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Activity 1

20 mins

A Diagram for Each Fraction

Standards Alignment

Building On

Instructional Routines

None

First time implementing?

Learn how to use instructional routines to facilitate problem-based learning!

Materials

To Gather

Straightedges

Activity Narrative

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.

Representation: Internalize Comprehension. Use visual details, such as color or arrows, to illustrate connections between representations. For example, use the same color for the numerator and the shaded portion of the corresponding diagram.
Supports accessibility for: Visual-Spatial Processing

Launch

Groups of 2
Give each student a straightedge
Record and display the fraction .
“Describe to your partner what the diagram would look like for this fraction.”
30 seconds: partner discussion
Record and display the fraction .
“Describe what the diagram would look like for this fraction.”
30 seconds: partner discussion
Share responses.
“In an earlier lesson, we looked at fractions with 1 for the numerator. Now let’s look at fractions with other numbers for the numerator.”
As a class, read aloud the word name of each fraction in the task.

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.)

Activity 2

15 mins

Diagrams for Some Other Fractions

Standards Alignment

Building On

Instructional Routines

None

First time implementing?

Learn how to use instructional routines to facilitate problem-based learning!

Materials

To Gather

Materials from a previous lesson

Straightedges

Activity Narrative

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.

MLR2 Collect and Display. Collect the language students use to reason about fractions greater than one. Display words and phrases, such as “fraction,” “numerator,” “denominator,” “1 whole,” “greater than,” and “equal-size parts.” During the activity, invite students to suggest ways to update the display: “What are some other words or phrases we should include?” Invite students to borrow language from the display as needed.
Advances: Conversing, Reading

Launch

Groups of 2
Give each student a straightedge and access to their fraction strips from a previous lesson.
“How can you show with fraction strips?” (Find the strip showing fourths and highlight 3 parts, or fourths.)
“How can you show ?”
1 minute: partner discussion
If students say that they don’t have enough strips to show 8 fourths, ask them to combine their strips with another group’s.
Invite groups to share their representations of . Students may use different fractional parts (fourths and halves, or fourths and eighths).
Display two strips that show fourths side by side, as shown.
Count the fourths: “, , . . . , .”
“How many fourths did we count?” (8) “How many wholes was that?” (2)

Activity Synthesis

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.)