The associative property is a fundamental property of addition and multiplication that states that the grouping of numbers does not affect the result of the operation. In other words, when adding or multiplying three or more numbers, the result is the same regardless of how the numbers are grouped.

For addition, the associative property can be expressed as:

(a + b) + c = a + (b + c)

In other words, when adding three or more numbers, the sum is the same regardless of how the numbers are grouped.

For multiplication, the associative property can be expressed as:

(a * b) * c = a * (b * c)

This means that when multiplying three or more numbers, the product is the same regardless of how the numbers are grouped.

Understanding the associative property is important in simplifying calculations and understanding the properties of numbers and operations.

Study GuideAssociative Property Worksheet/Answer key

Associative Property Worksheet/Answer key

Associative Property Worksheet/Answer key

Associative Property

Number and Operations (NCTM)

Understand meanings of operations and how they relate to one another.

Understand and use properties of operations, such as the distributivity of multiplication over addition.

Compute fluently and make reasonable estimates.

Develop fluency in adding, subtracting, multiplying, and dividing whole numbers.

Select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools.

Algebra (NCTM)

Represent and analyze mathematical situations and structures using algebraic symbols.

Identify such properties as commutativity, associativity, and distributivity and use them to compute with whole numbers.

Use mathematical models to represent and understand quantitative relationships.

Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.

Grade 3 Curriculum Focal Points (NCTM)

Number and Operations and Algebra: Developing understandings of multiplication and division and strategies for basic multiplication facts and related division facts

Students understand the meanings of multiplication and division of whole numbers through the use of representations (e.g., equal-sized groups, arrays, area models, and equal 'jumps' on number lines for multiplication, and successive subtraction, partitioning, and sharing for division). They use properties of addition and multiplication (e.g., commutativity, associativity, and the distributive property) to multiply whole numbers and apply increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving basic facts. By comparing a variety of solution strategies, students relate multiplication and division as inverse operations.