Unit Plan 3 (Grade 3 Math): Arrays & Area Models—Structure of Multiplication

Focus: Use arrays and area models to represent and solve multiplication; connect rows × columns to factors × product and introduce area with unit squares.

Grade Level: 3

Subject Area: Mathematics (Operations & Algebraic Thinking; Measurement & Data)

Total Unit Duration: 5 sessions (one week), 45–60 minutes per session

I. Introduction

Students build conceptual understanding of multiplication by organizing objects into arrays and covering rectangles with unit squares as early area models. They relate rows × columns to factors × product, explore the commutative property by rotating arrays, and choose representations that fit story problems.

Essential Questions

• How do arrays and area models show the structure of multiplication?
• Why does rows × columns match factors × product?
• When should I use equal groups, an array, or an area model, and why?

II. Objectives and Standards

Learning Objectives — Students will be able to:

1. Build, draw, and label arrays; explain how rows and columns determine the product.
2. Use unit squares to create simple area models that match multiplication situations.
3. Write and interpret equations with an unknown to represent arrays and area coverings.
4. Explain the commutative property using arrays (rotate to show a × b = b × a).
5. Choose a best-fit representation (equal groups, array, area model) and justify the choice.

Standards Alignment — CCSS Grade 3

• 3.OA.1: Interpret products of whole numbers as equal groups/arrays (e.g., 5 groups of 7; 5 rows of 7).
• 3.OA.3: Use multiplication within 100 to solve word problems involving equal groups, arrays, and measurement quantities; represent with equations and a symbol for the unknown.
• 3.MD.5 (intro): Recognize area as an attribute of plane figures and understand area measurement by covering with unit squares (conceptual launch, not full formula work).
• Mathematical Practices: MP.7 (look for and make use of structure) threaded; MP.4 (model) and MP.2 (reason) supported.

Success Criteria — Student Language

• I can build and label an array and match it to an equation.
• I can cover a rectangle with unit squares to show its area and connect it to multiplication.
• I can explain how rows and columns are my factors, and the total is the product.
• I can show that a × b has the same total as b × a by rotating my array.