Compiled by Dr. Yuwadee Wongbundhit, Executive Director Curriculum and Instruction

Transcription

1 SUNSHINE STATE STANDARDS MATHEMATICS ENCHMARKS AND 2005 TO 2009 CONTENT FOCUS Compiled by Dr. Yuwadee Wongbundhit, Executive Director

2 OVERVIEW The purpose of this report is to compile the content focus of the Mathematics Florida Comprehensive Assessment Test (FCAT) from the 2005 to 2009 March administrations and the scope of the Florida Mathematics Sunshine State Standards (SSS). The SSS benchmarks are grouped by strands. The report includes the following: SSS mathematics strands A-E. enchmarks code and description as delineated in the SSS. Item format, as per the way the benchmarks are assessed on the FCAT. Score points showing the maximum points to be earned for each assessed benchmark. Potential Outcomes of Report Usage Instructional Focus Calendar To prepare an effective instructional focus calendar and mini-assessments, this report should be used with the appendix, FCAT Content Focus, and the Content Scores Report to help in identifying instructional needs. Mathematical Content Focus It is highly recommended to conduct a more in-depth and effective study of grade-specific benchmark. A thorough review of the FCAT Mathematics Item Specifications document includes, but is not limited to, an analysis of the following criteria: 1. benchmark clarification 2. content limits 3. item format o use of graphics o item style o general guidelines o sample items 4. cognitive complexity of mathematics items Instructional Focus To assist in increasing the efficacy of mathematics teaching and learning, this report should be used with the Lessons Learned FCAT, Sunshine State Standards and Instructional Implications For questions and concerns regarding this report, please contact Dr. Yuwadee Wongbundhit, Executive Director,, at or by at ywongbundhit@dadeschools.net.

3 SSS MATHEMATICS ENCHMARKS ASSESSED AT Strand enchmark Description Item Format A MA.A A MA.A A A MA.A MA.A A MA.A A MA.A Associates verbal names, written word names, and standard numerals with integers, rational numbers, irrational numbers, real numbers, and complex with A numbers. Understands the relative size of integers, rational numbers, irrational numbers, and real numbers. Understands concrete and symbolic representations of real and complex numbers in real-world situations. Understands that numbers can be represented in a variety of equivalent forms, including integers, fractions, decimals, percents, scientific notation, exponents, radicals, absolute value, and logarithms. (Also assesses A and A.1.4.3) Understands and uses the basic concepts of limits and infinity. Understands and uses the real number system MC with A MC, GR NA with A.3.4.1, A.3.4.2, and A Understands the structure of the complex number A MA.A NA system. Understands and explains the effects of addition, subtraction, multiplication, and division on real numbers, A MAA341 MA.A including square roots, exponents, and appropriate MC inverse relationships. (Also assesses A.2.4.2) Selects and justifies alternative strategies, such as using properties of numbers, including inverse, identity, A MA.A distributive, associative, transitive, that allow operational shortcuts for computational procedures in real-world or MC mathematical problems. (Also assesses A and A.3.3.2) A MA.A Adds, subtracts, multiplies, and divides real numbers, including square roots and exponents, using appropriate methods of computing, such as mental mathematics, MC, GR paper and pencil, and calculator. (Also assesses A.2.4.2) A MA.A Uses estimation strategies in complex situations to predict results and to check the reasonableness of MC results. (Also assesses A and.3.4.1) A MA.A Applies special number relationships such as sequences and series to real-world problems. NA A Total Number Sense, Concepts, and Operations MC: multiple-choice GR: gridded-response SR: short-response ER: extended-response NA: not assessed 1

