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Learn how to perform arithmetic with negative numbers, fractions, and decimals. Solve real-world problems involving measurement, data, and geometry.

## Content

### Interpreting Numbers and Operations

• Construct and interpret numerical expressions.
• Use number lines to visualize addition, subtraction, and negative numbers.
• Understand the place value system in base ten and apply it to perform arithmetic with multi-digit numbers.
• Interpret exponentiation as repeated multiplication.

### Fractions and Computation

• Leverage equivalent fractions as a strategy to add and subtract fractions.
• Generalize previous understandings of multiplication and division to multiply and divide fractions.
• Apply the order of operations to evaluate arithmetic expressions.
• Estimate the results of arithmetic expressions using number sense and rounding.

### Measurement and Data

• Convert units of measurement.
• Analyze patterns and relationships and visualize them in the coordinate plane.

### Geometry

• Classify two-dimensional shapes based on their properties.
• Understand how volume relates to addition and multiplication.
1.
The Number System
9 topics
1.1. Numerical Expressions
 1.1.1. Evaluating Whole Number Expressions 1.1.2. Evaluating Whole Number Expressions Containing Parentheses 1.1.3. Creating and Interpreting Numerical Expressions 1.1.4. Using Terminology to Create Expressions 1.1.5. Working With Numerical Expressions: Multiplication and Division 1.1.6. Working With Numerical Expressions: Addition and Subtraction
1.2. Negative Numbers
 1.2.1. Representing Negative Numbers on a Number Line 1.2.2. Comparing Negative Numbers 1.2.3. Absolute Value
2.
Multiplying & Dividing Whole Numbers
16 topics
2.3. Multiplying Whole Numbers
 2.3.1. Multiplying Whole Numbers by Powers of Ten Using Place Value 2.3.2. Two-Digit by One-Digit Multiplication Using the Standard Algorithm 2.3.3. Multi-Digit by One-Digit Multiplication Using the Standard Algorithm 2.3.4. Two-Digit by Two-Digit Multiplication Using the Standard Algorithm 2.3.5. Multi-Digit by Two-Digit Multiplication Using the Standard Algorithm 2.3.6. Three-Digit by Three-Digit Multiplication Using the Standard Algorithm
2.4. Dividing Whole Numbers
 2.4.1. Two-Digit by One-Digit Division Using the Standard Algorithm 2.4.2. Three-Digit by One-Digit Division Using the Standard Algorithm 2.4.3. Four-Digit by One-Digit Division Using the Standard Algorithm 2.4.4. Dividing Numbers by One-Digit Numbers: Interpreting the Remainder 2.4.5. Using Fractions to Represent Division of Whole Numbers 2.4.6. Dividing by Two-Digit Numbers by Connecting Multiplication and Division 2.4.7. Dividing by Two-Digit Numbers With Remainders by Connecting Multiplication and Division 2.4.8. Dividing Numbers by Two-Digit Numbers Using Box Models 2.4.9. Three-Digit by Two-Digit Division Using the Standard Algorithm 2.4.10. Four-Digit by Two-Digit Division Using the Standard Algorithm
3.
14 topics
3.5. Adding and Subtracting Fractions and Whole Numbers
 3.5.1. Adding Fractions and Whole Numbers Using Models 3.5.2. Adding Fractions and Whole Numbers 3.5.3. Subtracting Fractions and Whole Numbers Using Models 3.5.4. Subtracting Fractions and Whole Numbers
 3.6.1. Estimating Sums and Differences of Fractions Using Benchmarks 3.6.2. Adding Fractions With Unlike Denominators Using Models 3.6.3. Subtracting Fractions With Unlike Denominators Using Models 3.6.4. Adding Fractions With Unlike Denominators 3.6.5. Subtracting Fractions With Unlike Denominators 3.6.6. Adding and Subtracting Fractions With Unlike Denominators: Word Problems
3.7. Adding and Subtracting Mixed Numbers
 3.7.1. Adding Mixed Numbers With Unlike Denominators 3.7.2. Subtracting Mixed Numbers With Unlike Denominators 3.7.3. Subtracting Mixed Numbers With Unlike Denominators Using Improper Fractions 3.7.4. Adding and Subtracting Mixed Numbers With Unlike Denominators: Word Problems
4.
Multiplying & Dividing Fractions
26 topics
4.8. Multiplying Fractions
