Unit Plan 35 (Grade 5 Math): Geometry Synthesis—Attributes to Hierarchies

Focus: Apply properties to classify figures, explain category relationships (hierarchies), and solve coordinate-geometry problems in the first quadrant.

Grade Level: 5

Subject Area: Mathematics (Geometry; Coordinate Connections)

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

I. Introduction

Students pull together everything they know about attributes (sides, angles, parallel/perpendicular, symmetry) to build classification trees and hierarchies. They justify why a figure belongs to a category (and all its parent categories) and use the coordinate plane to verify attributes (lengths along grid lines, parallel/ perpendicular to axes). Emphasis is on clear definitions, evidence, and why a hierarchy works.

Essential Questions

• Which attributes determine a figure’s category, and how do those categories nest?
• How can a coordinate graph help me verify attributes like equal lengths or right angles?
• What makes a classification or hierarchy explanation convincing?

II. Objectives and Standards

Learning Objectives — Students will be able to:

1. Describe and use attributes (e.g., number of parallel sides, equal sides, right angles) to classify 2D figures.
2. Explain hierarchies: how a figure in one category also belongs to parent categories (e.g., every square is a rectangle and a parallelogram).
3. Create and critique classification trees and Venn/branch diagrams using precise definitions.
4. Use the coordinate plane (first quadrant) to plot, read coordinates, and check properties (e.g., horizontal/vertical sides, equal lengths on grid lines).
5. Communicate reasoning with labeled diagrams, coordinates, and because statements tied to definitions.

Standards Alignment — CCSS Grade 5

• 5.G.3: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.
• 5.G.4: Classify two-dimensional figures in a hierarchy based on properties.
• 5.G.1–2 (connection): Use a coordinate system to represent/interpret points in the first quadrant and graph points to model and check geometric properties in context.

Success Criteria — Student Language

• I can name the attributes a figure has and use them to classify it.
• I can explain how a figure moves up the hierarchy (e.g., square → rectangle → parallelogram → quadrilateral).
• I can plot points and use the grid to check lengths and right angles.
• I can give a clear because statement using the definition of the category.