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.

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

- 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.

- 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.

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

- 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.

Addition & Subtraction
13 topics

3.5. Adding Whole Numbers

3.5.1. | Adding Two-Digit Whole Numbers | |

3.5.2. | Adding Three-Digit and Two-Digit Numbers | |

3.5.3. | Adding Three-Digit Numbers | |

3.5.4. | Adding Numbers Up to Five Digits | |

3.5.5. | Adding Numbers Up to Seven Digits | |

3.5.6. | Adding Three Multi-Digit Numbers | |

3.5.7. | Estimating Multi-Digit Addition |

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. Adding Fractions

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. Adding Mixed Numbers

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 |