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### 6.N Number & Operations

- 6.N.1 Read, write, and represent integers and rational numbers expressed as fractions, decimals, percents, and ratios; write positive integers as products of factors; use these representations in real-world and mathematical situations.
- 6.N.1.1 Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.
- 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, decimals, and percents. Select among these representations to solve problems.
- 6.N.1.5 Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents.
- 6.N.1.6 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.2 Add and subtract integers in order to solve real-world and mathematical problems.
- 6.N.2.1 Estimate solutions to addition and subtraction of integers 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; use efficient and generalizable procedures including but not limited to standard algorithms.

- 6.N.3 Understand the concept of ratio and its relationship to fractions and percents and to the multiplication and division of whole numbers. Use ratios to solve real-world and mathematical problems.
- 6.N.3.1 Identify and use ratios to compare quantities. 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 and percents to solve problems in various contexts, including those involving mixture and concentrations.
- 6.N.3.4 Use multiplicative reasoning and representations to solve ratio and unit rate problems.

- 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 Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.

### 6.A Algebraic Reasoning & Algebra

- 6.A.1 Recognize and represent relationships between varying quantities; translate from one representation to another; use patterns, tables, graphs and rules to solve real-world and 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 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 solve real-world and mathematical problems.

- 6.A.3 Use equations and inequalities to represent real-world and mathematical problems and use the idea of maintaining equality to solve equations. Interpret solutions in the original context.
- 6.A.3.1 Represent real-world or 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 solve real-world and mathematical problems involving equations in the form x + p = q and px = q, where x, 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.

### 6.GM Geometry & Measurement

- 6.GM.1 Calculate area of squares, parallelograms, and triangles to solve real-world and mathematical problems.
- 6.GM.1.1 Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm.
- 6.GM.1.2 Develop and use formulas to determine the area of triangles.
- 6.GM.1.3 Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.

- 6.GM.2 Understand and use relationships between angles in geometric figures.
- 6.GM.2.1 Solve problems using the relationships between the angles (vertical, complementary, and supplementary) formed by intersecting lines.
- 6.GM.2.2 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.3 Choose appropriate units of measurement and use ratios to convert within measurement systems to solve real-world and mathematical problems.
- 6.GM.3.1 Estimate weights, capacities and geometric measurements using benchmarks in customary and metric measurement systems with appropriate units.
- 6.GM.3.2 Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.

- 6.GM.4 Use translations, reflections, and rotations to establish congruency and understand symmetries.
- 6.GM.4.1 Predict, describe, and apply translations (slides), reflections (flips), and rotations (turns) to a two-dimensional figure.
- 6.GM.4.2 Recognize that translations, reflections, and rotations preserve congruency and use them to show that two figures are congruent.
- 6.GM.4.3 Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures.
- 6.GM.4.4 Identify and describe the line(s) of symmetry in two-dimensional shapes.

### 6.D Data & Probability

- 6.D.1 Display and analyze data.
- 6.D.1.1 Calculate the mean, median, and mode for a set of real-world data.
- 6.D.1.2 Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.
- 6.D.1.3 Create and analyze box and whisker plots observing how each segment contains one quarter of the data.

- 6.D.2 Use probability to solve real-world and 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.