4 SSS MATHEMATICS ENCHMARKS ASSESSED AT Strand enchmark Description Item Format MA Uses concrete and graphic models to derive formulas for finding perimeter, area, surface area, circumference, and volume of two and three-dimensional shapes, including rectangular solids, cylinders, cones, and pyramids. (Also assesses and.1.4.2) MC, GR, SR MA MA MA MA MA MA MA Uses concrete and graphic models to derive formulas for finding rate, distance, time, angle measures, and arc lengths. (Also assesses.1.2.2) Relates the concepts of measurement to similarity and proportionality in real-world situations. Selects and uses direct (measured) or indirect (not measured) methods of measurement as appropriate. Solves real-world problems involving rated measures (miles per hour, feet per second). (Also assesses.2.3.2) Solves real-world and mathematical problems involving estimates of measurements, including length, time, weight/mass, temperature, money, perimeter, area, and volume, and estimates the effects of measurement errors on calculations. Determines the level of accuracy and precision, including absolute and relative errors or tolerance, required in real-world measurement situations. Selects and uses appropriate instruments, t technology, and techniques to measure quantities in order to achieve specified degrees of accuracy in a problem situation. MC, GR with C MC MC, GR with A Total Measurements C MA.C Uses properties and relationships of geometric shapes to construct formal and informal proofs. (Also assesses C and C.1.3.1). MC, GR Understands geometric concepts such as perpendicularity, parallelism, tangency, congruency, C MA.C similarity, reflections, symmetry, and transformations MC, GR, including flips (reflections), slides (translations), turns ER (rotations), enlargements, rotations, and fractals. (Also assesses.1.4.3, C.1.4.1, and C.3.4.1) Analyzes and applies geometric relationships involving C MA.C planar cross-sections (the intersection of a plane and a three- dimensional figure). MC Represents and applies geometric properties and C MA.C relationships to solve real-world and mathematical problems including ratio, proportion, and properties of MC, GR right triangle trigonometry. (Also assesses C.2.4.1) C MA.C Using a rectangular coordinate system (graph), applies and algebraically verifies properties of two- and threedimensional figures, including distance, midpoint, slope, MC, GR parallelism, and perpendicularity. (Also assesses C and D.2.4.1) C Total Geometry and Spatial Sense NA NA MC: multiple-choice GR: gridded-response SR: short-response ER: extended-response NA: not assessed 2

5 SSS MATHEMATICS ENCHMARKS ASSESSED AT Strand enchmark Description Item Format D MA.D D MA.D D D MA.D MA.D Describes, analyzes, and generalizes relationships, patterns, and functions using words, symbols, variables, tables, and graphs. Determines the impact when changing parameters of given functions. Represents real-world problem situations using finite graphs, matrices, sequences, series, and recursive relations. Uses systems of equations and inequalities to solve realworld problems graphically, algebraically, and with matrices. (Also assesses D.2.3.1, D.2.3.2, and D.2.4.1) MC, GR MC, GR, SR with C and D MC, GR, SR D Total Algebraic Thinking E MA.E Interprets data that has been collected, organized, and MC, GR, displayed in charts, tables, and plots. (Also assesses ER E and E.1.4.3) Calculates measures of central tendency (mean, E MA.E median, and mode) and dispersion (range, standard deviation, and variance) for complex sets of data and determines the most meaningful measure to describe the data. (Also assesses E.1.4.3) MC, GR Analyzes real-world data and makes predictions of larger populations by applying formulas to calculate E MA.E measures of central tendency and dispersion using the with E sample population data, and using appropriate and E technology, including calculators and computers. Determines probabilities using counting procedures, E MA.E tables, tree diagrams, and formulas for permutations and combinations. (Also assesses E.2.4.2) MC, GR E E E MA.E MA.E MA.E Determines the probability for simple and compound events as well as independent and dependent events. Designs and performs real-world statistical experiments that involve more than one variable, then analyzes results and reports findings. (Also assesses E and E.3.4.2) Explains the limitations of using statistical techniques and data in making inferences and valid arguments. with E MC with E E Total Data Analysis and Probability Grand Total MC: multiple-choice GR: gridded-response SR: short-response ER: extended-response NA: not assessed 3

6 Appendix Overview of FCAT Mathematics Content Focus What is content focus? Content focus is a descriptor that defines the specific content measured by each FCAT test item. Sunshine State Standards (SSS) benchmarks are often very broad statements of knowledge or skills. As test items are developed, the Department of Education and committees of educators identify a more specific statement within the SSS benchmark that describes the content addressed in each item. What information is included in the Content Focus Reports? The Content Focus Reports provide additional information about each reporting category for FCAT Mathematics March Administration. For each test s reporting categories, the reports provide the number of points for items in each category and the content focus for these items. How does the Department use content focus information? Department staff and the FCAT development contractor keep a record of the content focus information to insure that, across the years, items are developed and used that measure the breadth of content in each SSS benchmark. How can I use these reports? District or school curriculum leaders and classroom teachers should find that these reports provide supplemental information on the strengths and weaknesses of instructional programs. The information may be used along with other feedback, such as classroom-level results on reporting categories. The District Report of Schools and the School Report of Students provide the number of points possible and the mean points earned for each reporting category. The mean points earned can be further analyzed by considering these Content Focus Reports.

