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Mathematics Sixth Grade Core Content for Assessment Crosswalk August 2006 Number Properties and Operations Version 3.0 Version 4.0 Version 4.1 Number Sense MA-6-1.1.1 MA-06-1.1.1 MA-06-1.1.1 Students will describe properties of, define, See 4.1=> Students will provide examples of and give examples of, and/or apply to both real- identify fractions, decimals and percents. world and mathematical situations: Fractions, DOK 1 decimals MA-6-1.2.1 Students will perform the following mathematical operations and/or procedures accurately and efficiently, and explain how they work in real-world and mathematical situations: Add, subtract, multiply, and divide fractions; add, subtract, and multiply decimals to solve problems MA-6-1.1.4 MA-06-1.1.1a MA-06-1.1.2 Students will describe properties of, define, See 4.1=> Students will describe and provide examples give examples of, and/or apply to both real- Code Change of representations of numbers (whole world and mathematical situations: Place value numbers, fractions in simplest form, mixed of whole numbers and decimals numbers, decimals, percents) and operations MA-6-1.1.5 in a variety of equivalent forms using models, Students will describe properties of, define, diagrams and symbols (e.g., number lines, 10 give examples of, and/or apply to both real- by 10 grids, rectangular arrays, number world and mathematical situations: Positive sentences), based on real-world and/or whole number exponents mathematical situations. MA-6-1.1.6 Students will describe properties of, define, give examples of, and/or apply to both real- world and mathematical situations: Representation of fractions and decimals and their operations 1 Mathematics Sixth Grade Core Content for Assessment Crosswalk August 2006 MA-6-1.3.1 MA-06-1.1.2 MA-06-1.1.3 Students will show connections and how Students will convert between any two of Students will convert between any two of connections are made between concepts and the following numbers: fractions, decimals, the following numbers: fractions, decimals skills, explain why procedures work, and make and percents (less than or equal to 100%; and percents (less than or equal to100%); generalizations about mathematics in and will compare these numbers. and will compare and order these numbers. meaningful ways for the following DOK - 2 DOK 2 relationships: How whole numbers, fractions and decimals, relate to each other (e.g., convert between forms of rational numbers, compare, order) Estimation MA-6-1.2.2 MA-06-1.2.1 MA-06-1.2.1 Students will perform the following Students will estimate to solve real-world Students will estimate to solve real-world mathematical operations and/or procedures and/or mathematical problems with whole and mathematical problems with whole accurately and efficiently, and explain how numbers, fractions, decimals, and numbers, fractions, decimals, and they work in real-world and mathematical percents, checking for reasonable and percents, checking for reasonable and situations: Estimate and predict computational appropriate computational results. appropriate computational results. results using whole numbers and decimals DOK - 2 DOK 2 Number Operations MA-6-1.2.1 MA-06-1.3.1 MA-06-1.3.1 Students will perform the following Students will add, subtract, multiply, Students will add, subtract, multiply and mathematical operations and/or procedures divide, and apply order of operations with divide, whole numbers, fractions and accurately and efficiently, and explain how whole numbers, fractions, and decimals to decimals to solve real-world problems and they work in real-world and mathematical solve real-world problems. apply order of operations to simplify situations: Add, subtract, multiply, and divide DOK - 2 numerical expressions. fractions; add, subtract, and multiply decimals DOK 2 to solve problems MA-6-1.2.2 Students will perform the following mathematical operations and/or procedures accurately and efficiently, and explain how they work in real-world and mathematical situations: Estimate and predict computational results using whole numbers and decimals 2 Mathematics Sixth Grade Core Content for Assessment Crosswalk August 2006 MA-6-1.3.3 MA-06-1.3.1a MA-06-1.3.2 Students will show connections and how See 4.1=> Students will explain how operations (addition connections are made between concepts and Code Change and subtraction; multiplication and division) are skills, explain why procedures work, and make inversely related. generalizations about mathematics in meaningful ways for the following relationships: How operations (addition and subtraction; multiplication and division) are inversely related MA-06-1.3.1b Students will check for reasonable and appropriate computational results, using a variety of methods (e.g., estimate, pencil and paper, calculator, rounding, mental math). Ratios and Proportional Reasoning MA-6-1.1.3 MA-06-1.4.1 MA-06-1.4.1 Students will describe properties of, define, See 4.1=> Students will describe and apply ratios to give examples of, and/or apply to both real- solve real-world problems. world and mathematical situations: Ratio DOK 2 MA-6-1.2.3 Students will perform the