3.A.2.2 Recognize, represent and apply the number properties (commutative, and identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems.
In a Nutshell
Although students know how most number sentences work, (example: one number plus another number equals the answer) they still do not have a clear understanding of “equality”. The properties of addition and multiplication demonstrate and prove the equality of equations. Using models and manipulatives, students can better understand the value of numbers and how the equal sign dictates the balance of equations.
Student Actions

Teacher Actions


Develop a deep and flexible conceptual understanding as students represent the commutative, identity, and associative properties of addition and multiplication with manipulatives and models.

Demonstrate mathematical reasoning by analyzing the context of a problem and determining when certain properties can be used to solve a problem.


Pose purposeful questions to help students recall prior knowledge and justify their thinking. Questions may include: What relationships do we notice with the numbers in this equation? Does this problem remind you of another problem you have seen before? How are these expressions alike? How does visualizing the problem help us? How do the properties help us understand the “equal sign”?

Implement tasks that encourage students to make connections to the three properties.

Facilitate mathematical discourse that emphasizes the idea of “equality.”

Key Understandings

Misconceptions


The equal sign can be represented as a solution to an answer, but also to show how an equation can be balanced on both sides.

Properties help them understand the value of expressions.


OKMath Framework Introduction
3rd Grade Introduction
3rd Grade Math Standards
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