7 FCAT MATHEMATICS CONTENT FOCUS enchmark 2005 Content Focus Number of Possible Number Sense, Concepts and Operations A142 Relative size of numbers 2 A144 Equivalent forms of numbers 2 A341 Determing the effects of multiple operations 1 A342 Order of operations 1 A343 Solving real world problems involving fractions/decimals 2 A343 Solving real world problems involving percents 2 A441 Number estimate 1 Measurement 141 Area Area of sector* Volume Distance/rate/time Rate Indirect measurement Volume conversion 1 Total 10 Geometry and Spatial Sense C141 Measurement of angles 1 C141 Properties of circles 1 C241 Properties of polygons 1 C241 Pythagorean theorem* 4 C241 Similarity 1 C242 Identifying planar cross sections 1 C341 Pythagorean theorem 1 C341 Similarity 1 C342 Parallelism 1 C342 Slope* 2 Algebraic Thinking D141 Generalizing relationships 3 D141 Numerical pattern 2 D142 Changing cost parameters 1 D142 Changing dimensions 1 D142 Changing measurement parameters* 2 D242 Equations* 2 D242 Graphing systems of equations/inequalities 2 D242 Solving systems of equations/inequalities 1 Data Analysis and Probability E141 Line graphs 1 E141 Multiple line graphs* 4 E142 Mean 1 E241 Combinations 1 E241 Compound event probability 1 E241 Single event probability 1 E341 Evaluating hypotheses 1 E341 Interpretation of data 1 *Includes Performance Task Item GRAND TOTAL Grade 10 Appendix: Page 1 of 5 Source:

8 FCAT MATHEMATICS CONTENT FOCUS enchmark 2006 Content Focus Number of Possible Number Sense, Concepts and Operations A142 Relative size of numbers 1 A144 Equivalent forms of numbers 2 A341 Determining effects of multiple operations 1 A342 Equivalent expressions 1 A343 Solving real world problems 1 A343 Solving real world problems involving percents 1 A343 Solving real world problems involving fractions/decimals 2 A441 Number estimate 1 A441 Area estimation 1 Measurement 141 Perimeter* Area Arc lengths Rate Rate/distance/time Indirect measurement Pythagorean theorem Rated measure 1 Total 10 Geometry and Spatial Sense C141 Interior angles of a polygon 1 C141 Properties of polygons 1 C241 Similarity 1 C241 Pythagorean theorem 1 C241 Properties of geometric figures* 4 C242 Identifying planar cross sections 1 C341 Transformations 1 C341 Pythagorean theorem 1 C342 Parabolic relations 1 C342 Midpoint* 2 Algebraic Thinking D141 Functions 1 D141 Relationship 1 D141 Numerical patterns 2 D141 Generalize patterns 1 D142 Changing measurement parameters* 3 D142 Changing dimensions 1 D242 Equations* 3 D242 Systems of equations/inequalities 1 D242 Solving systems of equations/inequalities 1 Data Analysis and Probability E141 Line graphs* 4 E141 Stem and leaf plots 1 E142 Median 1 E241 Combinations 1 E241 Single event probability 1 E241 Compound event probability 1 E341 Interpretation of data 2 *Includes Performance Task Item GRAND TOTAL Grade 10 Appendix: Page 2 of 5 Source:

