Lesson 9

Explain Equivalence

Lesson Purpose

The purpose of this lesson is for students to determine if two fractions are equivalent, and if they are, explain why they are equivalent.

Lesson Narrative

In earlier lessons, students developed their ability to use different representations and strategies to reason about equivalence and generate equivalent fractions. This lesson enables them to consolidate the work so far and communicate their understanding conceptually, before they move on to reason about equivalent fractions numerically in the next lesson.

Students work with some fractions in the hundredths. Although students might try to partition a number line into 100 parts, they are not expected to do so. The idea is to motivate students to look for another way—one that is less tedious and more general—to generate equivalent fractions. 

  • Engagement
  • MLR8

Learning Goals

Teacher Facing

  • Determine if given fractions are equivalent in a way that makes sense to them.
  • Given a pair of equivalent fractions, explain why they are equivalent.

Student Facing

  • Let’s talk about how we know whether two fractions are equivalent.

Required Materials

Materials to Gather

Materials to Copy

  • How Do You Know

Required Preparation

Activity 2:

  • Each group needs 4 sticky notes. 

CCSS Standards

Building On


Building Towards

Lesson Timeline

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

Teacher Reflection Questions

This lesson centers on explanations for equivalence. What representations and strategies did most students rely on to justify equivalence? What aspects of the explanation was manageable for them? What was more challenging than anticipated?

Suggested Centers

  • Get Your Numbers in Order (1–5), Stage 4: Denominators 2, 3, 4, 5, 6, 8, 10, 12, or 100 (Addressing)
  • Mystery Number (1–4), Stage 4: Fractions with Denominators 5, 8, 10, 12, 100 (Addressing)

Print Formatted Materials

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Student Task Statements pdf docx
Lesson Cover Page pdf docx
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Teacher Presentation Materials pdf docx
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