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Activity 1

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

None

Activity Narrative

The purpose of this activity is for students to make sense of non-unit fractions and the notation used to describe them. They learn that the denominator tells the number of equal parts into which the whole was partitioned and that the numerator tells the number of parts being described. Students write non-unit fractions that represent the shaded portions of area diagrams.

If needed, especially with the fractions greater than one, clarify that each rectangle represents one whole. The activity concludes with students practicing how to read non-unit fractions. The terms “numerator” and “denominator” will be introduced in a later lesson.

When students notice that the bottom part of the fraction stays the same and the top part of the fraction changes, representing the number of equal parts that are shaded, they look for and make use of structure (MP7).

Launch

Groups of 2
Display the table.
“Let's look at the first table.”
“The first three images are the squares we saw earlier. Let's name them again.” (One-fourth, three-fourths, four-fourths)
“Let’s complete the second row of the table together. This is the square we just worked with in the Warm-up, and the number that represents the total amount shaded is already in the table. How many of the parts are shaded?” (3)
“What is the size of each part?” ()
“Write ‘three-fourths’ to record how we read this fraction.”

Activity

“Work with your partner to complete the table.”
5–7 minutes: partner work time

Each shape in each row of the table represents 1. Use the shaded parts to complete the missing information in the table. Be prepared to explain your reasoning.

Table with shapes and information to find about the related fractions.

Table with shapes and information to find about the related fractions.

Student Response

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Advancing Student Thinking

Activity Synthesis

Display the completed table.
“Now that the table is complete, what do you notice? What do you wonder?” (The size of each part always has a 1 in the top part of the fraction. The bottom part of the fraction is the same for each equal-size part as well as for the total of equal parts that are shaded. The top part of the fraction is how many parts are shaded.)
“Let’s think about how we should describe or name the shaded part in each image.”
30 seconds: quiet think time
Invite students to name the shaded part in each image.
As students name the shaded part in each image, have them share how they used fraction notation to record the name.

Activity 2

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

Materials

To Copy (from Blackline Masters)

Card Sort Fraction Match Cards

Activity Narrative

The purpose of this activity is for students to match fractions to shaded diagrams. Reiterate that each rectangle represents one whole. Students also create their own cards, with shaded diagrams, to match given fraction cards.

Students observe and use structure as they identify that the top number in the fraction represents the number of shaded pieces while the bottom number represents the number of those pieces in one whole rectangle (MP7).

MLR8 Discussion Supports. Students should explain to their partner why the chosen cards match or do not match. Display the following sentence frame for all to see: “I notice _____ , so these two cards match/do not match.” Encourage students to challenge each other when they disagree.
Advances: Speaking, Representing

Launch

Groups of 2
Give each group a set of cards.

Activity

“This set of cards includes fractions and diagrams. Match each fraction to a shaded diagram. Work with your partner to explain your reasoning.”
"Some fractions or diagrams may not have a match. After you have found all the matches you can, work with your partner to explain why any remaining fractions or diagrams do not have a match."
7 minutes: partner work time
"Compare your matches with another group. If you disagree with any matches, take turns explaining why."
3–5 minutes: group work time
“Now work together with your partner to create a shaded diagram to match each of the fractions that did not have a match. Be ready to share your new cards with the class and explain why they match.”
5–7 minutes: partner work time
Monitor for students who notice that means the whole rectangle is shaded.

Your teacher will give you a set of cards.

Match each fraction to a diagram. Be ready to explain why some fractions do not have a matching diagram.
Compare your matches with another group.
Use Cards R, T, V, and X to create a shaded diagram for each fraction card that did not have a match. Be ready to share your new cards and explain why they match.

Student Response

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Advancing Student Thinking

Activity Synthesis

Invite 1 or 2 groups to display a rectangle they partitioned and shaded to match one of the fractions.
For each rectangle students share, discuss the fraction that it represents.
Display a diagram of , with all the parts shaded.
“_____ noticed that to show , we have to shade the whole rectangle. Look back over both activities for other fractions that are shown by shading the whole rectangle.” (, , and )
Consider asking: “How many _____s would it take to make a whole? How do you know?”
“These fractions are equivalent to 1 because they represent all the parts of the whole. We’ll work with other fractions like this as we learn about fractions.”