Report On The 2008 FCAT Mathematics Released Items
MATHEMATICSFlorida Solves!Report on the2008 FCAT MathematicsReleased ItemsGrades 5, 8 & 10 Florida Comprehensive Assessment Test
Copyright Statement for This Assessment and School Performance PublicationAuthorization for reproduction of this document is hereby granted to persons acting in an official capacity within the UniformSystem of Public K–12 Schools as defined in Section 1000.01(4), Florida Statutes. The copyright notice at the bottom of thispage must be included in all copies.All trademark and trade names found in this publication are the property of their respective owners and are not associated withthe publishers of this publication.Permission is NOT granted for distribution or reproduction outside of the Uniform System of Public K–12 Schools or forcommercial distribution of the copyrighted materials without written authorization from the Florida Department of Education.Questions regarding use of these copyrighted materials should be sent to the following:The AdministratorAssessment and School PerformanceFlorida Department of Education325 West Gaines StreetTallahassee, Florida 32399-0400Copyright 2008State of FloridaDepartment of State
Table of Contents2Preface3Sunshine State StandardsBackground Information About FCAT Mathematics Florida Comprehensive Assessment Test (FCAT) DesignMathematics Standards, Benchmarks, and StrandsTest Item FormatsHow FCAT Mathematics Is ScoredHolistic ScoringScoring Tools for FCAT Mathematics9Grade 5 Short-Response Performance TaskMathematics Short-Response Performance Task from FCAT 2008Anchor SetQualifying Set57Grade 8 Short-Response Performance TaskMathematics Short-Response Performance Task from FCAT 2008Anchor SetQualifying Set103Grade 10 Short-Response Performance TaskMathematics Short-Response Performance Task from FCAT 2008Anchor SetQualifying Set153AppendicesAppendix AAppendix BAppendix CFCAT Mathematics Short-Response and Extended-Response RubricsMathematics Reference SheetsScorer Bias1
Florida Solves!2008 Florida Reads! Writes! Solves! Inquires! CDPrefaceThe Florida Department of Education (DOE) began publishing Florida Writes! publications in 1992 as anannual report on the spring writing assessment that later became FCAT Writing. In 2002, the DOE addedannual publications for FCAT Reading, Mathematics, and Science that featured the short-response itemsreleased on the individual student reports. This set included the following publications: Florida Inquires! Report on the [year] FCAT Science Released Items (Grades 5, 8, and 11);Florida Reads! Report on the [year] FCAT Reading Released Items (Grades 4, 8, and 10);Florida Solves! Report on the [year] FCAT Mathematics Released Items (Grades 5, 8, and 10); andFlorida Writes! Report on the [year] FCAT Writing Assessment (three separate publications forGrades 4, 8, and 10).The 2006 and 2007 versions of these print publications are available on the DOE website athttp://fcat.fldoe.org/fcatflwrites.asp. The DOE will not produce these print publications in 2008 andbeyond but much of the information related to scoring appears on this CD, the Florida Reads! Writes!Solves! Inquires! CD (FRWSI CD). Additional information about FCAT reports can be found inUnderstanding FCAT Reports 2008 and on the FCAT home page of the Florida Department of Education(DOE) website at http://www.fldoe.org.The FRWSI CD provides educators with the annotated papers used to train handscorers for the releasedFCAT Writing prompts and released FCAT Reading, Mathematics, and Science performance tasks. Foreach featured item, the CD provides the item as it appeared on the test, a top-score response for that item,images of student responses, and annotated training papers from the anchor set and one qualifying set.The CD includes Reading, Writing, Mathematics, and Science on a single CD and provides generalinformation about FCAT performance tasks, the FCAT handscoring process, scoring rubrics, and FCATresources. This CD is produced annually and delivered to districts in July.This CD provides general information about the scoring of the FCAT Mathematics performancetasks and guidelines used to score the 2008 released short-response performance tasks. Eachmathematics task on this CD includes the following: the general rubric for each score point;the actual task as it appeared in 2008 on the FCAT;the scoring guide for that task, which includes an example of a top-score response;annotated anchor papers, representing the range of score points (2, 1, and 0); andannotated qualifying papers.The anchor papers and qualifying papers are student responses that were scored by a committee of Floridaeducators. The qualifying papers were used as a portion of the qualifying examination required forpotential scorers. Florida Department of Education FCAT 20082
