Number Lines & Arrays

This commutative property worksheet helps students visually demonstrate why addition and multiplication are commutative using number lines and arrays. Learners model expressions in different orders, compare results, and connect visual representations to equivalent symbolic expressions.

Instructional Objectives

• Skill Focus (Grades 3-5): Use number lines and arrays to model commutative addition and multiplication expressions.
• Conceptual Understanding (Grades 3-5): Recognize that changing the order of addends or factors does not change the sum or product.
• Algebraic Reasoning (Grades 4-5): Compare visual models to identify equivalent expressions written in different orders.
• Curriculum Alignment (Grades 3-5): Supports number operations, visual modeling, properties of operations, and conceptual reasoning standards.

By working with both number lines and arrays, students strengthen their ability to move between concrete models and abstract equations. The side-by-side comparisons reinforce structural awareness and deepen understanding of equivalence.

Learning Benefits

• Builds strong visual reasoning skills
• Strengthens the connection between models and equations
• Encourages careful comparison and explanation
• Effective for guided lessons, math centers, or independent practice

This printable worksheet provides clear, visual-based practice that helps students confidently model and explain the Commutative Property in both addition and multiplication.

This worksheet is part of our Commutative Property collection.