Numbers & Operations (N)
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6.N.1 Read, write, and represent rational numbers expressed as integers, fractions, decimals, percents, and ratios; use these representations in real-world and mathematical situations. |
6.N.1.1 Use manipulatives and models (e.g., number lines) to determine positive and negative numbers and their contexts, identify opposites, and explain the meaning of 0 (zero) in a variety of situations. |
6.N.1.2 Compare and order positive rational numbers, represented in various forms, or integers using the symbols "<", ">", and "=". |
6.N.1.3 Explain that a percent represents parts “out of 100” and ratios “to 100.” |
6.N.1.4 Determine equivalencies among fractions, mixed numbers, decimals, and percents. |
6.N.2 Read, write, and model whole number and integer operations to solve problems. |
6.N.2.1 Estimate solutions for integer addition and subtraction of problems in order to assess the reasonableness of results. |
6.N.2.2 Illustrate addition and subtraction of integers using a variety of representations. |
6.N.2.3 Add and subtract integers in a variety of situations; use efficient and generalizable procedures including but not limited to standard algorithms. |
6.N.2.4 Identify and represent patterns with whole-number exponents and perfect squares. Evaluate powers with whole-number bases and exponents |
6.N.2.5 Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. |
6.N.2.6 Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property. |
6.N.3 Explain and use the concept of ratio and its relationship to other rational numbers and to the multiplication and division of whole numbers. Use ratios to solve problems. |
6.N.3.1 Identify and use ratios to compare and relate quantities in multiple ways. Recognize that multiplicative comparison and additive comparison are different. |
6.N.3.2 Determine the unit rate for ratios. |
6.N.3.3 Apply the relationship between ratios, equivalent fractions, unit rates, and percents to solve problems in various contexts. |
6.N.4 Multiply and divide decimals, fractions, and mixed numbers; solve real-world and mathematical problems with rational numbers. |
6.N.4.1 Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers, and use the estimates to assess the reasonableness of results in the context of the problem. |
6.N.4.2 Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships. |
6.N.4.3 Multiply and divide fractions and decimals using efficient and generalizable procedures. |
6.N.4.4 Use mathematical modeling to solve and interpret problems including money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers. |
Algebraic Reasoning & Algebra (A)
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6.A.1 Recognize and represent relationships between varying quantities; translate from one representation to another; use patterns, tables, graphs, and rules to model and solve mathematical problems. |
6.A.1.1 Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. |
6.A.1.2 Represent relationships between two varying positive quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations. |
6.A.1.3 Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false. |
6.A.2 Use properties of arithmetic to generate equivalent numerical expressions and evaluate expressions involving positive rational numbers. |
6.A.2.1 Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to model and solve mathematical problems. |
6.A.3 Use equations and inequalities to model and solve mathematical problems and use the idea of maintaining equality to solve equations. Interpret solutions in the original context. |
6.A.3.1 Model mathematical situations using expressions, equations and inequalities involving variables and rational numbers. |
6.A.3.2 Use number sense and properties of operations and equality to model and solve mathematical problems involving equations in the form x + p = q and px = q, where p and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution. |
Geometry & Measurement (GM)
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6.GM.1 Use translations, reflections, and rotations to establish congruence and understand symmetry (not on a coordinate plane). |
6.GM.1.1 Predict, describe, and apply translations (slides), reflections (flips), and rotations (turns) to a two-dimensional figure. |
6.GM.1.2 Recognize that translations, reflections, and rotations preserve congruence and use them to show that two figures are congruent. |
6.GM.1.3 Identify and describe the line(s) of symmetry in two-dimensional shapes. |
6.GM.2 Use mathematical modeling to calculate the area of squares, parallelograms, and triangles to solve problems. |
6.GM.2.1 Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithms and finding unknown measures. |
6.GM.2.2 Develop and use formulas to determine the area of triangles and find unknown measures. |
6.GM.2.3 Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes. |
6.GM.3 Understand and use relationships between angles in geometric figures. |
6.GM.3.1 Solve problems using the relationships between the angles (vertical, complementary, and supplementary) formed by intersecting lines. |
6.GM.3.2 Develop and use the fact that the sum of the interior angles of a triangle is 180 ̊ to determine missing angle measures in a triangle. |
6.GM.4 Choose appropriate units of measurement and use ratios to convert within measurement systems to model and solve real-world and mathematical problems. |
6.GM.4.1 Estimate weights and capacities using benchmarks in customary and metric measurement systems with appropriate units. |
6.GM.4.2 Solve problems that require the conversion of lengths within the same measurement systems using appropriate units. |
Data & Probability (D)
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6.D.1 Interpret and analyze data. |
6.D.1.1 Interpret the mean, median, and mode for a set of data. |
6.D.1.2 Explain and justify which measure of center (mean, median, or mode) would provide the most descriptive information for a given set of data |
6.D.2 Use probability to model and solve mathematical problems; represent probabilities using fractions and decimals. |
6.D.2.1 Represent possible outcomes using a probability continuum from impossible to certain. |
6.D.2.2 Determine the sample space for a given experiment and determine which members of the sample space are related to certain events. Sample space may be determined by the use of tree diagrams, tables or pictorial representations. |
6.D.2.3 Demonstrate simple experiments in which the probabilities are known and compare the resulting relative frequencies with the known probabilities, recognizing that there may be differences between the two results. |
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