### I: Students will expand number sense to include operations with rational numbers.

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

I.1.d: Express numbers in scientific notation using positive powers of ten.

#### I.2: Explain relationships and equivalencies among rational numbers.

I.2.a: Place rational numbers on the number line.

I.2.b: Compare and order rational numbers, including positive and negative mixed fractions and decimals, using a variety of methods and symbols, including the number line and finding common denominators.

I.2.d: Relate percents less than 1% or greater than 100% to equivalent fractions, decimals, whole numbers, and mixed numbers.

I.2.e: Recognize that the sum of an integer and its additive inverse is zero.

#### I.3: Use number theory concepts to find prime factorizations, least common multiples, and greatest common factors.

I.3.a: Determine whether whole numbers to 100 are prime, composite, or neither.

I.3.b: Find the prime factorization of composite numbers to 100.

#### I.4: Model and illustrate meanings of operations and describe how they relate.

I.4.a: Relate fractions to multiplication and division and use this relationship to explain procedures for multiplying and dividing fractions.

#### I.5: Solve problems involving multiple steps.

I.5.a: Select appropriate methods to solve a multi-step problem involving multiplication and division of fractions and decimals.

I.5.c: Use estimation or calculation to compute results, depending on the context and numbers involved in the problem.

I.5.d: Solve problems involving ratios and proportions.

#### I.6: Demonstrate proficiency with the four operations, with positive rational numbers, and with addition and subtraction of integers.

I.6.a: Multiply and divide a multi-digit number by a two-digit number, including decimals.

I.6.b: Add, subtract, multiply, and divide fractions and mixed numbers.

### II: Students will use patterns, relations, and algebraic expressions to represent and analyze mathematical problems and number relationships.

#### II.1: Analyze algebraic expressions, tables, and graphs to determine patterns, relations, and rules.

II.1.a: Describe simple relationships by creating and analyzing tables, equations, and expressions.

II.1.b: Draw a graph and write an equation from a table of values.

II.1.c: Draw a graph and create a table of values from an equation.

#### II.2: Write, interpret, and use mathematical expressions, equations, and formulas to represent and solve problems that correspond to given situations.

II.2.a: Solve single variable linear equations using a variety of strategies.

II.2.b: Recognize that expressions in different forms can be equivalent and rewrite an expression to represent a quantity in a different way.

II.2.c: Evaluate and simplify expressions and formulas, substituting given values for the variables (e.g., 2x + 4; x = 2; therefore, 2 (2) + 4 = 8).

### III: Students will use spatial and logical reasoning to recognize, describe, and analyze geometric shapes and principles.

#### III.1: Identify and analyze attributes and properties of geometric shapes to solve problems.

III.1.a: Identify the midpoint of a line segment and the center and circumference of a circle.

III.1.b: Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms.

### IV: Students will understand and apply measurement tools and techniques and find the circumference and area of a circle.

#### IV.1: Describe and find the circumference and area of a circle.

IV.1.a: Explore the relationship between the radius and diameter of a circle to the circle?s circumference to develop the formula for circumference.

IV.1.b: Find the circumference of a circle using a formula.

IV.1.e: Find the area of a circle using a formula.

#### IV.2: Identify and describe measurable attributes of objects and units of measurement, and solve problems involving measurement.

IV.2.b: Convert units of measurement within the metric system and convert units of measurement within the customary system.

IV.2.d: Determine when it is appropriate to estimate or use precise measurement when solving problems.

IV.2.e: Derive and use the formula to determine the surface area and volume of a cylinder.

### V: Students will analyze, draw conclusions, and make predictions based upon data and apply basic concepts of probability.

#### V.1: Design investigations to reach conclusions using statistical methods to make inferences based on data.

V.1.b: Extend data display and comparisons to include scatter plots and circle graphs.

V.1.c: Compare two similar sets of data on the same graph and compare two graphs representing the same set of data.

V.1.d: Recognize that changing the scale influences the appearance of a display of data.

V.1.e: Propose and justify inferences and predictions based on data.

#### V.2: Apply basic concepts of probability and justify outcomes.

V.2.a: Write the results of a probability experiment as a fraction between zero and one, or an equivalent percent.

V.2.b: Compare experimental results with theoretical results (e.g., experimental: 7 out of 10 tails; whereas, theoretical 5 out of 10 tails).

V.2.c: Compare individual, small group, and large group results of a probability experiment in order to more accurately estimate the actual probabilities.

Correlation last revised: 5/24/2018

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