# FCAT MATHEMATICS CONTENT MATRIX GRADE 6 Benchmarks Grade Level Expectation Clarification Statement Content Limits

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1 MA.A.1.3.1: The student associates verbal names, written word names, and standard numerals with integers, fractions, decimals; numbers expressed as percents; numbers with exponents; numbers in scientific notation; radicals; absolute value; and ratios. MA.A.1.3.2: The student understands the relative size of integers, fractions, and decimals; numbers expressed as percents; numbers with exponents; numbers in scientific notation; radicals; absolute value; and ratios. MA.A.1.3.3: The student understands concrete and symbolic representations of rational numbers and irrational numbers in realworld situations. MA.A.1.3.4: The student understands that numbers can be represented in a variety of equivalent forms, including integers, fractions, decimals, percents, scientific notation, exponents, radicals, and absolute value. MA.A.2.3.1: The student understands and uses exponential and scientific notation. 1. Knows word names and standard numerals for whole numbers, fractions, decimals (through hundred-thousandths), and percents. 2. Reads and writes whole numbers and decimals in expanded form. 1. Compares and orders fractions and decimals using graphic models, number lines, and symbols. 2. Compares and orders fractions, decimals, and common percents. 1. Knows examples of positive rational numbers in real-world situations. 2. Describes the meanings of positive rational numbers using part/whole relationships and relative size comparisons in real-world situations. 3. Constructs models to represent positive rational numbers. 1. Knows the relationships among fractions, decimals, and percents. 2. Expresses a given quantity in a variety of ways, such as fractions, decimals, or numbers expressed as percents. 3. Knows whether numbers expressed in different forms are equal. 4. Converts a number expressed in one form to its equivalent in another form. 1. Knows the meaning and use of exponential notation (for example 2 3 =2x2x2=8) 2. Expresses whole numbers in exponential notation or in factored form. 3. Evaluates numerical expressions that contain exponential notation. Students will identify, order, and/or compare the relative size of numbers. Students will express numbers in equivalent forms. Students will represent or solve a simple problem using numbers in exponential notation. An item may utilize one format or a variety of formats, such as fractions, decimals, and percents. The place values of the fractional parts of decimal numbers should range from tenths through tenthousandths. In items that assess the relationships among fractions, decimals, or numbers expressed as percents, a real-world context should be used. Items will not include repeating decimals. Items will assess exponents no greater than

2 MA.A.2.3.2: The student understands the structure of number systems other than the decimal number system. MA.A.3.3.1: The student 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. MA.A.3.3.2: The student 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. 1. Compares the decimal number system to systems that do not use place value (for example, Roman numeral, ancient Egyptian). 1. Knows the effects of the four basic operations on whole numbers, fractions, mixed numbers, and decimals. 2. Uses models or pictures to show the effects of addition, subtraction, multiplication, and division, on whole numbers, decimals, fractions, and mixed numbers. 3. Knows and applies the commutative, associative, and distributive properties in the addition and multiplication of rational numbers. 4. Uses concrete models and real world examples to explore the inverse relationship of positive and negative numbers.. 1. Knows the appropriate operations to solve real-world problems involving whole numbers, decimals, and fractions. 2. Solves real-world problems involving whole numbers, fractions, decimals, and common percents using one-or two-step problems. 3. Applies order of operations when solving problems (parentheses, multiplication, division, addition, and subtraction). 4. Knows proportional relationships and describes such relationships in words, tables, or graphs. Students will recognize the appropriate operation for a stated effect, the effects of operations, and/or the relationships between operations. Students will simplify mathematical expressions using the correct order of operations or identify the correct order of operations. Items should include one and two-digit non-negative numbers, single-digit positive fractions, and/or decimals to the hundredths place. Items should not involve division by a fraction. Items should include one-or two-digit whole numbers and exponents up to the third power. In order to focus assessment on the order of operations, items should use numbers that students can solve without a calculator. MA.A.3.3.3: The student adds, 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. 1. Solves one-or two-step real-world problems involving whole numbers and decimals using appropriate methods of computation (for example, mental computation, paper and pencil, and calculator). 2. Justifies the choice of method for calculations, such as mental computation, concrete materials, algorithms, or calculators. Students will solve a single- or multi-step problem using appropriate computations. Items should involve only whole numbers and decimal numbers. Items may include problems dealing with percents used to find sales tax, discount, and simple interest

