4th Grade Math

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 "thrown in" 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 they've learned by solving real-world and mathematical problems, including multi-step problems, at multiple points throughout the course.