of scores for eac Reporting Category and a total test score. Eac SOL is assigned to only one reporting category. Will all SOL listed in te blueprint be assessed eac time te SOL tests are given? Due to te large number of SOL in a content area for a grade span, every SOL will not be assessed on every SOL test form. By necessity, to keep te lengt of a test reasonable, eac test will sample from te SOL witin a reporting category. However, every SOL is eligible for inclusion on eac form of an SOL test. 2

6 Algebra I Test Development Guidelines A. General Considerations 1. All items included in tis test will address te knowledge and skills specified in te 2001 Virginia Standards of Learning in Algebra I. 2. Te items will be free of stereotyping or bias directed at a particular age, gender, economic status, racial, etnic or religious group, or geograpic region. 3. Te test will be untimed. 4. Tere is no penalty for guessing. Students scores will be based on te number of correct answers out of te total number of operational items on te test. 5. Were appropriate, real-life examples and situations tat te student would likely encounter will be used to present data or ask questions. 6. Items will be appropriate for adolescents in terms of difficulty, interest, and reading level. 7. Students will be permitted scratc paper at any time during te test. 8. Students will be permitted to use only graping calculators during te test. Te calculator s memory must be reset prior to test administration, clearing all memory contents not built into te calculator s system. 9. Students will be permitted to use standard (e.g., inces) and metric rulers during te test. 10. Students will be provided a formula seet and an approximation of pi (π). A copy of te formula seet follows te expanded blueprint. B. Item Format 1. Eac item will be a multiple-coice item containing four coices. Coices suc as None of te above, All of te above, and Not ere will not be used. 2. Answer coices will be arranged vertically beneat te item stems unless space considerations prevent suc an arrangement. 3. Item stems will be in te form of questions or in te form of sentences tat require completion. Incomplete sentences will be followed by a das. 4. In most cases, numbers will be expressed as numerals. 5. Commas will be used in numerals of 4 or more digits. 6. Answer coices will be arranged in ascending or descending order, wen appropriate. 7. Any decimal fraction less tan 1 will include a leading zero. 8. Grapic displays, item stems, and answer coices will all appear on te same page. 9. Fractions will be written vertically. 10. Radicals beyond square roots will not be used. 11. Te symbol for subtraction will be differentiated from te symbol for a negative number (e.g., 3 7 = 4). C. Ancillary Materials 1. Ruler 2. Scratc paper 3. Graping calculator 4. Algebra I Formula Seet 3

7 Algebra I Blueprint Summary Table Reporting Categories No. of Items SOL Expressions and Operations 12 A.2 A.10 A.11 A.12 A.13 Relations and Functions 12 A.5 A.15 A.18 Equations and Inequalities 18 A.1 A.3 A.6 A.7 A.8 A.9 A.14 Statistics 8 A.4 A.16 A.17 Total Number of Operational Items 50 Field-Test Items* 10 Total Number of Items 60 *Tese field-test items will not be used to compute students scores on te test. 4

8 Expanded Blueprint Algebra I SOL Reporting Category: Expressions and Operations Number of Items: 12 Algebra I SOL in Tis Reporting Category: A.2 Te student will represent verbal quantitative situations algebraically and evaluate tese expressions for given replacement values of te variables. Students will coose an appropriate computational tecnique, suc as mental matematics, calculator, or paper and pencil. A.10 Te student will apply te laws of exponents to perform operations on expressions wit integral exponents, using scientific notation wen appropriate. A.11 Te student will add, subtract, and multiply polynomials and divide polynomials wit monomial divisors, using concrete objects, pictorial and area representations, and algebraic manipulations. A.12 Te student will factor completely first- and second-degree binomials and trinomials in one or two variables. Te graping calculator will be used as a tool for factoring and for confirming algebraic factorization. A.13 Te student will express te square root of a wole number in simplest radical form and approximate square roots to te nearest tent. Reporting Category: Relations and Functions Number of Items: 12 Algebra I SOL in Tis Reporting Category: A.5 Te student will create and use tabular, symbolic, grapical, verbal, and pysical representations to analyze a given set of data for te existence of a pattern, determine te domain and range of relations, and identify te relations tat are functions. A.15 Te student will, given a rule, find te values of a function for elements in its domain and locate te zeros of te function bot algebraically and wit a graping calculator. Te value of f(x) will be related to te ordinate on te grap. A.18 Te student will analyze a relation to determine weter a direct variation exists and represent it algebraically and grapically, if possible. 5