3 MA.A.4.3.1: The student uses estimation strategies to predict results and to check the reasonableness of results. MA.A.5.3.1: The student uses concepts about numbers, including primes, factors, and multiples, to build number sequences. 1. Knows an appropriate estimation technique for a given situation using whole numbers (for example, clustering, compatible number, front-end). 2. Estimates to predict results and to check reasonableness of results. 3. Determines whether an exact answer is needed or an estimate would be sufficient 1. Knows if numbers (less than or equal to 100) are prime or composite. 2. Finds the greatest common factor and least common multiple of two or more numbers. 3. Determines the prime factorization of a number less than or equal to Uses divisibility rules. Students will determine estimates and/or their appropriateness. The data presented to students may be either precise values, a range of values, or a combination of precise values and estimates of other values. Items should be limited to use of whole numbers only. MA.B.1.3.1: The student uses concrete and graphic models to derive formulas for finding perimeter, area, surface area, circumference, and volume of twoand three-dimensional shapes, including rectangular solids and cylinders. 1. Uses concrete and graphic models to create formulas for finding perimeter and area of plane figures and the volume of rectangular solids. 2. Uses concrete and graphic models to discover an approximation for π and creates a formula for finding circumference. Students will solve a problem involving linear measure, weight, capacity, time, temperature, perimeter, area, and volume. The number of two-or three dimensional figures assessed in an item should not exceed two. Items involving volume should emphasize meaning, not computation. Items involving area should be limited to triangles, rectangles, and parallelograms. Items involving volume/capacity should be limited to rectangular prisms. MA.B.1.3.2: The student uses concrete and graphic models to derive formulas for finding rates, distance, time, and angle measures. 1. Identifies a protractor as a tool for measuring angles and measures angles using a protractor. 2. Identifies and names angles according to their measure (including acute, right, obtuse, straight). 3. Classifies triangles according to the measurement of their angles and according to the length of their sides. 4. Determines the measure of a missing angle using angle relationships. Students will solve a problem involving angle measures. Items assessing the measure of a missing angle should use whole numbers of degrees

4 MA.B.1.3.3: The student 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. 1. Given a two-dimensional figure, creates a new figure by increasing or decreasing the original dimensions. 2. Knows the relationship between the area or perimeter of an original figure and that of a newly created figure. 3. Solves real-world or mathematical problems involving perimeter or area and how these are affected by changes in the dimensions of the figure. Students will determine the effects of changing dimensions on other measures or solve problems involving the effects of changing dimensions. The changes in dimensions of a figure that are increases should result in similar figures using scale factors that are whole numbers. The changes in dimensions of a figure that are decreases should result in similar figures using scale factors that are common-unit fractions with denominators of 2, 3, or 4. MA.B.1.3.4: The student constructs, interprets, and uses scale drawings such as those based on number lines and maps to solve real-world problems. 1. Knows proportional relationships in scale drawings. 2. Uses scale drawings to solve real-world problems including distance (as in map reading). Students will interpret and solve a problem using scale drawings. Measurements may be in either metric or customary units. MA.B.2.3.1: The student uses direct (measured) and indirect (not measured) measures to compare a given characteristic in either metric or customary units. 1. Compares objects according to their length, weight or mass, and capacity using customary or metric units. 2. Measures length, weight or mass, and capacity using appropriate measuring instruments. MA.B.2.3.2: The student solves problems involving units of measure and converts answers to a larger or smaller unit within either the metric or customary system. 1. Changes one customary or metric unit of measurement to another within the same system. 2. Uses concrete manipulatives or constructs models of square units (such as square inch and square meter) for measuring area and cubic units (such as cubic centimeter or cubic yard) for measuring volume. Students will solve a problem involving conversions to other units. All conversions of units must be within the same system of measurement (metric or customary). Items should involve only one-unit conversions (e.g., converting seconds to hours) and not mixed units (e.g., converting hours and minutes to seconds)

5 MA.B.3.3.1: The student solves real-world and mathematical problems involving estimates of measurements including length, time, weight/mass, temperature, money, perimeter, area, and volume, in either customary or metric units. 1. Estimates the measure (length, weight, or mass, and capacity) of an object or figure and then compares the estimate with the actual measurement of the object or figure. 2. Knows whether an exact answer is needed or an estimate is sufficient. 3. Estimates solutions to real-world problems by estimating the length, volume or capacity, weight or mass, perimeter, or area of objects or shapes in either customary or metric units. 4. Estimates solutions to real-world problems involving measurement, including estimates of time, temperature and money. MA.B.4.3.1: The student 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). MA.B.4.3.2: The student selects and uses appropriate instruments, technology, and techniques to measure quantities in order to achieve specified degrees of accuracy in a problem situation. 1. Selects the appropriate unit of measure for a given real-world situation. 2. Knows the approximate nature of measurement and measures to the specified degree of accuracy (for example, nearest centimeter or sixteenth of an inch.) 1. Selects and appropriate measurement tool (for example, scales, rulers, thermometers, measuring cups, protractors, gauges). 2. Determines the interval of a scale and reads the scales on a variety of measuring instruments. 3. Measures accurately with the measurement tools