Florida Solves!2008 Florida Reads! Writes! Solves! Inquires! CDSunshine State StandardsDevelopment of the Sunshine State Standards began in 1993, and the Standards were adopted by theState Board of Education in May 1996 to provide expectations for student achievement in Florida.The Standards were written in seven subject areas, each divided into four separate grade clusters(PreK–2, 3–5, 6–8, and 9–12). This format was chosen to provide flexibility to school districts indesigning curricula based on local needs. As Florida moved toward greater accountability for studentachievement at each grade level, the Sunshine State Standards were further refined. In the subjectareas of language arts, mathematics, science, and social studies, the Sunshine State Standards wereexpanded to include Grade Level Expectations (GLEs) for PreK–8.Background Information About FCAT Mathematics Florida Comprehensive Assessment Test (FCAT) DesignThe FCAT was originally designed to measure the reading and mathematics content defined by theSunshine State Standards. The state writing assessment, first administered in 1992, became part of theFCAT in 1998 and was expanded to include multiple-choice questions in 2006. A test of the scienceSunshine State Standards was added to the FCAT in 2003. The test questions and prompts are written tomeasure benchmarks from the Sunshine State Standards that identify what students are expected to knowand demonstrate in reading, mathematics, writing, and science.The FCAT is different from other tests students take in three important ways. First, the FCAT is theonly test administered in all Florida public schools that is directly linked to the SunshineState Standards.Second, the FCAT is designed to represent the kinds of tasks and activities expected as part of goodinstruction. In the FCAT Mathematics, Reading, and Science tests, this is accomplished by presentingon the test the types of information and questions that students encounter in the classroom. In FCATWriting , students respond to topics similar to those used in the classroom.Third, the FCAT demands a more in-depth understanding and application of information than is typicalof many standardized tests. The FCAT Mathematics, Reading, and Science tests require students toanalyze, synthesize, and evaluate information and to apply strategies or procedures they have learned.Similarly, FCAT Writing requires students to demonstrate and apply their writing skills by drafting anoriginal piece of writing in response to a real-world prompt, and respond to multiple-choice questionsthat assess students’ skills with sentence structure, spelling, usage, and grammar. Florida Department of Education FCAT 20083
Florida Solves!2008 Florida Reads! Writes! Solves! Inquires! CDMathematics Standards, Benchmarks, and StrandsThe Sunshine State Standards define the content standards for which test items are developed. TheSunshine State Standards identify the knowledge and skills that students are expected to acquire andinclude an expectation that students become creative and critical thinkers. The importance of thinkingskills and problem solving is identified in Florida’s System of School Improvement and Accountability, inStandard 4 of Goal 3: “Florida students use creative thinking skills to generate new ideas, make the bestdecisions, recognize and solve problems through reasoning, interpret symbolic data, and develop efficienttechniques for lifelong learning.” FCAT test items and performance tasks are developed with the intent ofreinforcing the thinking and problem-solving abilities envisioned by this standard.The term benchmark refers to a knowledge and skill statement presented in the Sunshine State Standards.The benchmarks are statements of expected student achievement and are specific to different grade levels.In some cases, for assessment purposes, two or more related benchmarks are grouped together becausethe assessment of one benchmark necessarily addresses the other benchmark. More information on theassessment of these benchmarks can be found in the FCAT Mathematics Test Item Specifications.The Sunshine State Standards contain benchmarks in the area of mathematics. For the purpose ofreporting FCAT results, mathematics benchmarks are organized into five reporting categories calledcontent strands.Strand 1Strand 2Strand 3Strand 4Strand 5Number Sense, Concepts, and OperationsMeasurementGeometry and Spatial SenseAlgebraic ThinkingData Analysis and ProbabilityThe specific content strand, standard, and benchmark for each performance task contained on this CD isfollowed by an image of the actual mathematics task as it appeared in 2008 on the FCAT. Florida Department of Education FCAT 20084
Florida Solves!2008 Florida Reads! Writes! Solves! Inquires! CDTest Item FormatsMathematics test items at Grades 5, 8, and 10 are framed in the context of the Sunshine State Standardscontent areas: the arts, social studies, science, mathematics, foreign language, literature, andhealth/physical education. Students are asked to solve problems that incorporate actual situations andnumerical values, such as the distance between planets in the solar system.On FCAT Mathematics tests, students respond to three kinds of questions. Multiple-choice questions require students to choose the correct answer from four possible choices. Gridded-response questions require students to solve a problem and to bubble their numeric answersin answer grids. Students must solve these problems on their own without being able to guess, as theycan with multiple-choice questions. In some cases, the correct answer can be represented in more thanone way, such as when one student uses decimal fractions