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

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1 SUNSHINE STTE STNDRDS MTHEMTICS ENCHMRKS ND 2005 TO 2009 CONTENT FOCUS GRDE 8 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 ssessment Test (FCT) 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 -E. enchmarks code and description as delineated in the SSS. Item format, as per the way the benchmarks are assessed on the FCT. 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, FCT 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. thorough review of the FCT 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 FCT, 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 MTHEMTICS ENCHMRKS SSESSED T GRDE 8 Strand enchmark Description Item Format M M M M M M M M M M M ssociates verbal names, written word names, and standard numerals with integers, fractions, decimals; ssessed numbers expressed as percents; numbers with with exponents; numbers in scientific notation; radicals; absolute value; and ratios. Understands the relative size of integers, fractions, and decimals; numbers expressed as percents; numbers with exponents; numbers in scientific notation; radicals; MC absolute value; and ratios. Understands concrete and symbolic representations of ssessed rational numbers and irrational numbers in real-world with situations. and D Understands that numbers can be represented in a variety of equivalent forms, including integers, fractions, decimals, percents, scientific notation, exponents, radicals, and absolute value. (lso assesses and.1.3.3) Understands and uses exponential and scientific notation. Understands the structure of number systems other than the decimal number system. Understands and explains the effects of addition, subtraction, multiplication, and division on whole numbers, fractions, including mixed numbers, and decimals, including the inverse relationships of positive and negative numbers. Selects the appropriate operation to solve problems involving addition, subtraction, multiplication, and division of rational numbers, ratios, proportions, and percents, including the appropriate application of the algebraic order of operations. dds, subtracts, multiplies, and divides whole numbers, decimals, and fractions, including mixed numbers, to solve real-world problems, using appropriate methods of computing, such as mental mathematics, paper and pencil, and calculator. Uses estimation strategies to predict results and to check the reasonableness of results. (lso assesses.4.2.1,.2.3.1, and.3.3.1) Uses concepts about numbers, including primes, factors, and multiples, to build number sequences. MC, GR MC, GR N MC MC, GR MC, GR MC ssessed with D and D Total Number Sense, Concepts, and Operations MC: multiple-choice GR: gridded-response SR: short-response ER: extended-response N: not assessed Page 1 of 3 GRDE 8

4 SSS MTHEMTICS ENCHMRKS SSESSED T GRDE 8 Strand enchmark Description Item Format M M M 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 and cylinders. (lso assesses and.2.3.1) Uses concrete and graphic models to derive formulas for finding rates, distance, time, and angle measures. (lso assesses and.2.3.1). Understands and describes how the change of a figure in such dimensions as length, width, height, or radius affects its other measurements such as perimeter, area, surface area, and volume. (lso assesses C.2.3.1) GR, SR MC, GR MC, GR M M M M Constructs, interprets, and uses scale drawings such as those based on number lines and maps to real-world problems. (lso assesses.2.3.1) Uses direct (measured) and indirect (not measured) ssessed measures to compare a given characteristic in either with.4.3.1, metric or customary units ,.1.3.2, and Solves problems involving units of measure and converts answers to a larger or smaller unit within either the metric or customary system. Solves real-world and mathematical problems involving estimates of measurements including length, ssessed with time, weight/mass, temperature, money, perimeter, area, and volume, in either customary or metric units. MC, GR MC, GR ssessed with M M Selects appropriate units of measurement and determines and applies significant digits in a real-world context. (Significant digits should relate to both instrument precision and to the least precise unit of measurement.) Selects and uses appropriate instruments, technology, and techniques to measure quantities in order to achieve specified degrees of accuracy in a problem situation. N N Total Measurements Understands the basic properties of, and relationships C M.C pertaining to, regular and irregular geometric shapes in two and three dimensions. (lso assesses C.1.2.1) MC C C C M.C M.C M.C Understands the geometric concepts of symmetry, reflections, congruency, similarity, perpendicularity, parallelism, and transformations, including flips (reflections), slides (translations), turns (rotations), and enlargements. (lso assesses.1.3.3, C.1.2.1, C.1.3.1, and C.3.3.1) MC, ER Predicts and verifies patterns involving tessellations (a covering of a plane with congruent copies with of the ssessed same pattern with no holes and no overlaps, like floor with C tiles). Represents and applies geometric properties and relationships to solve real-world and mathematical problems. (lso assesses C.2.3.1, C.2.3.2, and C.3.2.2) MC, SR C M.C Identifies and plots ordered pairs in all four quadrants of a rectangular coordinate system (graph) and applies MC simple properties of lines. C Total Geometry and Spatial Sense MC: multiple-choice GR: gridded-response SR: short-response ER: extended-response N: not assessed Page 2 of 3 GRDE 8

