6.N.3 Understand the relationship between integers, nonnegative decimals, fractions and percents.

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1 Crosswalk from 2003 to 2009 Standards - Grade 6 Bolded items are new to the grade level Standards 2009 Standards Notes Number and Operation 1.01 Develop number sense for negative 6.N.3 Understand the relationship between integers, nonnegative decimals, fractions and percents. a) Connect the model, number word, and number using a variety of representations, including the number line. b) Compare and order. c) Make estimates in appropriate situations Develop meaning for percents. 6.N.3.1 Compare integers and non-negative decimals, fractions and percents using the number line. 6.N.3 Understand the relationship between integers, nonnegative decimals, fractions and percents. Objective removed (instructional). Objective removed. a) Connect the model, number word, and 6.N.3.2 Represent percents as decimals and fractions; fractions number using a variety of representations. as decimals and percents; and decimals as fractions and percents. b) Make estimates in appropriate Objective moved to 7 th grade. situations Compare and order Objective moved to 8 th grade Develop fluency in addition, subtraction, multiplication, and division of nonnegative a) Analyze computational strategies. 6.N.1 Use a variety of strategies (including models, pictures, mental computation) to solve problems involving multiplication and division of non-negative 6.N.1.1 Compare numeric expressions using repeated multiplication and exponential notation. 6.N.1.2 Apply multiplication and division to non-negative fractions. 6.N.2.2 Understand when the associative and commutative properties hold true for nonnegative October 26, 2009 DRAFT Page 1

2 6.N.2 Use combinations of addition, subtraction, multiplication and division for non-negative rational numbers to solve multistep problems. 6.N.2.1 Use formal algorithms for all four operations for nonnegative b) Describe the effect of operations on size. c) Estimate the results of computations. d) Judge the reasonableness of solutions Develop fluency in the use of factors, multiples, exponential notation, and prime factorization Use exponential, scientific, and calculator notation to write very large and very small numbers Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil Estimate and measure length, perimeter, area, angles, weight, and mass of two- and three-dimensional figures, using appropriate tools. Included within: 6.N.1.1 and 6.N.1.2 Included within: 6.N.1.1 and 6.N.1.2 Included within: 6.N.1.1 and 6.N N.5 Understand large and small numbers using exponents and exponential notation. 6.N.5.2 Represent numbers as prime factors with exponents. 6.N.5.3 Compare numeric expressions using repeated multiplication and exponential notation. 6.N.5 Understand large and small numbers using exponents and exponential notation. 6.N.5.1 Represent numbers using scientific notation. Problem Solving included within essential standards. Measurement Angle measures moved to 8 th grade; using tools to estimate and measure length, perimeter, area, weight and mass is in Elementary. October 26, 2009 DRAFT Page 2

3 2.02 Solve problems involving perimeter/circumference and area of plane figures. 6.M.1 Use the relationship between customary and metric measurements to estimate measures given in one system to its measure in the other system. 6.M.1.1 Use the relationships between customary and metric measurements to make estimates between systems. 6.M.2 Use attributes of polygons and formulas to determine perimeter and area. 6.M.2.1 Calculate the perimeter of polygons. 6.M.2.2 Calculate the area of polygons. 6.M.3 Use the approximate value of! to calculate the circumference and area of circles. 6.M.3.1 Compare the ratio of the circumference to the diameter to identify an approximate value of!. Content in2003 Standards as 5 th grade objective: 2.01 Estimate the measure of an object in one system given the measure of that object in another system Identify and describe the intersection of figures in a plane Identify the radius, diameter, chord, center, and circumference of a circle; determine the relationships among them Transform figures in the coordinate plane and describe the transformation. 6.M.3.2 Use formulas to determine the area and circumference of circles. Geometry 6.G.1 Represent one- and two-dimensional geometric figures in the Cartesian coordinate system. 6.G.1.2 Describe the intersection of two or more geometric figures in the Cartesian coordinate system (e.g. intersection of a circle and a line). Included within: 6.M.3 6.G.1 Represent one- and two-dimensional geometric figures in the Cartesian coordinate system. 6.G.1.3 Summarize the effect of translations. 6.G.1.1 Identify the origin, axes, quadrants and coordinates on the Cartesian coordinate system. Rotations are in the 8 th grade. This standard does not expect recognition of transformation rules. October 26, 2009 DRAFT Page 3