and another student uses common fractionsto respond to a problem. Similarly, more than one answer can be correct, as can happen when there isa range of acceptable answers. Performance tasks require students to think about a problem, develop a strategy, and record theirstrategy and solution. There are two kinds of performance tasks: short-response tasks, which requireapproximately five minutes to answer, and extended-response tasks, which require about ten to fifteenminutes to answer.To emphasize the thinking required, the performance tasks in mathematics are labeled “Think, Solve,Explain.” For these questions, students are required to respond to a problem, and the response is laterscored by teams of trained scorers. About 20 percent of the total score points of a test are generated bythese performance tasks; the remaining score points come from multiple-choice andgridded-response questions.Examples of FCAT test items for all grade levels are contained in Sample Test Books for FCATReading, Writing , Mathematics, and Science. Sample Test Materials and released FCATMathematics test items and answer keys are distributed to school districts prior to the FCATadministration each year and can be downloaded from the FCAT home page on the DOE websiteat http://www.fldoe.org. (See the Resources section of this CD.) Florida Department of Education FCAT 20085
Florida Solves!2008 Florida Reads! Writes! Solves! Inquires! CDHow FCAT Mathematics Is ScoredThe FCAT is scored both manually and electronically. All completed answer documents are scannedusing a process called imaging, which involves capturing electronic images of the pages that includestudents’ answers in their own handwriting. Students’ multiple-choice and gridded responses aremachine-scored using computer programs that read the students’ bubbled answers and evaluate thembased on an answer key. Students’ answers to the performance tasks, however, must be scored by trainedscorers using a process commonly called handscoring.The handscoring of students’ written responses is conducted by professional scorers. These scorers arerequired to have college degrees and are specially trained to score student papers. Scorers may only usethe FCAT scoring rubrics and item-specific scoring criteria that have been established and validated bycommittees of Florida educators at FCAT Rangefinding meetings. (The general scoring rubrics can befound in Appendix A.)After mathematics performance tasks are field tested, committees of Florida mathematics teachers andadministrators works with Florida Department of Education staff at FCAT Rangefinding meetings toscore a sample of these papers. A top-score response for each task is defined, and papers representing thepossible scores for that task are identified (4, 3, 2, 1, and 0 for extended-response tasks and 2, 1, and 0 forshort-response tasks). In this way, clear definitions of each score point are developed, and model papers,called anchor papers, are selected to represent the range of responses for each possible score point.These field-test papers, scored by committees of Florida educators, become the training materials for theprofessional scorers. This process and the quality control measures (reliability and validity checks)implemented during scoring ensure that all performance tasks are scored according to the scoring criteriaset by Rangefinding committees. Each student response is read independently by at least two professionalscorers. For short-response performance tasks, if the scorers’ two scores are not identical, a third scorerreviews the scoring to resolve the difference. If the first two scores are adjacent, the higher of the twoscores is used. For extended-response performance tasks, a third scorer is used if the first two scores arenonadjacent, that is, if they differ by more than one point. This third scoring, called resolution scoring, isperformed by a scoring supervisor. All scoring is monitored by Florida Department of Education staff.Scores from the handscoring process are combined with scores from the machine-scoring process tocreate a record for each student. The student’s total scale score is created by a computer-based analysisprocedure that combines the scores from the various types of test items. Scale scores are used to reportstudent results because of their precision and because they can be equated from year to year. Equatingscores ensures the same standard of achievement is used each year. In this way, scores can becompared from year to year, and the progress of students and schools can be evaluated fairly.More information about the scoring of performance tasks can be found in the FCAT Handbook—A Resource for Educators, which is available on the DOE website athttp://fcat.fldoe.org/handbk/fcathandbook.asp. Florida Department of Education FCAT 20086