following mathematical operations and/or procedures accurately and efficiently, and explain how they work in real-world and mathematical situations: Apply ratios 3 Mathematics Sixth Grade Core Content for Assessment Crosswalk August 2006 Properties of Numbers and Operations MA-6-1.2.4 MA-06-1.5.1 MA-06-1.5.1 Students will perform the following See 4.1=> Students will identify and apply prime mathematical operations and/or procedures numbers, composite numbers, prime accurately and efficiently, and explain how factorization, factors, multiples and they work in real-world and mathematical divisibility to solve real-world and situations: Identify and use prime numbers, mathematical problems (e.g., prime composite numbers, prime factorization, factorization to determine a least common factors, multiples, divisibility to solve problems. multiple [LCM] or greatest common factor (e.g., prime factorization to determine LCM [GCF]). and GCF) DOK 2 MA-6-1.3.2 MA-06-1.5.2 MA-06-1.5.2 Students will show connections and how Students will identify how the commutative Students will identify the use of properties connections are made between concepts and properties, the associative properties, and (commutative properties of addition and skills, explain why procedures work, and make the identity properties for addition and multiplication, the associative properties of generalizations about mathematics in multiplication are used to simplify addition and multiplication and the identity meaningful ways for the following numerical expressions. properties for addition and multiplication) relationships: How properties such as DOK - 1 to simplify numerical expressions. commutative, associative, and identities show DOK 1 relationships among operations 4 Mathematics Sixth Grade Core Content for Assessment Crosswalk August 2006 Measurement Version 3.0 Version 4.0 Version 4.1 Measuring Physical Attributes MA-6-2.2.5 MA-06-2.1.1 MA-06-2.1.1 Students will perform the following Students will determine: Students will measure lengths (to the mathematical operations and/or procedures measures of rectangles and figures nearest eighth of an inch or the nearest accurately and efficiently, and explain how that can be divided into rectangular centimeter) and will determine and use in they work in real-world and mathematical shapes, including lengths to the real-world and mathematical problems: situations: Use formulas to find area and nearest eighth of an inch or nearest area and perimeter of triangles; perimeter of triangles (not requiring use of centimeter; and area and perimeter of quadrilaterals Pythagorean theorem as a strategy) and the area and perimeter of triangles (rectangles, squares); (using the quadrilaterals (rectangle, parallelogram, and quadrilaterals (rectangles, Pythagorean theorem will not be squares) squares). (Using the Pythagorean required as a strategy) and theorem will not be required as a area and perimeter of compound strategy.) figures composed of triangles and DOK - 2 quadrilaterals. DOK 2 MA-6-2.2.4 MA-06-2.1.1a MA-06-2.1.2 Students will perform the following See 4.1=> Students will estimate measurements in mathematical operations and/or procedures Code Change standard units including fractions and accurately and efficiently, and explain how decimals. they work in real-world and mathematical situations: Estimate measurements in standard units including fractions and decimals MA-06-2.1.1b MA-06-2.1.3 See 4.1=> Students will explain how measurements and Code Change measurement formulas are related or different (perimeter and area of rectangles). 5 Mathematics Sixth Grade Core Content for Assessment Crosswalk August 2006 Systems of Measurement MA-6-2.1.5 MA-06-2.2.1a MA-06-2.2.1 Students will describe properties of, define, Students will describe and provide examples Students will convert units within the same give examples of, and/or apply to both real- of U.S. Customary and metric units of measurement system and use these units to world and mathematical situations: U.S. measurement and use these units to solve solve real-world problems. customary and metric units of measure real-world and/or mathematical problems. Geometry Version 3.0 Version 4.0 Version 4.1 Shapes and Relationships MA-6-2.1.1 MA-06-3.1.1 MA-06-3.1.1 Students will describe properties of, define, Students will describe and provide Students will describe and provide give examples of, and/or apply to both real- examples of the basic geometric elements examples of the basic geometric elements world and mathematical situations: Segments, (points, rays, lines, segments, angles (points, rays, lines, segments, angles rays, lines, angles, and planes [acute, right, obtuse], planes, radius, [acute, right, obtuse], planes, radius, diameter, circumference). diameter, circumference). DOK - 2 DOK 1 MA-6-2.1.2 MA-06-3.1.2 MA-06-3.1.2 Students will describe properties of, define, Students will describe, and provide Students will describe and provide give examples of, and/or apply to both real- examples and properties of two- examples of the elements (e.g., sides, world and mathematical situations: Two- dimensional figures (circles, triangles, vertices, angles, congruent parts) of two- dimensional shapes, regular polygons, quadrilaterals, regular polygons), and will dimensional figures (circles, triangles, quadrilaterals (square, rectangle, rhombus, apply these properties and figures to solve quadrilaterals, regular polygons) and will parallelogram, trapezoid) and triangles (acute, real-world problems. apply these elements and figures to solve obtuse, right) DOK - 2 real-world and mathematical problems. MA-6-2.2.1 DOK 2 Students will perform the following mathematical operations and/or procedures accurately and efficiently, and explain how they work in real-world and mathematical situations: Identify characteristics (e.g., sides, vertices, angles, congruent parts) of two- dimensional shapes. 