4 3.04 Solve problems involving geometric figures in the coordinate plane Develop fluency with counting strategies to determine the sample space for an event. Include lists, tree diagrams, frequency distribution tables, permutations, combinations, and the Fundamental Counting Principle Use a sample space to determine the probability of an event Conduct experiments involving simple and compound events Determine and compare experimental and theoretical probabilities for simple and compound events Determine and compare experimental and theoretical probabilities for independent and dependent events Design and conduct experiments or surveys to solve problems; report and analyze results. 6.G.1.4 Summarize the effect of reflections across horizontal and vertical lines. 6.G.1 Represent one- and two-dimensional geometric figures in the Cartesian coordinate system. Statistics and Probability 6.S.2 Use strategies to identify sample spaces and probabilities. 6.S.2.1 Use tree diagrams and Fundamental Counting Principle to identify sample space and identify probabilities. 6.S.2.2 Use organized lists to display a sample space and identify probabilities. 6.S.2 Use strategies to identify sample spaces and probabilities. 6.S.1 Understand the relationships between experimental and theoretical probabilities for simple events. 6.S.1.1 Predict the outcomes of probability experiments for simple events based on theoretical probability. 6.S.1 Understand the relationships between experimental and theoretical probabilities for simple events. 6.S.1.2 Compare the outcomes from random experiments (experimental probability) to an expected outcome based on a theoretical probability. Only simple events are addressed in 6 th grade; compound events are in 7 th grade. Only simple events are addressed in 6 th grade; compound events are in 7 th grade. Objective moved to 8 th grade. Objective removed (instructional). 6.S.3 Understand graphical displays of data in terms of shape, measures of center and variability. 6.S.3.1 Represent data using dot October 26, 2009 DRAFT Page 4

5 5.01 Simplify algebraic expressions and verify the results using the basic properties of a) Identity. b) Commutative. c) Associative. d) Distributive. e) Order of operations Use and evaluate algebraic expressions Solve simple (one- and two-step) equations or inequalities. Algebra 6.N.2.1 Use formal algorithms for all four operations for nonnegative 6.A.1 Apply mathematical operations and properties for nonnegative rational numbers to solve one-step equations and inequalities. 6.A.1.1 Use verbal descriptions and algebraic equations and inequalities to represent problem situations. plots, stem-and-leaf plots (from 5 th grade) and histograms (from 7 th grade). 6.S.3.2 Interpret distributions of data in terms of measures of center (mean, median and mode) shape (clusters, peaks and gaps) and variability (range). 6.S.3.3 Compare the meanings and uses of means, medians and modes. 6.S.3.4 Interpret information from a data set in terms of supporting or refuting statements about the data group. Objective moved to 8 th grade. Solving two-step equations and inequalities using the properties of equality moved to 7 th grade. October 26, 2009 DRAFT Page 5

6 5.04 Use graphs, tables, and symbols to model and solve problems involving rates of change and ratios. 6.A.1.2 Use mathematical operations and properties to solve one-step equations. 6.A.1.3 Use mathematical operations and properties to solve inequalities. 6.N.4 Use the concept of unit rate to solve problems. 6.N.4.1 Use ratio tables or graphs to represent unit rates. 6.N.4.2 Use unit rates to solve problems. 6.A.2.1 Analyze patterns of arithmetic sequences to determine the rule that defines the pattern. 6.A.2.3 Use a given rule to determine the pattern. Using graphs, tables, and symbols to model and solve problems involving rates of change moved to 7 th grade. 6.A.2 Analyze patterns to determine the rule that enables accurate predictions of missing numbers, including the n th term, of arithmetic sequences (x 1, x 2, x 3,... x n ). 6.A.2.2 Use the rule to predict the n th term of a arithmetic sequence. Content in 2003 Standards as 5 th grade objective: 5.01 Describe, extend, and generalize numeric and geometric patterns using tables, graphs, words and symbols. 6.A.3 Analyze the data presented in qualitative graphs in terms of position, time, change and rate of change. 6.A.3.1 Represent the essential elements of a scenario in graphical form. October 26, 2009 DRAFT Page 6

7 6.A.3.2 Analyze the data presented in a qualitative graph to solve problems or answer questions. October 26, 2009 DRAFT Page 7

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