6 MA.C.1.3.1: The student understands the basic properties of, and relationships pertaining to regular and irregular geometric shapes in two- and threedimensions. 1. Identifies, draws, and uses symbolic notation to denote the attributes of two-dimensional geometric figures (including points, parallel and perpendicular lines, planes, rays, and parts of a circle). 2. Knows and draws angles (including acute, obtuse, right, and straight). 3. Analyzes relationships among two dimensional geometric figures (for example, the diagonal of a rectangle divides the rectangle into two congruent triangles each having one half the area of the rectangle). 4. Uses appropriate measuring devices (including ruler and protractor) as needed in analysis of figures. 5. Knows the attributes of and draws threedimensional figures (including rectangular solids and cylinders). 6. Knows the properties of two-and threedimensional figures. Students will identify and/or analyze two- and threedimensional shapes using their basic properties and relationships. Items will assess identifying points, parallel and perpendicular lines, planes, rays, parts of a circle, diagonals, and types of angles. Items assessing threedimensional figures should use rectangular prisms or right circular cylinders only. Items should utilize only a single figure, with no comparisons to other figures or transformations. MA.C.2.3.1: The student understands the geometric concepts of symmetry, reflections, congruency, similarity, perpendicularity, parallelism, and transformations, including flips, slides, turns, and enlargements. 1. Uses manipulatives and drawings to solve problems requiring spatial visualization. 2. Describes and applies the property of symmetry in figures. 3. Recognizes and draws congruent and similar figures 4. Identifies and performs the various transformations (reflection, translation, rotation) of a given figure on a coordinate plane. Students will identify and/or apply various geometric concepts, including symmetry, congruency, similarity, and transformations, including reflections, translations, or rotations. Items should assess only geometric concepts of twodimensional figures. MA.C.2.3.2: The student predicts and verifies patterns involving tessellations (a covering of a plane with congruent copies of the same pattern with no holes and no overlaps, like floor tiles). 1. Constructs tiling patterns to cover a plane. 2. Identifies a tessellation. 3. Identifies geometric shapes that can be tessellated. 4. Tessellates using translation and other desired transformations. Not assessed at Grade 6-6 -

7 MA.C.3.3.1: The student represents and applies geometric properties and relationships to solve realworld and mathematical problems. 1. Observes, explains, and makes conjectures regarding geometric properties and relationships (among angles, triangles, squares, rectangles, parallelograms). 2. Applies known geometric properties (for example, symmetry, congruence) to solve real-world and mathematical problems. Students will apply geometric properties and relationships to solve problems. Items will not assess threedimensional figures. MA.C.3.3.2: The student identifies and plots ordered pairs in all four quadrants of a rectangular coordinate system (graph) and applies simple properties of lines. 1. Identifies the x- and y- axes in a coordinate plane and identifies the coordinates of a given point in the first quadrant. 2. Plots specific points in the first quadrant of the Cartesian coordinate system. Students will identify the coordinates of a point or identify a point, given its coordinates. Items will assess the first quadrant only, but will allow for the display of all four quadrants. MA.D.1.3.1: The student describes a wide variety of patterns, relationships, and functions through models, such a manipulatives, tables, graphs, expressions, equations, and inequalities. 1. Describes, predicts, and creates numerical and geometric patterns through models (for example, manipulatives, tables, graphs). 2. States in worlds a rule for a pattern. 3. Predicts outcomes based on patterns. 4. Finds patterns in real-world situations. 5. Describes relationships and patterns using words, tables, symbols, variables, expressions, or equations. 6. Given initial terms in a pattern, supplies specific missing term in the pattern (for example, given first four terms, supplies sixth term). Students will recognize, analyze, and/or apply patterns, sequences, relationships, and functions in a variety of settings. Items will assess numerical and graphic patterns. Items should not use more than two variables or include more than two operations Items involving function tables should be able to be solved using a pattern in the y- values or a pattern in the relationship between the x- and y-values. MA.D.1.3.2: The student creates and interprets tables, graphs, equations, and verbal descriptions to explain cause-and-effect relationships. 1. Interprets and creates function tables and graphs (first quadrant). 2. Substitutes values for variables in expressions and describes the results or patterns observed. 3. Graphs (first quadrant) functions from function tables to explain cause-and-effect relationships. Students will interpret function tables and graphs, substitute values for variables in expressions, and describe the results or patterns observed. Items involving graphing functions should be from the first quadrant and limited to plotting points with whole numbers coordinates. Items should include no more than two operations. Items should rely primarily on tables or graphs to present and/or interpret cause-andeffect relationships