9 FCAT MATHEMATICS CONTENT FOCUS enchmark 2007 Content Focus Number of Possible Number Sense, Concepts and Operations A142 Relative size of numbers 1 A144 Equivalent forms of numbers 2 A341 Determining effects of multiple operations 1 A342 Equivalent expressions 1 A343 Solving real world problems 2 A343 Solving real world problems involving fractions/decimals 1 A343 Solving real world problems involving percents 1 A441 Area estimate 1 A441 Length estimate 1 Measurement 141 Area Capacity* Circumference Arc lengths Rate Rate/distance/time Indirect measurement Pythagorean theorem Rated measures 1 Total 10 Geometry and Spatial Sense C141 Angles 1 C141 Circles 1 C241 Properties of geometric figures 1 C241 Pythagorean theorem* 4 C241 Transformations 1 C242 Plane/rectangular prism 1 C341 Similar figures 1 C341 Transformations 1 C342 Distance 1 C342 Slope* 2 Algebraic Thinking D141 Functions 1 D141 Generalize patterns 1 D141 Number sequences 1 D141 Numerical patterns 2 D142 Changing cost parameters* 2 D142 Changing cost parameters 1 D142 Changing dimensions 1 D242 Equations* 2 D242 Functions 1 D242 Graphing systems of equations/inequalities 1 D242 Solving systems of equations/inequalities 1 Data Analysis and Probability E141 Circle graphs* 4 E141 Interpretation of data 1 E142 Range 1 E241 Combinations 1 E241 Compound event probabilty 1 E241 Single event probability 1 E341 Evaluating and formulating hypotheses 1 E341 Table 1 *Includes Performance Task Item GRAND TOTAL Grade 10 Appendix: Page 3 of 5 Source:

10 FCAT MATHEMATICS CONTENT FOCUS enchmark 2008 Content Focus Number of Possible Number Sense, Concepts and Operations A142 Order of numbers 1 A144 Equivalent forms of numbers 2 A341 Extracting square roots 1 A342 Operational shortcuts 1 A343 Solving real-world problems involving fractions/decimals 2 A343 Solving real-world problems involving percents 2 A441 Length estimate 1 A441 Number estimate 1 Measurement 141 Arc lengths* Circumference Volume Arc measures Rate Rate/distance/time Indirect measurement Pythagorean theorem Rated measures 1 Total 10 Geometry and Spatial Sense C141 Measurement of angles 1 C141 Two-dimensional figures 1 C241 Angle relationships in geometric figures 2 C241 Properties of geometric figures* 4 C242 Plane/square pyramid 1 C341 Reflections 1 C341 Similar figures 1 C342 Midpoint* 2 C342 Parabolic relations 1 Algebraic Thinking D141 Functions 2 D141 Graphic patterns 1 D141 Numerical patterns 2 D142 Changing cost parameters* 3 D142 Changing measurement parameters 1 D242 Equations 1 D242 Functions 1 D242 Graphing equations/inequalities* 2 D242 Systems of equations/inequalities 1 Data Analysis and Probability E141 Charts 1 E141 Circle graphs* 4 E142 Median 1 E241 Combinations 1 E241 Compound event probability 1 E341 Single event probability 1 E341 Evaluating and formulating hypotheses 2 *Includes Performance Task Item GRAND TOTAL Grade 10 Appendix: Page 4 of 5 Source:

11 FCAT MATHEMATICS CONTENT FOCUS enchmark 2009 Content Focus Number of Possible Number Sense, Concepts and Operations A142 Relative size of numbers 1 A144 Equivalent forms of numbers 1 A144 Equivalent forms of numbers 1 A341 Determining effects of multiple operations 1 A342 Order of operations 1 A343 Solving real-world problems 1 A343 Solving real-world problems involving fractions/decimals 1 A343 Solving real-world problems involving percents 1 A343 Solving real-world problems 1 A441 Area estimate 2 Measurement 141 Circumference Volume* Surface area Rate Time Pythagorean theorem Indirect measurement Rated measures 1 Total 10 Geometry and Spatial Sense C141 Measurement of angles 1 C141 Two-dimensional figures 1 C241 Angle relationships in geometric figures 2 C241 Properties of geometric figures* 4 C242 Plane/square pyramid 1 C341 Reflections 1 C341 Similar figures 1 C342 Midpoint* 2 C342 Parabolic relations 1 Algebraic Thinking D141 Functions 1 D141 Functions 1 D141 Number sequences 1 D141 Numerical patterns 2 D142 Changing parameters 1 D142 Changing dimensions 1 D142 Changing cost parameters* 2 D242 Expressions 1 D242 Graphing equations/inequalities* 2 D242 Solving systems of equations/inequalities 1 D242 Graphing systems of equations/inequalities 1 Data Analysis and Probability E141 Circle graphs* 4 E141 Line graphs 1 E142 Mean 1 E241 Single event probability 1 E241 Compound event probability 1 E241 Combinations 1 E341 Interpretation of data 1 E341 Evaluating and formulating hypotheses 1 *Includes Performance Task Item GRAND TOTAL Grade 10 Appendix: Page 5 of 5 Source: