The commutative property is a fundamental concept in mathematics that applies to addition and multiplication. The property states that the order of the numbers does not change the result when adding or multiplying them.

For addition, the commutative property can be stated as: a + b = b + a. In other words, the sum of two numbers remains the same regardless of the order in which they are added.

For multiplication, the commutative property can be stated as: a * b = b * a. This means that the product of two numbers remains the same regardless of the order in which they are multiplied.

It's important to note that the commutative property does not apply to subtraction or division. This property is a foundational concept in arithmetic and is used to simplify calculations and solve mathematical problems.

.Study GuideCommutative Property Worksheet/Answer key

Commutative Property Worksheet/Answer key

Commutative Property Worksheet/Answer key

Commutative 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.