 4.8.1. Multiplying Fractions by Unit Fractions Using Models 4.8.2. Multiplying Fractions Using Models 4.8.3. Multiplying Fractions 4.8.4. Multiplying Fractions: Word Problems 4.8.5. Interpreting Fraction Multiplication 4.8.6. Multiplying Mixed Numbers by Whole Numbers 4.8.7. Multiplying Mixed Numbers by Whole Numbers: Word Problems 4.8.8. Multiplying Mixed Numbers by Fractions 4.8.9. Multiplying Mixed Numbers 4.8.10. Multiplying Mixed Numbers: Word Problems 4.8.11. Connecting Fraction Multiplication and Area 4.8.12. Finding Areas Using Fraction Multiplication 4.8.13. Fraction Multiplication Number Sense
4.9. Dividing Fractions
 4.9.1. Dividing Fractions Using Properties of Division 4.9.2. Dividing Whole Numbers by Unit Fractions Using Models 4.9.3. Dividing Whole Numbers by Unit Fractions 4.9.4. Dividing Unit Fractions by Whole Numbers Using Models 4.9.5. Dividing Unit Fractions by Whole Numbers 4.9.6. Reciprocals 4.9.7. Dividing Whole Numbers by Fractions Using Models 4.9.8. Dividing Whole Numbers by Fractions 4.9.9. Dividing Fractions by Whole Numbers Using Models 4.9.10. Dividing Fractions by Whole Numbers 4.9.11. Dividing Fractions and Whole Numbers: Word Problems 4.9.12. Dividing Fractions Using Models 4.9.13. Dividing Fractions
5.
Decimals
15 topics
5.10. Decimals
 5.10.1. The Place Value System With Decimals 5.10.2. Comparing Place Values With Decimals 5.10.3. Reading and Writing Decimals Written in Words 5.10.4. Converting From Standard Form to Expanded Form With Decimals 5.10.5. Converting From Expanded Form to Standard Form With Decimals 5.10.6. Equivalent Decimals 5.10.7. Comparing Decimals Using Place Value 5.10.8. Rounding Down Decimals 5.10.9. Rounding Up Decimals
 5.11.1. Estimating Decimal Addition and Subtraction 5.11.2. Adding Decimals 5.11.3. Decimal Addition With Unequal Numbers of Decimals 5.11.4. Subtracting Decimals 5.11.5. Decimal Subtraction With Unequal Numbers of Decimals 5.11.6. Estimating Decimal Addition and Subtraction With Benchmarks
6.
Multiplying & Dividing Decimals
17 topics
6.12. Multiplying Decimals
 6.12.1. Multiplying Decimals by Powers of Ten Using Place Value 6.12.2. Multiplying Decimals by Powers of Ten Using Decimal Point Placement 6.12.3. Estimating Decimal Multiplication 6.12.4. Multiplying a Decimal by a One-Digit Whole Number 6.12.5. Multiplying a Decimal by a Multi-Digit Whole Number 6.12.6. Multiplying Two-Digit Decimals 6.12.7. Multiplying Two-Digit Decimals by Three-Digit Decimals 6.12.8. Multiplying Three-Digit Decimals
6.13. Dividing Decimals
 6.13.1. Dividing Decimals by Powers of Ten Using Place Value 6.13.2. Dividing Decimals by Powers of Ten Using Decimal Point Placement 6.13.3. Estimating Decimal Division 6.13.4. Dividing Decimals Using Strategies Based on Place Value 6.13.5. Division of Whole Numbers With Decimal Quotients 6.13.6. Division of Whole Numbers With Decimal Quotients and Rounding 6.13.7. Dividing Decimals Using the Standard Algorithm 6.13.8. Dividing Three-Digit Decimals by Two-Digit Decimals 6.13.9. Dividing Four-Digit and Five-Digit Decimals
7.
Exponents
10 topics
7.14. Exponents
 7.14.1. Powers of Ten With Exponents 7.14.2. Multiplying a Whole Number by a Power of Ten With Exponents 7.14.3. Multiplying a Decimal Number by a Power of Ten With Exponents 7.14.4. Introduction to Exponents 7.14.5. Evaluating Exponents 7.14.6. Evaluating Larger Exponents 7.14.7. Evaluating Exponents With Fractional Bases 7.14.8. Evaluating Exponents With Decimal Bases 7.14.9. Comparing Exponents 7.14.10. Evaluating Whole Number Expressions Containing Exponents
8.
Measurement & Data
12 topics
8.15. Units
 8.15.1. Converting Units of Length to Larger Units 8.15.2. Converting Units of Volume to Larger Units 8.15.3. Converting Units of Weight to Larger Units 8.15.4. Converting Units of Time to Larger Units
8.16. Representing and Interpreting Data
 8.16.1. Operations on Fractions With Line Plots 8.16.2. Further Operations on Fractions With Line Plots
8.17. Coordinates
 8.17.1. Describing the Coordinate Plane 8.17.2. Solving Real World Problems Using Coordinates 8.17.3. Coordinate Planes as Maps
8.18. Patterns and Relationships
 8.18.1. Connecting Patterns 8.18.2. Comparing Patterns 8.18.3. Graphing Patterns
9.
Geometry
7 topics
9.19. Volume
 9.19.1. Understanding Volume Using Unit Cubes 9.19.2. Volumes of Right Rectangular Prisms 9.19.3. Volumes of Right Rectangular Prisms: Word Problems
9.20. 2D Shapes
 9.20.1. Polygons 9.20.2. Quadrilaterals 9.20.3. Rectangles, Rhombuses, and Squares 9.20.4. Classifying Quadrilaterals