Unit Plan 15 (Grade 3 Math): Area Formula A = l×w & Additive Area
Use A = l × w to find rectangle area, label in square units, and decompose rectilinear shapes into smaller rectangles to add their areas using the distributive property.
Focus: Use multiplication to compute rectangle area with A = l × w; decompose rectilinear figures into rectangles and use additive area to find totals.
Grade Level: 3
Subject Area: Mathematics (Measurement & Data • Operations & Algebraic Thinking)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students move from tiling and arrays to a general area formula for rectangles: A = l × w (with square units). They apply the formula to compute areas efficiently and decompose complex rectilinear shapes into non-overlapping rectangles, using additive area and the distributive property to justify their work.
Essential Questions
- How does A = l × w come from counting rows and columns of unit squares?
- Why can I decompose a rectilinear figure into rectangles and add the areas?
- How does the distributive property help me find area without counting every square?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Derive and explain A = l × w from arrays and row/column counts of unit squares.
- Compute the area of rectangles using multiplication and label results with square units (e.g., cm², in²).
- Decompose rectilinear figures into non-overlapping rectangles and add the sub-areas to find the total.
- Use the distributive property to break a side length (e.g., l × (w₁ + w₂)) and compute area via partial products.
- Explain and defend strategies with clear diagrams, equations, and units.
Standards Alignment — CCSS Grade 3
- 3.MD.7a–b: Relate area to multiplication and addition; find the area of a rectangle by tiling and by using A = l × w.
- 3.MD.7c: Use the distributive property to decompose a rectangle into parts and add the areas.
- 3.MD.7d: Recognize area as additive; find areas of rectilinear figures by decomposing and adding.
- 3.OA.1: Interpret products of whole numbers (a × b as a groups of b).
- 3.OA.5: Apply properties of operations (including distributive) as strategies to multiply.
- Mathematical Practices: MP.4 (Model), MP.6 (Precision), MP.7 (Structure), MP.8 (Regularity).
Success Criteria — Student Language
- I can explain A = l × w and show it with an array.
- I can find area of rectangles using multiplication and write square units.
- I can decompose a shape into rectangles and add the areas to get the total.
- I can use the distributive property to make a hard problem easier and explain my steps.