5 SSS MTHEMTICS ENCHMRKS SSESSED T GRDE 8 Strand enchmark Description Item Format D D D D M.D M.D M.D M.D Describes a wide variety of patterns, relationships, and functions through models, such as manipulatives, tables, graphs, expressions, equations, and inequalities. (lso assesses.5.3.1) Creates and interprets tables, graphs, equations, and verbal descriptions to explain cause-and- effect relationships. (lso assesses.5.3.1) Represents and solves real-world problems graphically, with algebraic expressions, equations, and inequalities. (lso assesses.1.3.3) Uses algebraic problem-solving strategies to solve realworld problems involving linear equations and inequalities MC, GR MC, GR, SR MC, SR MC, GR D Total lgebraic Thinking E M.E Collects, organizes, and displays data in a variety of forms, including tables, line graphs, charts, and bar MC, GR, graphs, to determine how different ways of presenting SR data can lead to different interpretations. (lso assesses E.1.3.3) Understands and applies the concepts of range and E M.E central tendency (mean, median, and mode). (lso MC, GR assesses E.1.3.3) E M.E nalyzes real-world data by applying appropriate ssessed formulas for measures of central tendency and with E organizing data in a quality display, using appropriate and E technology, including calculators and computers. E M.E Compares experimental results with mathematical expectations of probabilities. MC E M.E Determines odds for and odds against a given situation. (lso assesses E.2.2.2) MC Formulates hypotheses, designs experiments, collects and interprets data, and evaluates hypotheses by E M.E making inferences and drawing conclusions based on statistics (range, mean, median, and mode) and tables, graphs, and charts. (lso assesses E.3.3.2) MC E M.E Identifies the common uses and misuses of probability or statistical analysis in the everyday world. ssessed with E E Total Data nalysis and Probability Grand Total MC: multiple-choice GR: gridded-response SR: short-response ER: extended-response N: not assessed Page 3 of 3 GRDE 8

6 ppendix Overview of FCT Mathematics Content Focus What is content focus? Content focus is a descriptor that defines the specific content measured by each FCT test item. Sunshine State Standards (SSS) benchmarks are often very broad statements of knowledge or skills. s 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 FCT Mathematics March dministration. 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 FCT 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 FCT MTHEMTICS CONTENT FOCUS GRDE 8 enchmark 2005 Content Focus Number of Possible Number Sense, Concepts and Operations 132 Relative size of numbers Fractions/percents Exponential notation Scientific notations Distributive property Effects of operations Order of operations Decimal computation Fractional computation Percent decrease Whole number computation Time estimate 1 Measurement 131 Volume* Perimeter Time Rate Change in volume Change in area Scale drawing Customary capacity 1 Geometry and Spatial Sense C131 ngles 1 C131 Two-dimensional figures 1 C231 Perpendicularity 1 C231 Similarity* 4 C331 Reflections* 2 C331 Similarity 1 C332 Coordinate identifying 1 C332 Slope 1 lgebraic Thinking D131 Functions 1 D131 Number sequences 1 D132 Evaluating expressions 1 D132 Generalizing rules/expressions* 2 D231 Equations* 2 D231 Graphic representations of equations/inequalities 1 D232 Solving equations 3 D232 Translating inequalities 1 Data nalysis and Probability E131 Line graphs 1 E131 Scatter plots 1 E131 Interpretation of data* 4 E132 Mean 2 E132 Median 1 E232 Odds 1 E331 Interpretation of data 2 * Includes Performance Task Item GRND TOTL Grade 8 ppendix: Page 1 of 5 Source:

8 FCT MTHEMTICS CONTENT FOCUS GRDE 8 enchmark 2006 Content Focus Number of Possible Number Sense, Concepts and Operations 132 Order of numbers Fractions/percents Scientificl notation Inverse operations Effects of operations Order of operations Decimal computation Sales tax Percent computation rea estimate Estimate 1 Measurement 131 Surface area* rea Time Rate Change in volume Change in area Scale drawing Customary capacity 1 Geometry and Spatial Sense C131 ngles 1 C131 Circles 1 C231 Similarity* 4 C231 Pythagorean theorem 1 C331 Transformations* 2 C331 Reflections 1 C332 Coordinate identifying 1 C332 Midpoint 1 lgebraic Thinking D131 Functions 1 D131 Graphic patterns 1 D132 Linear equations 1 D132 Solving equations* 2 D231 Equations* 2 D231 Inequalities 1 D232 Solving inequalities 1 D232 Solving equations 2 D232 Translating inequalities 1 Data nalysis and Probability E131 Multiple bar graphs 1 E131 Comparing graphs* 4 E132 Mean 2 E132 Median 1 E231 Comparing theoretical and empirical probabilities 1 E232 Probability 1 E331 Interpretation of data 2 *Includes Performance Task Item GRND TOTL Grade 8 ppendix: Page 2 of 5 Source:

