### I: Students will expand number sense to understand, perform operations, and solve problems with rational numbers.

#### I.1: Represent rational numbers in a variety of ways.

I.1.a: Demonstrate multiple ways to represent whole numbers, decimals, fractions, percents, and integers using models and real-life examples.

I.1.b: Simplify numerical expressions with whole number exponents using order of operations, and recognize that any positive number to the 0 power is 1.

I.1.c: Represent numbers greater than one using scientific notation.

I.1.d: Select the most appropriate form of a rational number for a given context.

#### I.2: Compare and order rational numbers, including positive and negative fractions, positive and negative mixed numbers, and positive and negative decimals.

I.2.a: Identify, read, and locate rational numbers on a number line.

I.2.b: Compare pairs of rational numbers in different forms.

I.2.c: Order rational numbers with and without a number line.

#### I.3: Explain relationships and equivalences among rational numbers.

I.3.a: Find equivalent forms for common fractions, decimals, percents, and ratios, including repeating or terminating decimals.

I.3.d: Recognize and use the inverse operations of adding and subtracting a fixed number, multiplying and dividing by a fixed number, and computing squares of whole numbers and taking square roots of perfect squares.

#### I.4: Model meanings of ratios and operations with rational numbers.

I.4.a: Demonstrate that the fraction a/b represents a divided by b.

I.4.b: Recognize percents as ratios based on 100 and decimals as ratios based on powers of 10.

#### I.5: Solve problems involving rational numbers.

I.5.a: Compute fluently using all four operations with integers and positive fractions and decimals.

I.5.b: Solve problems using factors, multiples, prime factorization, relatively prime numbers, and common divisibility rules.

I.5.c: Solve application problems involving rational numbers.

I.5.d: Determine if an answer is reasonable using estimation.

### II: Students will use proportional reasoning to solve problems.

#### II.1: Solve problems involving ratios, rates, proportions and percentages.

II.1.b: Solve percent problems using ratio and proportion, including problems involving discounts, interest, taxes, tips, and percent increase or decrease.

II.1.c: Solve problems involving proportions, rates, and measures.

#### II.2: Apply the properties of proportionality to different units of measurement.

II.2.a: Convert from one unit of measurement to an equivalent unit of measurement in the same system using a given conversion factor.

II.2.b: Understand that in a proportional relationship, all dimensions change by the same scale factor.

### III: Students will develop fluency with the language and operations of algebra to analyze and represent relationships.

#### III.1: Evaluate, simplify, and solve algebraic expressions and equations.

III.1.b: Translate verbal expressions into algebraic expressions.

III.1.c: Simplify and evaluate algebraic expressions.

III.1.d: Show that performing the same operation on both sides of an equation will produce an equivalent equation.

III.1.e: Solve single-variable linear equations and inequalities of the formax + b = c, ax + b < c, or ax + b > c.

#### III.2: Represent relationships using graphs, tables, and other models.

III.2.a: Identify integer coordinates when given the graph of a point on a rectangular coordinate system.

III.2.b: Graph ordered pairs of integers on a rectangular coordinate system.

III.2.c: Model real-world problems using graphs, tables, equations, manipulatives, and pictures.

### IV: Students will use algebraic, spatial, and logical reasoning to solve geometry and measurement problems.

#### IV.1: Draw, label, and describe attributes of geometric figures to determine geometric relationships.

IV.1.c: Draw, label, and describe attributes of angles, triangles, and quadrilaterals.

#### IV.2: Determine measurements in metric and customary units using appropriate tools and formulas.

IV.2.b: Measure length, area, volume, and angles to appropriate levels of precision.

IV.2.c: Calculate the measurement of everyday objects using formulas for perimeters and areas of triangles and quadrilaterals, and circumferences and areas of circles.

### V: Students will understand concepts from probability and statistics and apply statistical methods to solve problems.

#### V.1: Use basic concepts of probability to determine the likelihood of an event and compare the results of various experiments.

V.1.a: Write the results of a probability experiment as a fraction, ratio, or decimal, between zero and one, or as a percent between zero and one hundred, inclusive.

V.1.b: Compare experimental results with theoretical probability.

V.1.c: Compare individual, small group, and large group results of a probability experiment.

#### V.2: Display and compare data to make predictions and formulate conclusions.

V.2.a: Display data using tables, scatter plots, and circle graphs.

V.2.b: Compare two similar sets of data on the same graph.

V.2.c: Compare two different kinds of graphs representing the same set of data.

V.2.d: Propose and justify inferences and predictions based on data.

Correlation last revised: 5/24/2018

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