### 1: Number Sense, Properties, and Operations

#### 1.1: Understand the structure and properties of our number system. At their most basic level numbers are abstract symbols that represent real-world quantities

1.1: The decimal number system describes place value patterns and relationships that are repeated in large and small numbers and forms the foundation for efficient algorithms

1.1.a: Students can: Explain that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

1.1.b: Students can: Read, write, and compare decimals to thousandths.

1.1.b.i: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form.

1.1.b.ii: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

1.1.d: Students can: Convert like measurement units within a given measurement system.

1.1.d.i: Convert among different-sized standard measurement units within a given measurement system.

1.1.d.ii: Use measurement conversions in solving multi-step, real world problems.

#### 1.2: Are fluent with basic numerical and symbolic facts and algorithms, and are able to select and use appropriate (mental math, paper and pencil, and technology) methods based on an understanding of their efficiency, precision, and transparency

1.2: Formulate, represent, and use algorithms with multi-digit whole numbers and decimals with flexibility, accuracy, and efficiency

1.2.a: Students can: Fluently multiply multi-digit whole numbers using standard algorithms.

1.2.b: Students can: Find whole-number quotients of whole numbers.

1.2.b.i: Use strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.

1.2.b.ii: Illustrate and explain calculations by using equations, rectangular arrays, and/or area models.

1.2.c: Students can: Add, subtract, multiply, and divide decimals to hundredths.

1.2.c.i: Use concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

1.2.c.ii: Relate strategies to a written method and explain the reasoning used.

1.2.d: Students can: Write and interpret numerical expressions.

1.2.d.i: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

1.3: Formulate, represent, and use algorithms to add and subtract fractions with flexibility, accuracy, and efficiency

1.3.a: Students can: Use equivalent fractions as a strategy to add and subtract fractions.

1.3.a.i: Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

1.3.a.ii: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions with like denominators.

1.3.a.iii: Solve word problems involving addition and subtraction of fractions referring to the same whole.

#### 1.3: Understand the structure and properties of our number system. At their most basic level numbers are abstract symbols that represent real-world quantities

1.4: The concepts of multiplication and division can be applied to multiply and divide fractions

1.4.a: Students can: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b).

1.4.b: Students can: Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.

1.4.c: Students can: Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. In general, (a/b) × (c/d) = ac/bd.

1.4.d: Students can: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths.

1.4.d.i: Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

1.4.f: Students can: Solve real world problems involving multiplication of fractions and mixed numbers.

### 2: Patterns, Functions, and Algebraic Structures

#### 2.1: Make sound predictions and generalizations based on patterns and relationships that arise from numbers, shapes, symbols, and data

2.1: Number patterns are based on operations and relationships

2.1.a: Students can: Generate two numerical patterns using given rules.

2.1.b: Students can: Identify apparent relationships between corresponding terms.

2.1.c: Students can: Form ordered pairs consisting of corresponding terms from the two patterns, and graphs the ordered pairs on a coordinate plane.

2.1.d: Students can: Explain informally relationships between corresponding terms in the patterns.

2.1.f: Students can: Explain, extend, and use patterns and relationships in solving problems, including those involving saving and checking accounts such as understanding that spending more means saving less.

### 4: Shape, Dimension, and Geometric Relationships

#### 4.1: Understand quantity through estimation, precision, order of magnitude, and comparison. The reasonableness of answers relies on the ability to judge appropriateness, compare, estimate, and analyze error

4.1: Properties of multiplication and addition provide the foundation for volume an attribute of solids.

4.1.a: Students can: Model and justify the formula for volume of rectangular prisms.

4.1.a.i: Model the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes.

4.1.a.ii: Show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base.

4.1.a.iii: Represent threefold whole-number products as volumes to represent the associative property of multiplication.

4.1.b: Students can: Find volume of rectangular prisms using a variety of methods and use these techniques to solve real world and mathematical problems.

4.1.b.i: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

4.1.b.ii: Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths.

#### 4.2: Make claims about relationships among numbers, shapes, symbols, and data and defend those claims by relying on the properties that are the structure of mathematics

4.2: Geometric figures can be described by their attributes and specific locations in the plane

4.2.a: Students can: Graph points on the coordinate plane to solve real-world and mathematical problems.

4.2.b: Students can: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

4.2.c: Students can: Classify two-dimensional figures into categories based on their properties.

4.2.c.i: Explain that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

4.2.c.ii: Classify two-dimensional figures in a hierarchy based on properties.

Correlation last revised: 9/22/2020

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