Florida Solves!2008 Florida Reads! Writes! Solves! Inquires! CDHolistic ScoringWhat is holistic scoring? Student responses to the FCAT Mathematics performance tasks are scoredholistically. The term holistic is used to emphasize the importance of the whole work, including theinterdependence of its parts. A rubric is used to evaluate student responses to each task. Different rubricsare used for the two different types of tasks, short- and extended-response. Holistic scoring is a method ofevaluation that is used in many state assessments and involves judging a student response for its totaleffect. No single factor is weighted to the exclusion of any other.Analytic scoring, on the other hand, is a method of scoring in which separate judgments or ratings aremade for each of several traits. In mathematics, for example, the scorer might evaluate such traits asprocedures (computation), reasoning, and communication, giving a separate score for each. It isimportant to note that separate analytic judgments are not made when scoring the FCAT performancetasks. By scoring holistically, scorers take all traits into consideration and give a single, overall score.Potential bias issues are also discussed with scorers. (See Appendix C.)What is a rubric? A rubric is a general guide for scoring. It identifies the performance features to beevaluated and describes how performance varies across the scoring scale. For the FCAT Mathematicsextended-response tasks, a 4-point rubric is used (4, 3, 2, 1, 0). A 2-point rubric (2, 1, 0) is used for shortresponse tasks. (Appendix A includes the 2-point and 4-point rubrics used for scoring the FCATMathematics performance tasks.) The 2-point rubric precedes each short-response performance task onthis CD as well.What are anchor papers? Anchor papers (also called rangefinding papers) are actualunedited student responses demonstrating typical performance for each point in the rubric. Thesepapers are used to train professional scorers to recognize, for example, what a score point 4response looks like or what a score point 2 response looks like. Anchor papers also help scorersassign score points during live scoring.What are qualifying papers? Qualifying papers are sets of student responses given to potentialscorers to test their understanding of the scoring criteria for each item. These papers have been pre-scoredby committees of Florida educators and the DOE. In order to qualify to score student responses,potential scorers must receive a passing score on the qualifying sets.What are annotations? Annotations explain the reasoning associated with a particular score on aspecific student response. They describe the strengths and weaknesses of a paper. Annotations are used totrain scorers by giving them insights into the skills and processes that students use in responding toperformance tasks. Florida Department of Education FCAT 20087
Florida Solves!2008 Florida Reads! Writes! Solves! Inquires! CDScoring Tools for FCAT MathematicsTwo additional scoring tools are available for scorers of the FCAT Mathematics performance tasks. General Scoring Rubrics are available for both the short-response tasks and the extended-responsetasks. (See Appendix A.) These rubrics describe the characteristics associated with each score point.Because they are general, these rubrics apply to all mathematics performance tasks.The Example of a Top-Score Response displays one example of a correct and complete response forthat particular task. For those tasks that have more than one acceptable answer, the top-scoreresponse provides the range of acceptable answers.When used in combination with the anchor responses and annotations, these scoring tools give scorersand teachers a clear and comprehensive understanding of how to interpret and evaluate students’responses to the FCAT Mathematics performance tasks. Florida Department of Education FCAT 20088
Florida Solves!2008 Florida Reads! Writes! Solves! Inquires! CDGrade 5Short-Response Performance Task Calculators are not used on Grade 5 FCAT Mathematics.Any formulas that students need for answering Grade 5 FCATMathematics questions are provided with the questions.General Short-Response Scoring RubricScoreDescription2A score of two indicates that the student has demonstrated a thoroughunderstanding of the mathematics concepts and/or procedures embodied inthe task. The student has completed the task correctly, in a mathematicallysound manner. When required, student explanations and/or interpretations areclear and complete. The response may contain minor flaws that do not detractfrom the demonstration o
annotated anchor papers, representing the range of score points (2, 1, and 0); and . numerical values, such as the distance between planets in the solar system. On FCAT Mathematics tests, students respond to three kinds of questions. . Sample Test Books . for FCAT Reading, Writing , Mathematics, and Science. Sample Test Materials and .
FCAT What is the FCAT 2.0? FCAT – Florida Comprehensive Assessment Test The FCAT is a test given to Florida students to determine what they know and can do in reading, math, writing, and science. The FCAT was developed by the state of Florida and first administered in 1998. FCAT 2.0 Reading, Math and Science will be
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February 10-17 Delivery of Spring 2015 FCAT/FCAT 2.0 Retake and/or NGSSS EOC Assessments Test Administration Manuals, via Comet Delivery Services. - February 18, 20 or 23 Attend mandatory Spring 2015 FSA, FCAT/FCAT 2.0, and EOC Assessments School Assessment Coordinator live training. Attend mandatory District ITS training.
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