### I: Students will expand number sense to include integers and perform operations with whole numbers, simple fractions, and decimals.

#### I.1: Represent whole numbers and decimals from thousandths to one billion, fractions, percents, and integers.

I.1.a: Read and write numbers in standard and expanded form.

I.1.b: Demonstrate multiple ways to represent whole numbers, decimals, fractions, percents, and integers using models and symbolic representations (e.g., 108 = 2 x 50 + 8; 108 = 102 + 8; 90% = 90 out of 100 squares on a hundred chart).

I.1.c: Identify, read, and locate fractions, mixed numbers, decimals, and integers on the number line.

#### I.2: Explain relationships and equivalencies among integers, fractions, decimals, and percents.

I.2.a: Compare fractions by finding a common denominator.

I.2.b: Order integers, fractions (including mixed numbers), and decimals using a variety of methods, including the number line.

I.2.d: Represent commonly used fractions as decimals and percents in a variety of ways (e.g., models, fraction strips, pictures, calculators, algorithms).

I.2.e: Model and calculate equivalent forms of a fraction (including simplest form).

#### I.3: Use number theory concepts to develop and use divisibility tests; classify whole numbers to 50 as prime, composite, or neither; and find common multiples and factors.

I.3.b: Use strategies for classifying whole numbers to 50 as prime, composite, or neither.

I.3.c: Rewrite a composite number between 2 and 50 as a product of only prime numbers.

I.3.d: Find common multiples and factors and apply to adding and subtracting fractions.

#### I.4: Model and illustrate meanings of multiplication and division.

I.4.a: Represent division-with-remainder using whole numbers, decimals, or fractions.

I.4.c: Model multiplication of fractions and decimals (e.g., tenths multiplied by tenths, a whole number multiplied by tenths, or a whole number with tenths multiplied by tenths) in a variety of ways (e.g., manipulatives, number line and area models, patterns).

#### I.5: Solve problems involving one or two operations.

I.5.a: Determine when it is appropriate to use estimation, mental math strategies, paper and pencil, and algorithms.

I.5.d: Interpret division-with-remainder problems as they apply to the environment (e.g., If there are 53 people, how many vans are needed if each van holds 8 people?).

#### I.6: Demonstrate proficiency with multiplication and division of whole numbers and compute problems involving addition, subtraction, and multiplication of decimals and fractions.

I.6.b: Divide multi-digit dividends by a one-digit divisor with fluency, using efficient procedures.

I.6.c: Add and subtract decimals with fluency, using efficient procedures.

I.6.d: Add and subtract fractions with fluency.

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

#### II.2: Use algebraic expressions, inequalities, or equations to represent and solve simple real-world problems.

II.2.a: Use properties and the order of operations involving addition, subtraction, multiplication, division, and the use of parentheses to compute with whole numbers, decimals, and fractions.

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

#### III.1: Describe relationships between two- and three-dimensional shapes and analyze attributes and properties of geometric shapes.

III.1.a: Draw, label, and describe line segments, rays, lines, parallel lines, and perpendicular lines.

III.1.c: Classify triangles and quadrilaterals and analyze the relationships among the shapes in each classification (e.g., a square is a rectangle).

#### III.2: Specify locations in a coordinate plane.

III.2.a: Locate points defined by ordered pairs of integers.

III.2.b: Write an ordered pair for a point in a coordinate plane with integer coordinates.

III.2.c: Specify possible paths between locations on a coordinate plane and compare distances of the various paths.

### IV: Students will determine area of polygons and surface area and volume of three-dimensional shapes.

#### IV.2: Recognize, describe, and determine surface area and volume of three-dimensional shapes.

IV.2.c: Derive and use the formula to determine the volume of a right prism with a triangular or rectangular base.

### V: Students will construct, analyze, and construct reasonable conclusions from data and apply basic concepts of probability.

#### V.1: Formulate and answer questions using statistical methods to compare data, and propose and justify inferences based on data.

V.1.a: Construct, analyze, and display data using an appropriate format (e.g., line plots, bar graphs, line graphs).

V.1.d: Identify and calculate the mean, median, mode, and range.

#### V.2: Apply basic concepts of probability.

V.2.a: Describe the results of experiments involving random outcomes using a variety of notations (e.g., 4 out of 9, 4/9).

V.2.b: Recognize that probability is always a value between 0 and 1 (inclusively).

Correlation last revised: 5/24/2018

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.