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# Mathematics - Mastery Expectations Grade 6

 Mathematics – Mastery Expectations Grade 6 Note: * = No state testing Number Sense & Operations 6N1 Demonstrate an understanding of positive integer exponents, in particular, when used in powers of ten. 6N2 Demonstrate an understanding of place value to billions and thousandths. 6N3 Represent and compare very large (billions) and very small (thousandths) positive numbers in various forms such as expanded notation without exponents. 6N4 Demonstrate an understanding of fractions as a ratio of whole numbers, as parts of unit wholes, as parts of a collection, and as locations on the number line. 6N5 Identify and determine common equivalent fractions, mixed numbers, decimals, and percents. 6N6 Find and position integers, fractions, mixed numbers, and decimals (both positive and negative) on the number line. 6N7 Compare and order integers (including negative integers), and positive fractions, mixed numbers, decimals, and percents. 6N8 Apply number theory concepts-including prime and composite numbers, prime factorization, greatest common factor, least common multiple, and divisibility rules for 2, 3, 4, 5, 6, 9 and 10 – to the solution of problems. 6N9 Select and use appropriate operations to solve problems involving addition, subtraction, multiplication, division, and positive integer exponents with whole numbers, and with positive fractions, mixed numbers, decimals, and percents. 6N10 Use the number line to model addition and subtraction of integers, with the exception of subtracting negative integers. 6N11 Apply the Order of Operations for expressions involving addition, subtraction, multiplication, and division with grouping symbols (+, -, x, รท ) 6N12 Demonstrate an understanding of the inverse relationship of addition and subtraction, and use that understanding to simplify computation and solve problems. 6N13 Accurately and efficiently add, subtract, multiply, and divide (with double-digit divisors) whole numbers and positive decimals. 6N14 Accurately and efficiently add, subtract, multiply, and divide positive fractions and mixed numbers. Simplify fractions. 6N15 Add and subtract integers, with the exception of subtracting negative integers. 6N16 Estimate results of computations with whole numbers, and with positive fractions, mixed numbers, decimals, and percents. Describe reasonableness of estimates. Patterns, Relations & Algebra 6P1 Analyze and determine the rules for extending symbolic, arithmetic, and geometric patterns and progressions. 6P2 Replace variables with given values and evaluate/simplify. 6P3 Use the properties of equality to solve problems, e.g., if Δ + 7 = 13, then Δ = 13 – 7, therefore Δ = 6; if 3 x Δ = 15, then 1/3 x 3 x Δ = 1/3 x 15, therefore Δ = 15. 6P4 Represent real situations and mathematical relationships with concrete models, tables, graphs, and rules in words and with symbols, e.g., input – output tables. 6P5 Solve linear equations using concrete models, tables, graphs, and paper-pencil methods. 6P6 Produce and interpret graphs that represent the relationship between two variables in everyday situations. 6P7 Identify relationships between 2 variables with a constant rate of change. Contrast these with relationships where the rate of change is not constant. Geometry 6G1 Identify polygons based on their properties, including types of interior angles, perpendicular or parallel sides, and congruence of sides, e.g., squares, rectangles, rhombuses, parallelograms, trapezoids, and isosceles, equilateral, and right triangles. 6G2 Identify three-dimensional shapes (e.g., cubes, prisms, spheres, cones, and pyramids) based on their properties, such as edges and faces. 6G3 Identify relationships among points, lines, and planes, e.g., intersecting, parallel, perpendicular. 6G4 Graph points and identify coordinates of points on the Cartesian coordinate plane (all four quadrants). 6G5 Find the distance between two points on horizontal or vertical number lines. 6G6 Predict, describe, and perform transformations on two-dimensional shapes, e.g., translations, rotations, and reflections. 6G7 Identify types of symmetry, including line and rotational. 6G8 Determine if two shapes are congruent by measuring sides or a combination of sides and angles, as necessary; or by motions or series of motions. 6G9 Match three-dimensional objects and their two-dimensional representations, e.g., nets, projections, and perspective drawings Measurement 6M1 Apply the concepts of area and perimeter to the solution of problems. Apply formulas where appropriate. 6M2 Identify measure, describe, classify, and construct various angles, triangles, and quadrilaterals. 6M3 Solve problems involving proportional relationships and units of measurement, e.g., same system unit conversions, scale models, maps and speed. 6M4 Find area of triangles and parallelograms. Recognize that shapes with the same number of sides but different appearances can have the same area; Develop strategies to find the area of more complex shapes. 6M5 Identify, measure, and describe circles and the relationships of the radius, diameter, circumference, and area (e.g., d = 2r, p = C/d), and use the concepts to solve problems. 6M6 Find volumes and surface areas of rectangular prisms. 6M7 Find the sum of angles in simple polygons, up to eight sides (with and w/o measuring the angles). Data Analysis, Statistics and Probability 6D1 Describe and compare data sets using the concepts of median, mean, mode, maximum and minimum, and range. 6D2 Construct and interpret stem and leaf plots, line plots, and circle graphs. 6D3 Use tree diagrams and other models (e.g., lists and tables) to represent possible or actual outcomes of trials. Analyze the outcomes. 6D4 Predict the probability of outcomes of simple experiments (e.g., rolling a die) and test the predictions. Use appropriate ratios between 0 and 1 to represent the probability of the outcome and associate the probability with the likelihood of the event.