Lesson 6

Hierarchy of Quadrilaterals

Lesson Purpose

The purpose of this lesson is for students to continue to build the hierarchy of quadrilaterals. Students use categories and subcategories to see that if a shape is a square it is also a rhombus and also a parallelogram.

Lesson Narrative

The purpose of this lesson is for students to first relate squares and rhombuses and then relate rectangles and parallelograms. They see that if a shape is a square then it is also a rhombus and if a shape is a rectangle then it is also a parallelogram. But there are rhombuses that are not squares and there are parallelograms that are not rectangles. Students record these observations on the anchor chart from previous lessons. This gives students a chance to organize the quadrilaterals in a hierarchy and highlight the relationships they see between the properties of the shapes they worked with in this lesson. Students should have access to straight edges, protractors, and patty paper throughout this lesson.

When students define shapes and make explicit connections between shapes and categories, they reason abstractly and quantitatively (MP2).

  • Representation

Learning Goals

Teacher Facing

  • Classify parallelograms in a hierarchy based on angle measurements and side lengths.
  • Explain why a square is also a rhombus.

Student Facing

  • Let’s explore the hierarchy of quadrilaterals.

Required Materials

Required Preparation

  • Gather diagram from a previous lesson.

Activity 1:

  • Each group of 2 needs 6 toothpicks.

CCSS Standards


Building Towards

Lesson Timeline

Warm-up 10 min
Activity 1 15 min
Activity 2 20 min
Lesson Synthesis 10 min
Cool-down 5 min

Teacher Reflection Questions

What surprised you about student thinking in Activity 2?

Suggested Centers

  • Which One? (K–5), Stage 7: Grade 5 Shapes (Addressing)
  • How Are They the Same? (1–5), Stage 5: Grade 5 Shapes (Addressing)
  • How Are They the Same? (1–5), Stage 4: Grade 4 Shapes (Supporting)

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