### 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 whole number system describes place value relationships and forms the foundation for efficient algorithms

1.1.a: Students can: Use place value and properties of operations to perform multi-digit arithmetic.

1.1.a.i: Use place value understanding to round whole numbers to the nearest 10 or 100.

1.1.a.ii: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

#### 1.2: Understand that equivalence is a foundation of mathematics represented in numbers, shapes, measures, expressions, and equations

1.2: Parts of a whole can be modeled and represented in different ways

1.2.a: Students can: Develop understanding of fractions as numbers.

1.2.a.i: Describe a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; describe a fraction a/b as the quantity formed by a parts of size 1/b.

1.2.a.ii: Describe a fraction as a number on the number line; represent fractions on a number line diagram.

1.2.a.iii: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

1.2.a.iii.1: Identify two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

1.2.a.iii.2: Identify and generate simple equivalent fractions. Explain why the fractions are equivalent.

1.2.a.iii.3: Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

1.2.a.iii.4: Compare two fractions with the same numerator or the same denominator by reasoning about their size.

1.2.a.iii.5: Explain why comparisons are valid only when the two fractions refer to the same whole.

1.2.a.iii.6: Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.

#### 1.3: 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

1.3: Multiplication and division are inverse operations and can be modeled in a variety of ways

1.3.a: Students can: Represent and solve problems involving multiplication and division.

1.3.a.i: Interpret products of whole numbers.

1.3.a.ii: Interpret whole-number quotients of whole numbers.

1.3.a.iii: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.

1.3.a.iv: Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

1.3.a.v: Model strategies to achieve a personal financial goal using arithmetic operations.

1.3.b: Students can: Apply properties of multiplication and the relationship between multiplication and division.

1.3.b.i: Apply properties of operations as strategies to multiply and divide.

1.3.b.ii: Interpret division as an unknown-factor problem.

1.3.c: Students can: Multiply and divide within 100.

1.3.c.i: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations.

1.3.d: Students can: Solve problems involving the four operations, and identify and explain patterns in arithmetic.

1.3.d.i: Solve two-step word problems using the four operations.

1.3.d.ii: Represent two-step word problems using equations with a letter standing for the unknown quantity.

1.3.d.iii: Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

1.3.d.iv: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.

### 3: Data Analysis, Statistics, and Probability

#### 2.1: Solve problems and make decisions that depend on understanding, explaining, and quantifying the variability in data

3.1: Visual displays are used to describe data

3.1.a: Students can: Represent and interpret data.

3.1.a.i: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories.

3.1.a.ii: Solve one- and two-step 'how many more' and 'how many less' problems using information presented in scaled bar graphs.

3.1.a.iii: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters.

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

#### 3.1: 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

4.1: Geometric figures are described by their attributes

4.1.a: Students can: Reason with shapes and their attributes.

4.1.a.i: Explain that shapes in different categories may share attributes and that the shared attributes can define a larger category.

4.1.a.i.1: Identify rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

4.1.a.ii: Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.

#### 3.2: 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

4.2: Linear and area measurement are fundamentally different and require different units of measure

4.2.a: Students can: Use concepts of area and relate area to multiplication and to addition.

4.2.a.ii: Find area of rectangles with whole number side lengths using a variety of methods.

4.2.a.iii: Relate area to the operations of multiplication and addition and recognize area as additive.

4.2.b: Students can: Describe perimeter as an attribute of plane figures and distinguish between linear and area measures.

4.2.c: Students can: Solve real world and mathematical problems involving perimeters of polygons.

4.2.c.i: Find the perimeter given the side lengths.

4.2.c.ii: Find an unknown side length given the perimeter.

4.2.c.iii: Find rectangles with the same perimeter and different areas or with the same area and different perimeters.

4.3: Time and attributes of objects can be measured with appropriate tools

4.3.a: Students can: Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

4.3.a.i: Tell and write time to the nearest minute.

4.3.a.ii: Measure time intervals in minutes.

4.3.a.iii: Solve word problems involving addition and subtraction of time intervals in minutes using a number line diagram.

4.3.a.iv: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).

4.3.a.v: Use models to add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units.

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.