# Operations and Algebraic Thinking

## Narrative for the (OA) Operations and Algebraic Thinking

Algebraic thinking is about generalizing arithmetic operations and operating on unknown quantities.  It involves recognizing and analysing patterns and developing generalizations about these patterns.  In algebra, symbols can be used to represent generalizations. Operations and Algebraic Thinking deals with the basic operations - addition, subtraction, multiplication, and division - the relationships they model, the kinds of problems they can be used to solve, as well as, their mathematical properties and relationships.

Students in Grade 3 begin the step to formal algebraic language by using a letter for the unknown quantity in expressions or equations for one and two-step problems. As with two-step problems at Grade 2, which involve only addition and subtraction, the Grade 3 two-step word problems vary greatly in difficulty and ease of representation. More difficult problems may require two steps of representation and solution rather than one

Students focus on understanding the meaning and properties of multiplication and division and on finding products of single-digit multiplying and related quotients.  These skills and understandings are crucial; students will rely on them for years to come as they learn to multiply and divide with multi-digit whole number and to add, subtract, multiply and divide with fractions and with decimals.

All of the understandings of multiplication and division situations, of the levels of representation and solving, and of patterns culminate by the end of Grade 3 in fluent multiplying and dividing all single-digit numbers and 10. This is the outcome of a carefully designed learning process that heavily involves the interplay of practice and reasoning about the relationship between multiplication and division facts.

## Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and proficiency scales for individual standards within the Domain.