The purpose of this activity is to activate what students know about the meaning and size of non-unit fractions. Students match a set of fractions with diagrams that represent them. There are 3 sets of equivalent fractions to prompt students to share what they know about equivalent fractions.

To add movement to the activity, students can check their matches with other groups in the room before the Activity Synthesis.

• Invite students to share how they went about making the matches. 
• Highlight explanations that emphasize the meanings of the numerator and denominator in a fraction.
• Ask students if they noticed that some diagrams have the same amount shaded, but the fractions they represent have different numbers. “Which diagrams show this?” (A and L, B and H, C and E, I and K)
• “What does it mean that the diagrams representing those fractions are the same?” (The fractions are the same size or have the same value. The term “equivalent” may or may not come up at this point.)

This activity extends students’ reasoning about the meaning of a fraction’s numerator and denominator and the size of non-unit fractions to include fractions greater than 1. Students see the size of 1 whole marked in a couple of diagrams and learn that the same size applies to all diagrams. Students are prompted to both interpret diagrams and create them: they write a fraction to represent the shaded part of a diagram and partition a diagram to represent a given fraction.

Some students may benefit from having physical manipulatives to help them conceptualize fractions that are greater than 1. Consider using fraction strips to support those students. For instance, ask them to fold as many strips as needed to represent 4 halves or 5 fourths.

• Select students to share their completed diagrams.
• “How did you know how many equal parts to partition each diagram into and how many parts to shade?“ (Divide each 1 whole portion into as many equal parts as the number in the denominator. Shade as many parts as the number in the numerator.)
• “How did you partition a diagram into fourths?” (Split each 1 whole into 2 halves, and then split each half into 2 equal parts again.)
• “How did you partition a diagram into eighths?” (Split each fourth into 2 equal parts.)