6 Mathematics Sixth Grade Core Content for Assessment Crosswalk August 2006 MA-6-2.1.3 MA-06-3.1.3a MA-06-3.1.3 Students will describe properties of, define, Students will describe, provide examples of, Students will describe, provide examples of give examples of, and/or apply to both real- and identify properties (e.g., vertices, angles, and identify elements (e.g., vertices, angles, world and mathematical situations: Three- faces, edges, congruent parts) of common faces, edges, congruent parts) of common dimensional geometric shapes including three-dimensional figures (spheres, cones, three-dimensional figures (spheres, cones, spheres, cones, cylinders, prisms, (with cylinders, prisms, and pyramids). cylinders, prisms, and pyramids). polygonal bases), and pyramids (with polygonal bases) MA-6-2.2.1 Students will perform the following mathematical operations and/or procedures accurately and efficiently, and explain how they work in real-world and mathematical situations: Identify characteristics (e.g., sides, vertices, angles, congruent parts) of two- dimensional shapes MA-6-2.1.4 MA-06-3.1.4 MA-06-3.1.4 Students will describe properties of, define, Students will describe and provide Students will identify and describe give examples of, and/or apply to both real- examples of congruent and similar figures, congruent figures and will apply congruent world and mathematical situations: and will apply congruent and similar figures to solve real-world and Congruence, symmetry, and similarity figures to solve real-world problems. mathematical problems. DOK - 2 DOK 2 MA-06-3.1.4a MA-06-3.1.5 See 4.1=> Students will identify similar figures and apply Code Change similar figures to solve real-world and mathematical problems. Transformations of Shapes MA-6-2.1.4 MA-06-3.2.1a MA-06-3.2.1 Students will describe properties of, define, Students will describe, provide examples of, Students will describe, provide examples of give examples of, and/or apply to both real- and apply line symmetry to real-world and/or and apply line symmetry to real-world and world and mathematical situations: mathematical situations. mathematical problems. Congruence, symmetry, and similarity 7 Mathematics Sixth Grade Core Content for Assessment Crosswalk August 2006 MA-6-2.2.3 MA-06-3.2.2 MA-06-3.2.2 Students will perform the following Students will transform (translate and reflect Students will: mathematical operations and/or procedures across a horizontal or vertical line) figures in reflect figures across a horizontal accurately and efficiently, and explain how the first quadrant of the coordinate plane and or vertical line in the first quadrant; they work in real-world and mathematical determine new coordinates of the shape after translate figures in a plane in the situations: Move shapes in Quadrant I transformation. first quadrant and coordinate plane: translate, rotate, reflect DOK - 2 determine the coordinates of the image after transformation in the first quadrant. DOK 2 MA-6-2.2.3 MA-06-3.2.2a MA-06-3.2.3 Students will perform the following Students will move shapes in Quadrant I of the Students will identify rotations of figures in the mathematical operations and/or procedures coordinate plane: rotate (turn). plane (90˚ and 180˚). accurately and efficiently, and explain how they work in real-world and mathematical situations: Move shapes in Quadrant I coordinate plane: translate, rotate, reflect Coordinate Geometry MA-6-4.1.3 MA-06-3.3.1 MA-06-3.3.1 Students will describe properties of, define, Students will identify and graph ordered Students will identify and graph ordered give examples of, and/or apply to both real- pairs on a positive coordinate system, pairs on a positive coordinate system world and mathematical situations: Quadrant I, correctly identifying the origin, axes, and (Quadrant I), correctly identifying the ordered pairs, x and y axis, origin ordered pairs; and will apply graphing in origin, axes and ordered pairs; and will the coordinate system to solve real-world apply graphing in the coordinate system to problems. solve real-world and mathematical DOK - 2 problems. DOK 2 8 Mathematics Sixth Grade Core Content for Assessment Crosswalk August 2006 Data Analysis and Probability Version 3.0 Version 4.0 Version 4.1 Data Representations MA-6-3.2.1 MA-06-4.1.1 MA-06-4.1.1 Students will perform the following See 4.1=> Students will analyze and make inferences mathematical operations and/or procedures from data displays (drawings, accurately