Unit Plan 25 (Grade 3 Math): Partitioning Shapes & Unit Fractions of Areas
Partition shapes into equal areas, label each part as a unit fraction (1/b), and use models to justify fair shares in real-world contexts.
Focus: Partition shapes into equal areas; express each part’s area as a unit fraction of the whole and model fair shares in context.
Grade Level: 3
Subject Area: Mathematics (Geometry • Fractions as Area)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students learn to partition shapes (rectangles, circles, irregular polygons) into equal areas and name each part as a unit fraction of the whole (e.g., 1/2, 1/3, 1/4). They connect fair shares to area, not just the number of pieces, and use drawings and manipulatives to reason about “same size” parts that may look different.
Essential Questions
- What makes a partition fair (equal area), and how can I prove it?
- How does 1/b name the area of one part when a whole is split into b equal parts?
- How can models help me decide and communicate whether parts are equal in area?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Partition shapes into equal areas using multiple strategies (folding, grids, symmetry, benchmarks).
- Label each part as a unit fraction (1/b) of the whole and explain why the parts are equal in area.
- Use models (drawings, grid paper, pattern blocks) to represent and justify fair shares in real contexts.
- Describe and critique partition strategies using precise vocabulary and evidence.
Standards Alignment — CCSS Grade 3
- 3.G.2: Partition shapes into parts with equal areas; express the area of each part as a unit fraction of the whole.
- 3.NF.1 (connection): Understand a fraction 1/b as one part when the whole is partitioned into b equal parts; a/b as a parts of size 1/b.
- MP.4: Model with mathematics (use diagrams, grids, and manipulatives to show equal-area partitions).
- (Supporting) MP.6: Attend to precision (labels, fraction notation, equal-area arguments).
Success Criteria — Student Language
- I can partition a shape into equal areas and label each part 1/b.
- I can explain how I know the parts are equal in area (not just equal-looking).
- I can use a model to show a fair share in a story problem and justify my choice.