Unit Plan 25 (Grade 5 Math): Shape Hierarchies—Quadrilaterals and Beyond
5th graders build hierarchies of 2D figures using definitions and properties—organizing shapes like squares, rectangles, and parallelograms to explain relationships, justify classifications, and reason with if–then logic.
Focus: Build and use hierarchies of two-dimensional figures (e.g., square → rectangle → parallelogram; square at the overlap of rectangle and rhombus) to classify, justify, and explain relationships using definitions and property logic.
Grade Level: 5
Subject Area: Mathematics (Geometry)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students extend property-based classification to hierarchical thinking. They learn that categories and subcategories are organized by defining attributes, not looks. Using trees and Venn-style maps, students place figures (especially quadrilaterals) into a structure that makes relationships clear (e.g., every square is a rectangle and a rhombus, and hence a parallelogram and a quadrilateral). The unit also invites “beyond quadrilaterals” thinking by comparing how triangle categories (right, isosceles) form simpler hierarchies.
Essential Questions
- How do definitions and attributes determine where a shape belongs in a hierarchy?
- Why do subcategory attributes automatically satisfy broader category attributes?
- How do trees and Venn-style diagrams help us see and justify relationships among figures?
- How can we defend “A square is always a rectangle” (and more) using if–then reasoning?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Construct hierarchy diagrams (tree or Venn-style) for quadrilaterals (and compare to other polygons).
- Use definitions and defining attributes (parallel/perpendicular lines, right angles, equal sides) to place shapes in the correct subcategory.
- Explain inclusion relationships with clear if–then chains (e.g., “If a quadrilateral has four right angles, then it is a rectangle; therefore it is also a parallelogram and quadrilateral.”).
- Create and critique justifications and counterexamples using precise vocabulary.
- Resolve classification disagreements by appealing to accepted definitions (e.g., inclusive trapezoid: at least one pair of parallel sides).
Standards Alignment — CCSS Grade 5
- 5.G.4: Classify two-dimensional figures in a hierarchy based on properties.
- Mathematical Practices emphasized: MP.1 (persevere), MP.3 (justify/critique), MP.6 (precision), MP.7 (structure).
Success Criteria — Student Language
- I can build a hierarchy that organizes shapes by definitions.
- I can use if–then statements to show how a shape fits multiple categories.
- I can place a square at the overlap of rectangle and rhombus and explain why.
- I can use a counterexample to show when a classification doesn’t work.