8 MA.D.2.3.1: The student represents and solves real-world problems graphically with algebraic expressions, equations, and inequalities. 1. Uses variables to represent numbers and relationships. 2. Translates verbal expressions into algebraic expressions. 3. Translates simple algebraic expressions, equations or formulas representing real-world relationships into verbal expressions or sentences. 4. Uses pictures, models, manipulatives or other strategies to solve simple one-step linear equations with rational solutions. Students will recognize representations of or solutions for real-world problems presented verbally or graphically as equations and/or expressions. Items involving graphing of functions should be from the first quadrant and limited to plotting points with whole numbers coordinates. Items may include only one variable and no more than two operations. MA.D.2.3.2: The student uses algebraic problem-solving strategies to solve real-world problems involving linear equations and inequalities. 1. Knows how to solve simple equations representing real-world situations, using pictures, models, manipulatives (such as algebra tiles), or other strategies. 2. Uses concrete materials to solve equations and inequalities and explains reasoning orally or in writing. Students will represent and/or solve problems involving equations and/or inequalities. Items involve simple equations or inequalities. Items should include only one variable and no more than two operations. MA.E.1.3.1: The student collects, organizes, and displays data in a variety of forms, including tables, line graphs, charts, bar graphs, to determine how different ways of presenting data can lead to different interpretations. 1. Reads and analyzes data displayed in a variety of forms (charts, pictographs, stemand-leaf plots). 2. Generates and collects data for analysis. 3. Chooses appropriate titles, scales, labels, keys, and intervals for displaying data in graphs. 4. Constructs, interprets, and explains displays of data, such as tables and graphs (singleand multiple-bar graphs and single- and multiple-line graphs). Students will read and interpret data displayed in a variety of forms and determine appropriate titles, scales, labels, keys, and intervals. Items may include charts, pictographs, stem-and-leaf plots, single- and multiple-bar graphs, single- and multipleline graphs, circle graphs, and Venn diagrams. The data presented should represent eight or fewer categories

9 MA.E.1.3.2: The student understands and applies the concepts of range and central tendency (mean, median, and mode). FCAT MATHEMATICS CONTENT MATRIX 1. Organizes items in a set of data. 2. Finds the range, mean, median, and mode of a set of data. 3. Describes real-world data by applying and explaining appropriate procedures for finding measures of central tendency. Students will apply the concepts of range, mean, median, and/or mode to solve a problem. Items will assess finding the range, mean, median, or mode of a set of data presented in a chart, list, table, graph, or plot. No more than ten pieces of data should be used for calculations of the mean. Calculations of the mean should involve only wholenumber data. No more than three categories of information should be used in data sets. MA.E.1.3.3: The student analyzes real-world data by applying appropriate formulas for measures of central tendency and organizing data in a quality display, using appropriate technology, including calculators and computers. 1. Describes a set of data by using the measures of central tendency. 2. Uses technology, such as graphing calculators and computer spreadsheets, to create graphs. MA.E.2.3.1: The student compares experimental results with mathematical expectations of probabilities. 1. Determines all possible outcomes of an event using a tree diagram or organized list. 2. Calculates simple mathematical probabilities. 3. Uses manipulatives to obtain experimental results, compares results to mathematical expectations, and discusses the validity of the experiment. Students will identify possible outcomes and/or compare results of experiments (empirical data) with the expected results (theoretical probabilities) of experiments. Items may include probabilities for independent and dependent events. Items involving determining all possible outcomes should not exceed 24. Mathematical expectations of probabilities will be assessed using simple empirical data or theoretical probabilities. MA.E.2.3.2: The student determines odds for and odds against a given situation. 1. Examines and describes situations that include finding the odds for and against a specified outcome. Students will determine the probability or likelihood of a simple event occurring. Items will assess the likelihood or probability of an outcome occurring. Probabilities should be expressed as fractions. Benchmark Grade Level Expectation Clarification Statement Content Limits - 9 -

10 MA.E.3.3.1: The student formulates hypotheses, designs experiments, collects and interprets data, and evaluates hypotheses by making inferences and drawing conclusions based on statistics (range, mean, median, and mode) and tables, graphs, and charts. FCAT MATHEMATICS CONTENT MATRIX 1. With classmates, formulates hypotheses based on research and prior data, designs an appropriate experiment, collects and analyses data using appropriate statistics, and displays and interprets results in appropriate tables or graphs. Students will formulate and analyze hypotheses, use statistical results, and/or identify common uses or misuses of statistical information. Common misuses of probability and statistics should be limited to: incomplete or incorrect graphs over-generalized results use of raw data, percents, or statistics (range, median, mean, mode) to misrepresent the data collected misinterpretation of the likelihood and significance of the results non-representative samples MA.E.3.3.2: The student identifies the common uses and misuses of probability or statistical analysis in the everyday world. 1. Explores uses and misuses of statistics in real world situations such as advertisements and polls

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