9 Expanded Blueprint Algebra I SOL Reporting Category: Equations and Inequalities Number of Items: 18 Algebra I SOL in Tis Reporting Category: A.1 Te student will solve multistep linear equations and inequalities in one variable, solve literal equations (formulas) for a given variable, and apply tese skills to solve practical problems. Graping calculators will be used to confirm algebraic solutions. A.3 Te student will justify steps used in simplifying expressions and solving equations and inequalities. Justifications will include te use of concrete objects; pictorial representations; and te properties of real numbers, equality, and inequality. A.6 Te student will select, justify, and apply an appropriate tecnique to grap linear functions and linear inequalities in two variables. Tecniques will include slope-intercept, x- and y-intercepts, graping by transformation, and te use of te graping calculator. A.7 Te student will determine te slope of a line wen given an equation of te line, te grap of te line, or two points on te line. Slope will be described as rate of cange and will be positive, negative, zero, or undefined. Te graping calculator will be used to investigate te effect of canges in te slope on te grap of te line. A.8 Te student will write an equation of a line wen given te grap of te line, two points on te line, or te slope and a point on te line. A.9 Te student will solve systems of two linear equations in two variables bot algebraically and grapically and apply tese tecniques to solve practical problems. Graping calculators will be used as bot a primary tool of solution and to confirm an algebraic solution. A.14 Te student will solve quadratic equations in one variable bot algebraically and grapically. Graping calculators will be used bot as a primary tool in solving problems and to verify algebraic solutions. 6

10 Expanded Blueprint Algebra I SOL Reporting Category: Statistics Number of Items: 8 Algebra I SOL in Tis Reporting Category: A.4 Te student will use matrices to organize and manipulate data, including matrix addition, subtraction, and scalar multiplication. Data will arise from business, industrial, and consumer situations. A.16 Te student will, given a set of data points, write an equation for a line of best fit and use te equation to make predictions. A.17 Te student will compare and contrast multiple one-variable data sets, using statistical tecniques tat include measures of central tendency, range, and box-and-wisker graps. 7

11 Algebra I Formula Seet Geometric Formulas b r l b s 1 2 A = b b A = b l w V = lw S.A.= 2(lw + l + w) 1 V = 3 r 2 S.A.= r(l + r) p = 4s A = s 2 s b 1 b 2 1 A = 2 (b 1 + b 2 ) V = r 2 S.A.= 2 r( + r) r l B V = B S.A.= lp + B w r a c l p = 2(l + w) A = lw C = 2 r A = r 2 b c 2 = a 2 + b 2 milligram mg gram g kilogram kg milliliter ml liter L kiloliter kl millimeter mm centimeter cm meter m kilometer km square centimeter cm 2 cubic centimeter cm 3 Abbreviations ounce pound quart gallon inc foot yard mile square inc square foot cubic inc cubic foot oz lb qt gal. in. ft yd mi. sq in. sq ft cu in. cu ft Pi Quadratic Formula x = b ± b2 4ac 2a volume total surface area area of base V S.A. B year mont our minute second yr mon r min sec 2003 by te Commonwealt of Virginia Department of Education, James Monroe Building, 101 N. 14t Street, Ricmond, Virginia, All rigts reserved. Except as permitted by law, tis material may not be reproduced or used in any form or by any means, electronic or mecanical, including potocopying or recording, or by any information storage or retrieval system witout written permission from te copyrigt owner. Please contact te Commonwealt of Virginia Department of Education at (804) , Division of Assessment and Reporting, to request written permission