Lesson 9 Explain Equivalence

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

Warm-up Number Talk: Familiar Numbers

Find the value of each expression mentally.

Activity 1 Pointed Discussion

Andre, Lin, and Clare are representing on a number line.

  • Andre said, “Oh, no! We’ll need to partition the line into 100 equal parts and count 70 parts just to mark one point!”

  • Lin said, “What if we mark instead? We could partition the line into just 10 parts and count 7 parts.”

  • Clare said, “What if we partition the line into 5 parts and mark ?

Do you agree with any of them? Explain or show your reasoning.

Number line, scale from 0 to 1.
Number line, scale from 0 to 1.
Number line, scale from 0 to 1.

Activity 2 How Do You Know?

Poster with two fractions. 1 fifth.  2 tenths.  

Around the room you will find six posters, each showing either two or three fractions.

With your group, visit at least two posters: one with two fractions and one with three fractions.

  1. For the set of 2 fractions:

    • Explain or show how you know the fractions are equivalent.

    • Write a new equivalent fraction on a sticky note and add it to the poster. Think of a fraction that hasn’t already been written by someone else.

      • We visited poster , which shows and .

      • New equivalent fraction:

  2. For the set of 3 fractions:

    • Identify 2 fractions that are equivalent. Explain your reasoning.

    • We visited poster , which shows , , and .

Practice Problem

Problem 1

Explain why the fractions and are equivalent.