Our fully accredited, Common Core-aligned 4th Grade Math course draws on students' knowledge of basic arithmetic
to develop concrete models on which to base higher-level arithmetic techniques. Once a thorough understanding of
these concrete models is established, students use them to obtain computational fluency in the four fundamental
arithmetic operations. Students gain a solid grasp of other types of numbers (fractions and decimals), including
mastering some operations with these objects. Finally, students further develop their reasoning and modeling
skills, including applying them to real-world situations involving data, geometry, and units.

Upon completing our 4th-Grade course, students will gain mastery of multi-digit addition and subtraction and build solid foundations in multi-digit multiplication, multi-digit division, and fraction addition and multiplication. Students will have begun their journey into algebra, creating mathematical equations based on comparison statements, using letters to represent numbers, and recognizing patterns. Students will be proficient in several geometry fundamentals and their notations. In addition, students will be able to solve real-world and mathematical multistep problems using their knowledge of the fundamental arithmetic procedures.

Success in understanding higher-level procedures such as multi-digit addition and subtraction requires a solid foundation in the place value system. For this reason, students must master basic place value operations (e.g., converting between standard and expanded form, equivalent place value representations, carrying, borrowing, and rounding) before applying these techniques in their respective domains. Place value manipulations are covered as separate skills and not â€œthrown inâ€ at the same time as learning the higher-level procedures, thus avoiding cognitive interference.

High-level arithmetic procedures such as long addition, subtraction, multiplication, division, and fraction addition are first tackled in a highly scaffolded manner, developing one core skill at a time using concrete models. Once the students have demonstrated mastery of these procedures, the underlying processes are extracted, and scaffolding via models is removed, to allow students to develop proficiency and fluency in the underlying techniques in a more abstract setting.

After successfully completing the 4th Grade Math course, students will be fully prepared for the 5th Grade Math course, where several key concepts are further developed.

- The place value system for whole numbers, including comparing whole numbers to any digit, and rounding.
- Addition and subtraction of multi-digit whole numbers up to seven digits.
- Multi-digit multiplication using area models and place value strategies.
- Multi-digit by one-digit division using area models, box models, and place value strategies.
- Techniques for estimating multi-digit addition, subtraction, multiplication, and division.
- Fractions essentials, including creating equivalent fractions, lowest common denominators, writing fractions in lowest terms, and writing fractions in equivalent forms (e.g., converting between mixed numbers and improper fractions). Comparing fractions using various strategies.
- Addition and subtraction of fractions and mixed numbers with like denominators, multiplying fractions and whole numbers.
- Decimals, including converting between fractions and decimals, comparing decimals, and adding decimal fractions (including cases with unlike denominators).
- Measurement and Data: Units and unit conversions, representing and interpreting data using line plots.
- Geometry fundamentals: Points, lines, rays, segments, parallel and perpendicular lines, circles, angles, and measures of angles.
- Algebraic thinking: Using letters to represent numbers, creating and solving simple algebraic problems, and creating and deducing relationships between numbers (number patterns).
- Exercise all the skills theyâ€™ve learned by solving real-world and mathematical problems, including multi-step problems, at multiple points throughout the course.

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
43 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 Fraction Models Using Common Denominators | |

6.14.5. | 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 Fractions With Like Denominators: Word Problems | |

6.15.5. | Subtracting Fractions With Like Denominators: Word Problems | |

6.15.6. | Decomposing Fractions Into Sums Using Models | |

6.15.7. | 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 Mixed Numbers With Like Denominators: Word Problems | |

6.16.5. | 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
21 topics

7.19. Units

7.19.1. | Units of Length | |

7.19.2. | Units of Mass | |

7.19.3. | Units of Time | |

7.19.4. | Units of Volume | |

7.19.5. | Converting Metric Units of Length to Smaller Units | |

7.19.6. | Converting Customary Units of Length to Smaller Units | |

7.19.7. | Converting Units of Volume to Smaller Units | |

7.19.8. | Converting Units of Mass to Smaller Units | |

7.19.9. | 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 |