By Janet Caldwell, Karen Karp, Jennifer Bay-Williams, Rose Mary Zbiek

What is the relationship between addition and subtraction? How do you know whether an algorithm will always work? Can you explain why order matters in subraction but not in addition, or why it is false to assert that the sum of any two whole numbers is greater than either number?

It is organized around two big ideas and supported by smaller, more specific, interconnected ideas (essential understandings). Gaining an understanding about addition and subtraction is essential as they are the foundation for students’ later learning of multiplication and division.

Essential Understanding Series topics: • Number and Numeration for Grades Pre-K—2 • Addition and Subtraction for Grades Pre-K—2 • Geometry for Grades Pre-K—2 • Reasoning and Proof for Grades Pre-K—8 • Multiplication and Division for Grades 3—5 • Rational Numbers for Grades 3—5 • Algebraic Ideas and Readiness for Grades 3—5 • Geometric Shapes and Solids for Grades 3—5 • Ratio, Proportion, and Proportionality for Grades 6—8 • Expressions and Equations for Grades 6—8 • Measurement for Grades 6—8 • Data Analysis and Statistics for Grades 6—8 • Function for Grades 9—12 • Geometric Relationships for Grades 9—12 • Reasoning and Proof for Grades 9—12 • Statistics for Grades 9—12