9 FCT MTHEMTICS CONTENT FOCUS GRDE 8 enchmark 2007 Content Focus Number of Possible Number Sense, Concepts and Operations 132 Order of numbers Fractions/percents Scientific notation Effects of operations Order of operations Decimal computation Percent computation Whole number computation rea estimate 2 Measurement 131 Circumference Perimeter Surface area* Rate Change in area Change in dimensions Scale drawing Metric length 1 Geometry and Spatial Sense C131 ngles 1 C131 Irregular polygons 1 C231 Pythagorean theorem 1 C231 Reflections* 4 C331 Transformations 1 C331 Transformations* 2 C332 Coordinate identifying 1 C332 Midpoint 1 lgebraic Thinking D131 Functions 1 D131 Graphic patterns 1 D132 Generalizing rules/expressions 1 D132 Linear equations* 2 D231 Equations* 2 D231 One-variable expressions 1 D232 Evaluating equations 2 D232 Solving equations 1 D232 Translating equations or expressions 1 Data nalysis and Probability E131 Circle graphs 1 E131 Venn diagrams* 4 E132 Mean 1 E132 Median 2 E231 Comparing theoretical and empirical probabilities 1 E232 Probability 1 E331 Collection and interpretation of data 1 E331 Interpretation of data 1 *Includes Performance Task Item GRND TOTL Grade 8 ppendix: Page 3 of 5 Source:

10 FCT MTHEMTICS CONTENT FOCUS GRDE 8 enchmark 2008 Content Focus Number of Possible Number Sense, Concepts and Operations 132 Order of numbers Scientific notation Scientific notation Inverse operations Effects of operations Order of operations Whole number computation Percent computation Decimal computation Percent increase Number estimate rea estimate 1 Measurement 131 Circumference Volume rea* Time Rate Change in volume Change in dimensions Scale drawing Customary capacity 1 Geometry and Spatial Sense C131 ngles 1 C131 Parallel lines 1 C231 Reflections 1 C231 Reflections* 4 C331 Perpendicularity 1 C331 Transformations* 2 C332 Coordinate plotting 1 C332 Midpoint 1 lgebraic Thinking D131 Functions 2 D132 Evaluating expressions 1 D132 Linear equations* 2 D231 Equations* 2 D231 One-variable expressions 1 D232 Evaluating expressions 1 D232 Solving equations 3 Data nalysis and Probability E131 Histograms 1 E131 Venn diagrams* 4 E132 Mean 2 E132 Median 1 E231 Comparing theoretical and empirical probabilities 1 E232 Probability 1 E331 Evaluating hypotheses 1 E331 Interpretation of data 1 *Includes Performance Task Item GRND TOTL Grade 8 ppendix: Page 4 of 5 Source:

11 FCT MTHEMTICS CONTENT FOCUS GRDE 8 enchmark 2009 Content Focus Number of Possible Number Sense, Concepts and Operations 132 Relative size of numbers Fractions/decimals Exponential notation Effects of operations Inverse operations Order of operations Whole number computation Percent computation Decimal computation Volume estimate rea estimate 1 Measurement 131 rea of composite shapes rea of rectangles rea of composite shapes* Rate/average Rate Change in perimeter Change in volume Scale drawing Customary capacity 1 Geometry and Spatial Sense C131 ngles 1 C131 ngle measures 1 C231 Dilations* 4 C231 Reflections 1 C331 Transformations* 2 C331 Transformations 1 C332 Coordinate identifying 1 C332 Midpoint 1 lgebraic Thinking D131 Expressions 1 D131 Graphic patterns 1 D132 Generalizing rules/expressions 1 D132 Linear equations* 2 D231 Equations* 3 D232 Translating equations or expressions 1 D232 Expressions 1 D232 Solving equations 2 Data nalysis and Probability E131 Venn diagrams* 4 E131 Histograms 1 E132 Mean 2 E132 Range 1 E231 Determining outcomes 1 E232 Probability 1 E331 Collection of data 1 E331 Interpretation of data 1 *Includes Performance Task Item GRND TOTL Grade 8 ppendix: Page 5 of 5 Source:

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

SUNSHINE STATE STANDARDS MATHEMATICS ENCHMARKS AND 2005 TO 2009 CONTENT FOCUS Compiled by Dr. Yuwadee Wongbundhit, Executive Director OVERVIEW The purpose of this report is to compile the content focus