and efficiently, and explain how tables/charts, pictographs, bar graphs, they work in real-world and mathematical circle graphs, line plots, Venn diagrams, situations: Organize, represent, analyze, and line graphs, stem-and-leaf plots). interpret sets of data using tables, graphs DOK 3 (e.g., bar, line), and plots (e.g., single stem- and-leaf) MA-6-3.2.2 Students will perform the following mathematical operations and/or procedures accurately and efficiently, and explain how they work in real-world and mathematical situations: Construct and interpret displays of data (e.g., tables, line graph, line plot, steam- and-leaf plot) MA-6-3.3.1 MA-06-4.1.1a MA-06-4.1.2 Students will show connections and how See 4.1=> Students will explain how different connections are made between concepts and Code Change representations of data (e.g., tables, graphs, skills, explain why procedures work, and make diagrams, plots) are related. generalizations about mathematics in meaningful ways for the following relationships: How different representations of data (e.g tables, stem-and-leaf, bar graph, line plot) are related 9 Mathematics Sixth Grade Core Content for Assessment Crosswalk August 2006 MA-6-3.1.3 MA-06-4.1.2 MA-06-4.1.4 Students will describe properties of, define, Students will construct data displays (bar Students will determine and construct give examples of, and/or apply to both real- graphs, line plots, Venn diagrams, tables, appropriate data displays (bar graphs, line world and mathematical situations: line graphs), and will explain why the type plots, Venn diagrams, tables, line graphs) Characteristics and appropriateness of graphs of display is appropriate for the data. and will explain why the type of display is (e.g., bar, line), and plots (e.g., single stem- DOK - 2 appropriate for the data. and-leaf) DOK 2 MA-6-3.2.1 Students will perform the following mathematical operations and/or procedures accurately and efficiently, and explain how they work in real-world and mathematical situations: Organize, represent, analyze, and interpret sets of data using tables, graphs (e.g., bar, line), and plots (e.g., single stem- and-leaf) MA-6-3.2.2 Students will perform the following mathematical operations and/or procedures accurately and efficiently, and explain how they work in real-world and mathematical situations: Construct and interpret displays of data (e.g., tables, line graph, line plot, steam- and-leaf plot) MA-6-3.3.1 Students will show connections and how connections are made between concepts and skills, explain why procedures work, and make generalizations about mathematics in meaningful ways for the following relationships: How different representations of data (e.g., tables, stem-and-leaf, bar graph, line plot) are related 10 Mathematics Sixth Grade Core Content for Assessment Crosswalk August 2006 Characteristics of Data Sets MA-6-3.1.1 MA-06-4.2.1 MA-06-4.2.1 Students will describe properties of, define, See 4.1=> Students will determine and apply the give examples of, and/or apply to both real- mean, median, mode and range of a set of world and mathematical situations: Meaning of data. central tendency (mean, median, mode) DOK 2 MA-3.2.3 Students will perform the following mathematical operations and/or procedures accurately and efficiently, and explain how they work in real-world and mathematical situations: Find mean, median, mode, and range Experiments and Samples (not assessed at this level) 11 Mathematics Sixth Grade Core Content for Assessment Crosswalk August 2006 Probability MA-6-3.2.6 MA-06-4.4.1 MA-06-4.4.1 Students will perform the following mathematical Students will describe or determine (e.g., Students will describe or determine (e.g., operations and/or procedures accurately and tables, tree diagrams) the sample space tables, tree diagrams) the sample space efficiently, and explain how they work in real-world of an event. of an event for a real-world or and mathematical situations: Use counting DOK - 2 mathematical situation. techniques, tree diagrams, and tables to solve DOK 2 probability problems MA-6-3.3.4 Students will show connections and how connections are made between concepts and skills, explain why procedures work, and make generalizations about mathematics in meaningful ways for the following relationships: How probability and statistics are used to make predictions and/or draw conclusions MA-6-3.2.4 MA-06-4.4.2 MA-06-4.4.2 Students will perform the following mathematical Students will determine simple Students will determine single event operations and/or procedures accurately and probabilities based on the results of an probabilities based on the results of an efficiently, and explain how they work in real-world experiment and will make inferences experiment and will make inferences and mathematical situations: Determine sample based on the data. based on the data. space of a simple event (e.g., flipping a coin, DOK - 3 DOK 3 number cube, spinners) MA-6-3.2.5 Students will perform the following mathematical operations and/or procedures accurately and efficiently, and explain how they work in real-world and mathematical situations: Make predictions (e.g. fair and unfair games) and draw conclusions from statistical data and probability experiments (e.g., flipping a coin, number cube, spinners) MA-06-4.4.3 Students will explore the theoretical probability of simple events. 