Learn to add, subtract, multiply, and divide numbers with multiple digits. Encounter different types of numbers including fractions and decimals, and learn about lines and angles in geometry.

## Content

### Place Value

• Convert between equivalent forms of numbers using place value representations.
• Use place value as a tool for comparing and rounding whole numbers.

### Whole Number Arithmetic

• Use the standard algorithms to add and subtract multi-digit whole numbers.
• Draw connections between multiplication, division, multiples, and factors.
• Use visual models (such as area models and box models) to multiply and divide multi-digit whole numbers.
• Use the standard algorithms to multiply and divide multi-digit whole numbers.
• Apply whole number arithmetic to solve problems in real-world contexts.
• Use rounding as a technique for quickly estimating the result of whole number arithmetic.

### Fractions and Decimals

• Visualize and compare fractions using models.
• Understand the relationship between fractions and division.
• Reduce fractions to lowest terms.
• Convert between mixed numbers and improper fractions.
• Add and subtract fractions with like denominators.
• Use place value to convert between fraction and decimal representations.

### Measurement and Data

• Convert between units of measurement.
• Visualize data using line plots.

### Geometry

• Measure angles and classify angles as right, straight, full, null, acute, obtuse, or reflex depending on their measure.
• Identify parallel lines, perpendicular lines, and lines of symmetry.
1.
Operations & Algebraic Thinking
9 topics
1.1. Operations on Numbers
 1.1.1. Evaluating Expressions Involving Addition and Multiplication 1.1.2. Evaluating Expressions Containing Multiplication and Division 1.1.3. Solving Multistep Word Problems Using Number Operations 1.1.4. Further Solving Multistep Word Problems Using the Four Operations
1.2. Thinking Algebraically
 1.2.1. Interpreting Multiplication Equations as a Comparison 1.2.2. Representing Comparison Statements as Equations 1.2.3. Word Problems Involving Additive and Multiplicative Comparison 1.2.4. Generating Patterns 1.2.5. Identifying Patterns
2.
The Number System
15 topics
2.3. Place Value
 2.3.1. Place Value With Numbers Up to Four Digits 2.3.2. Place Value With Numbers Up to Seven Digits 2.3.3. Writing Whole Numbers in Words 2.3.4. Reading Whole Numbers Written in Words 2.3.5. Converting From Standard Form to Expanded Form 2.3.6. Converting From Expanded Form to Standard Form 2.3.7. Equivalent Place Value Representations 2.3.8. More on Equivalent Place Value Representations 2.3.9. Equivalent Place Value Representations and Borrowing
2.4. Comparing Whole Numbers
 2.4.1. Comparing Place Values 2.4.2. Comparing Whole Numbers 2.4.3. Comparing Whole Numbers Using Place Value 2.4.4. Rounding Down Whole Numbers 2.4.5. Rounding Up Whole Numbers 2.4.6. Rounding Up the Digit 9
3.
13 topics
3.6. Subtracting Whole Numbers
 3.6.1. Subtracting Two-Digit Numbers 3.6.2. Subtracting Two-Digit Numbers From Three-Digit Numbers 3.6.3. Subtracting Three-Digit Numbers 3.6.4. Subtracting Numbers Up to Five Digits 3.6.5. Subtracting Numbers Up to Seven Digits 3.6.6. Estimating Multi-Digit Subtraction
4.
Multiplication
20 topics
4.7. Factors, Products, and Multiples
 4.7.1. Products and Factors 4.7.2. The Factors of a Number 4.7.3. Prime and Composite Numbers 4.7.4. The Multiples of a Number 4.7.5. Least Common Multiples 4.7.6. Connecting Factors and Multiples 4.7.7. Greatest Common Factors
4.8. Multiplying Whole Numbers
 4.8.1. Multiplying by 10, 100, and 1,000 Using Place Value 4.8.2. Multiplying by 10, 100, and 1,000 Using the Pattern of Zeros 4.8.3. Rewriting Numbers Ending in Zeros 4.8.4. Multiplying Whole Numbers Ending in Zeros 4.8.5. Multiplying Numbers Using Repeated Addition 4.8.6. Multiplying Numbers Using Repeated Subtraction 4.8.7. Estimating Multi-Digit Multiplication
4.9. Multiplying Whole Numbers Using Models
