Algebraic Thinking is the ability to generalize, represent, justify, and reason with abstract mathematical structures and relationships. Algebraic Thinking is important for developing a deep understanding of arithmetic and helps students make connections between many components of their early math studies.
Algebraic Thinking allows students to move away from thinking and working with particular numbers and measures to understanding and reasoning with generalized relationships among them. Algebraic Thinking practices occur in these mathematical domains:
- Equivalence, expressions, equations and inequalities: Includes developing an understanding of the equal sign as expressing a relationship between equivalent quantities, representing and reasoning with expressions that include unknown quantities, and reasoning with and describing relationships among quantities that may or may not be equivalent;
- Generalizing and reasoning with arithmetic relationships: Includes reasoning about the structure of arithmetic expressions and relationships including core properties of number and Operations;
- Functional thinking: Includes representing and reasoning with generalized relationships between co-varying quantities using verbal, symbolic, graphical, and tabular (using tables) representations; and
- Proportional Reasoning: Includes reasoning abstractly about the relationship between two generalized quantities.