Number Sense and Operations

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1 Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N N.14 6.N.15 Demonstrate an understanding of positive integer exponents when used in powers of ten. Demonstrate an understanding of fractions as a ratio of whole numbers. Identify and convert between mixed numbers and fractions. Find and position integers, fractions, mixed numbers and decimals both positive and negative on a number line. Compare and order integers, including negative integers and positive fractions, mixed numbers, decimals and percents. Apply number theory concepts, including prime factorization, greatest common factor and least common multiple to the solution of problems. Select and use appropriate operations to solve problems involving addition, subtraction, multiplication, division and positive integer exponents with whole numbers, fractions, mixed numbers, decimals and percents. Apply the order of operations for expressions involving addition, subtraction, multiplication and division with parentheses Demonstrate an understanding of the inverse relationship of addition and subtraction and use that understanding to simplify computations and solve problems Accurately and efficiently add, subtract, multiply and divide with double digit divisors and positive decimals Accurately and efficiently add, subtract, multiply and divide positive fractions and mixed numbers. Simplify fractions. A. Convert improper fractions to mixed numbers B. Find equivalent fractions Add and subtract integers, with the exception of subtracting negative integers Use the number line to model addition and subtraction of integers Estimate the results of computations with whole numbers, fractions, mixed numbers, decimals and percents. Describe the reasonableness. Translate between scientific notation and standard notation for large and small numbers APS Math Benchmarks Page 1 of 5

2 Pattern, Relations, and Algebra 6.P.1 6.P.2 6.P.3 6.P.4 6.P.5 Evaluate algebra variable expressions with given values and simplify 3x-Y Use the properties of equality to solve one-step equations Represent real situations and mathematical relationships with concrete models, tables, graphs and rules in words and symbols Produce and interpret graphs that represent the relationship between two variables in everyday situations Identify and describe relationships between two variables with a constant rate of change. Contrast these with relationships where the rate of change is not constant. APS Math Benchmarks Page 2 of 5

3 Geometry 6.G.1 6.G.2 6.G.3 6.G.4 6.G.5 6.G.6 6.G.7 6.G.8 6.G.9 Identify polygons based on their properties including types of interior angles, perpendicular or parallel sides and congruence of sides Identify three-dimensional shapes (e.g. cubes, spheres, prisms and cones) based on their properties such as edges and faces Identify relationships between points, lines and planes, (e.g. intersecting and parallel) Graph points and identify coordinates of points on the Cartesian Coordinate Plane, (all four quadrants) Find the distance between two points on a horizontal or vertical number line Predict, describe and perform transformations on two-dimensional shapes, (e.g. rotation, translation and reflection) Identify types of line and rotational symmetry Determine if two shapes are congruent by measuring sides or a combination of sides and angles or by a series of motions, (e.g. rotations and reflections) Match three-dimensional objects with their two-dimensional representations. APS Math Benchmarks Page 3 of 5

4 Measurement 6.M.1 6.M.2 6.M.3 6.M.4 6.M.5 6.M.6 6.M.7 Use formulas for calculations of area and perimeter Identify, measure, describe, classify and construct various angles, triangles, and quadrilaterals Solve problems involving proportional relationships and units of measurement, (e.g. scale models and maps) Find areas of triangles and parallelograms. Develop strategies to find area of more complex shapes. Identify, measure and describe circles and the relationships of circumference and area and use concepts to solve problems Find volume and surface areas of rectangular prisms Find the sum of the angles in simple polygons (up to eight sides) with and without measuring the angles. APS Math Benchmarks Page 4 of 5

5 Data Analysis, Statistics, and Probability 6.D.1 Use tree diagrams and other models such as lists and tables to represent possible or actual outcomes of trials. Analyze the outcomes 6.D.2 Predict the probability of outcomes of simple experiments (e.g. tossing a coin or rolling a die) and test the predictions 6.D.3 Use appropriate ratios between 0 and 1 to represent the probability of the outcome and associate the probability with the likelihood of the event APS Math Benchmarks Page 5 of 5

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