12 Mathematics Sixth Grade Core Content for Assessment Crosswalk August 2006 Algebraic Thinking Version 3.0 Version 4.0 Version 4.1 Patterns, Relations and Functions MA-6-4.1.2 MA-06-5.1.1 MA-06-5.1.1 Students will describe properties of, define, Students will extend and describe rules for Students will extend, describe rules for give examples of, and/or apply to both real- patterns from real-world and/or patterns and find a missing term in a world and mathematical situations: Functions mathematical problems pattern from real-world and mathematical using tables, graphs, and verbal rules DOK - 3 problems. MA-6-4.2.4 DOK 3 Students will perform the following mathematical operations and/or procedures accurately and efficiently, and explain how they work in real-world and mathematical situations: Identify, create, and continue patterns (give an informal description for the continuance of the pattern and/or generalize patterns through a verbal rule) MA-6-4.3.1 Students will show connections and how connections are made between concepts and skills, explain why procedures work, and make generalizations about mathematics in meaningful ways for the following relationships: How tables and graphs and recognize patterns relate to each other 13 Mathematics Sixth Grade Core Content for Assessment Crosswalk August 2006 MA-6-4.1.2 MA-06-5.1.2 MA-06-5.1.2 Students will describe properties of, define, See 4.1=> Students will create tables for functions give examples of, and/or apply to both real- and will apply the tables to solve real-world world and mathematical situations: Functions problems. using tables, graphs, and verbal rules DOK 2 MA-6-4.2.5 Students will perform the following mathematical operations and/or procedures accurately and efficiently, and explain how they work in real-world and mathematical situations: Create tables for functions MA-6-4.2.5 MA-06-5.1.2a MA-06-5.1.3 Students will perform the following Students will describe, define, provide Students will describe, define, provide mathematical operations and/or procedures examples of, and apply to real-world and/or examples of and apply to real-world and accurately and efficiently, and explain how mathematical situations functions using tables, mathematical problems functions using tables, they work in real-world and mathematical graphs and verbal rules. graphs and verbal rules. situations: Create tables for functions MA-6-4.3.1 MA-06-5.1.2b MA-06-5.1.4 Students will show connections and how See 4.1=> Students will explain how tables, graphs and connections are made between concepts and Code Change patterns relate to each other. skills, explain why procedures work, and make generalizations about mathematics in meaningful ways for the following relationships: How tables and graphs and recognize patterns relate to each other MA-6-4.3.2 MA-06-5.1.3a MA-06-5.1.5 Students will show connections and how See 4.1=> Students will explain how the change in one connections are made between concepts and Code Change quantity affects change in another quantity skills, explain why procedures work, and make (e.g., in tables or graphs, input/output tables). generalizations about mathematics in meaningful ways for the following relationships: How the change in one quantity affects a change in another quantity (e.g., in tables/graphs, input/output tables) 14 Mathematics Sixth Grade Core Content for Assessment Crosswalk August 2006 Variables, Expressions and Operations MA-6-4.2.1 MA-06-5.2.1 MA-06-5.2.1 Students will perform the following See 4.1=> Students will substitute values for mathematical operations and/or procedures variables (up to two different variables) and accurately and efficiently, and explain how evaluate algebraic expressions. they work in real-world and mathematical DOK 2 situations: Simplify numerical expressions MA-6-4.1.1 MA-06-5.2.1a MA-06-5.2.2 Students will describe properties of, define, Students will describe, define, and provide Students will describe, define and provide give examples of, and/or apply to both real- examples of variables and expressions with a examples of variables and expressions with a world and mathematical situations: Variables, missing value based on real-world and/or missing value based on real-world and expressions, and equations with a missing mathematical situations. mathematical problems. value Equations and Inequalities MA-6-4.2.2 MA-06-5.3.1 MA-06-5.3.1 Students will perform the following See 4.1=> Students will model and solve real-world mathematical operations and/or procedures and mathematical problems with simple accurately and efficiently, and explain how equations and inequalities (e.g., 8x = 4, they work in real-world and mathematical x+2 > 5). situations: Solve simple equations and DOK 2 inequalities MA-6-4.2.6 Students will perform the following mathematical operations and/or procedures accurately and efficiently, and explain how they work in real-world and mathematical situations: Matching verbal rules with expressions to solve everyday situations 15