 4.9.1. Two-Digit by One-Digit Multiplication Using Area Models 4.9.2. Multi-Digit by One-Digit Multiplication Using Area Models 4.9.3. Two-Digit by One-Digit Multiplication Using Place Value 4.9.4. Multi-Digit by One-Digit Multiplication Using Place Value 4.9.5. Two-Digit by Two-Digit Multiplication Using Area Models 4.9.6. Two-Digit by Two-Digit Multiplication Using Place Value
5.
Division
16 topics
5.10. Dividing Whole Numbers
 5.10.1. The Relationship Between Multiplication and Division 5.10.2. Understanding Remainders Using Models 5.10.3. Finding Remainders 5.10.4. Dividends, Divisors, Quotients, and Remainders 5.10.5. Division With Remainders 5.10.6. Interpreting Remainders in Context 5.10.7. Dividing by 10, 100, and 1,000 Using the Pattern of Zeros 5.10.8. Dividing by One-Digit Numbers by Connecting Multiplication and Division 5.10.9. Dividing Numbers Using Place-Value Strategies 5.10.10. Estimating Multi-Digit Division
5.11. Dividing Whole Numbers Using Models
 5.11.1. Two-Digit by One-Digit Division Using Area Models 5.11.2. Multi-Digit by One-Digit Division Using Area Models 5.11.3. More Multi-Digit by One-Digit Division Using Area Models 5.11.4. Two-Digit by One-Digit Division Using Box Models 5.11.5. Two-Digit by One-Digit Division Using Box Models With Remainders 5.11.6. Multi-Digit by One-Digit Division Using Box Models
6.
Fractions & Decimals
40 topics
6.12. Fractions
 6.12.1. Fraction Models 6.12.2. Writing Unit Fractions in Words 6.12.3. Writing Fractions in Words 6.12.4. Fraction Models for Improper Fractions 6.12.5. Finding Equivalent Fractions Using Area Models 6.12.6. Equivalent Fractions 6.12.7. Least Common Denominators 6.12.8. Writing Fractions in Lowest Terms 6.12.9. Interpreting Fractions as Division
6.13. Mixed Numbers
 6.13.1. Models for Mixed Numbers 6.13.2. Interpreting Division Problems as Mixed Numbers 6.13.3. Converting Improper Fractions to Mixed Numbers 6.13.4. Converting Mixed Numbers to Improper Fractions
6.14. Comparing Fractions
 6.14.1. Comparing Fractions 6.14.2. Comparing Fractions Using Unit Benchmarks 6.14.3. Comparing Fractions Using One-Half Benchmarks 6.14.4. Comparing Fractions Using Common Denominators
 6.15.1. Adding Fractions With Like Denominators Using Models 6.15.2. Adding Fractions With Like Denominators 6.15.3. Subtracting Fractions With Like Denominators 6.15.4. Adding and Subtracting Fractions With Like Denominators: Word Problems 6.15.5. Decomposing Fractions Into Sums Using Models 6.15.6. Decomposing Fractions Into Sums
 6.16.1. Adding Mixed Numbers With Like Denominators 6.16.2. Subtracting Mixed Numbers With Like Denominators 6.16.3. Subtracting Mixed Numbers With Like Denominators Using Improper Fractions 6.16.4. Adding and Subtracting Mixed Numbers With Like Denominators: Word Problems
6.17. Multiplying Fractions
 6.17.1. Multiplying Unit Fractions by Whole Numbers Using Models 6.17.2. Multiplying Fractions by Whole Numbers Using Models 6.17.3. Multiplying Fractions by Whole Numbers 6.17.4. Multiplying Fractions by Whole Numbers: Word Problems 6.17.5. Strategies to Simplify Whole Number and Fraction Multiplication
6.18. Decimals
 6.18.1. Decimal Fractions 6.18.2. Plotting Decimals on Number Lines 6.18.3. Comparing Decimals Up to Hundredths 6.18.4. Converting Fractions to Decimals 6.18.5. Converting Mixed Numbers to Decimals 6.18.6. Converting Decimals to Fractions 6.18.7. Converting Decimals to Mixed Numbers 6.18.8. Adding Decimal Fractions
7.
Measurement & Data
18 topics
7.19. Units
 7.19.1. Units 7.19.2. Converting Metric Units of Length to Smaller Units 7.19.3. Converting Customary Units of Length to Smaller Units 7.19.4. Converting Units of Volume to Smaller Units 7.19.5. Converting Units of Mass to Smaller Units 7.19.6. Converting Units of Time to Smaller Units
7.20. Representing and Interpreting Data
 7.20.1. Creating and Interpreting Line Plots 7.20.2. Creating and Interpreting Line Plots With Fractions
7.21. Geometry
 7.21.1. Points, Lines, Rays, and Segments 7.21.2. Angles and Measures of Angles 7.21.3. Connecting Angles and Circles 7.21.4. Measuring Angles Using a Protractor 7.21.5. Right, Straight, Full, and Null Angles 7.21.6. Acute, Obtuse, and Reflex Angles 7.21.7. Sums of Angles 7.21.8. Solving Angle Problems 7.21.9. Parallel and Perpendicular Lines 7.21.10. Modeling With Rectangles