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Launch

Groups of 2
Display the number line.
“What is an estimate that’s too high? Too low? About right?”
1 minute: quiet think time

Activity

“Discuss your thinking with your partner.”
1 minute: partner discussion
Record responses.

Student Task Statement

What number is represented by the point on the number line?

number line. Scale, 0 to 1. Unlabeled point, right of one fourth, left of one half.

Make an estimate that is:

too low	about right	too high

Student Response

to access Student Response.

Advancing Student Thinking

Are You Ready for More?

Activity 1

15 mins

The Greatest of Them All

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

First time implementing?

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

Materials

None

Activity Narrative

In earlier lessons, students compared two fractions that share the same denominator or the same numerator. In this activity, students use that understanding to compare a large set of fractions that are arranged into rows and columns. The fractions in each row share the same numerator and those in each column share the same denominator.

Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. Invite students to look at Column A first, then Column B, then Row 1. Provide access to pre-made fraction strips for thirds and fifths to help them get started. Check in with students to provide feedback and encouragement after each chunk, particularly in terms of looking for and making use of structure.
Supports accessibility for: Conceptual Processing, Organization, Social-Emotional Functioning

Launch

Groups of 2
Display the table of fractions.
“What do you notice? What do you wonder?”
1 minute: quiet think time
1 minute: partner discussion

Activity

“Take a few quiet minutes to complete the problems. Afterward, discuss your responses with your partner.”
6–7 minutes: independent work time
“When discussing with your partner, explain how you know which fraction is the greatest in each row, each column, and the entire table.”
3–4 minutes: partner discussion

Student Task Statement

Here are 25 fractions in a table.

	A	B	C	D	E
1
2
3
4
5

For each question, be prepared to explain your reasoning.

Identify the greatest fraction in each column (A, B, C, D, and E).
Identify the greatest fraction in each row (1, 2, 3, 4, and 5).
Which fraction is the greatest fraction in the entire table?

Activity Synthesis

Invite students to share their responses and reasoning. Highlight responses that clarify that:
- In each column, the fraction in row 5 is the greatest because it has the greatest numerator of all fractions with the same denominator. (The size of the fractional parts is the same, so the fraction with the most parts is greatest.)
- In each row, the fraction in Column A is greatest because it has the smallest denominator of all fractions with the same numerator. (The number of parts is the same, so the fraction with the largest parts is greatest.)
“How did you know that is the greatest fraction in the entire table?”
- It is the greatest fraction in row 5 and in Column A.
- It is more than 8 wholes. All the other fractions are less than that.

Activity 2

25 mins

Relative to and 1

Instructional Routines

None

First time implementing?

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

Materials

To Gather

Colored pencils

Activity Narrative

In this activity, students apply previous reasoning about the size of fractions and their knowledge about fractions that are equivalent to to classify and compare fractions. Along the way, students have opportunities to make new observations about the structure of fractions that are less than , greater than but less than 1, and greater than 1 (MP7).

The activity calls for the use of colors as a way to code fractions in different groups. If colored pencils are not available, students can code the fractions by putting circles, triangles, and squares around the fractions. In either case, a key or legend should be created.

MLR8 Discussion Supports. Encourage students to begin partner discussions by reading their written responses aloud. If time allows, invite students to revise or add to their responses based on the conversation that follows.
Advances: Conversing, Speaking

Launch

Groups of 2
Give each group 3 colored pencils.

Activity

“Take a few quiet minutes to answer the first 4 questions. Afterward, discuss your responses with your partner.”
“You will need to code the fractions by color or by shape.”
7–8 minutes: individual work time
5 minutes: partner discussion
Pause for a whole-class discussion before proceeding to the last question.
Invite students to share how they knew if a fraction is less than , or if it is greater than but less than 1. Record their responses.
“How did you describe the last group of fractions that don’t fall into the first two groups?” (fractions greater than 1)
Invite students to explain how they know those fractions are greater than 1.
“Now compare some fractions in the last problem.”
5 minutes: individual work time

Activity Synthesis

Invite students to share their strategies for comparing fractions in the last question of the this activity.

“How did you compare fractions in which neither the numerator nor the denominator are the same?” (We compared them to or 1.)

“How did the color coding (or comparison to

or 1) help?” (Knowing whether a fraction is greater or less than 1, or greater or less than

, can help us tell which one is greater. All the fractions circled in yellow (less than

) are less than all the numbers in green (greater than

but less than 1). All fractions in green are less than all fractions in purple (greater than 1).

Student Task Statement

Here is the same table you saw earlier.

	A	B	C	D	E
1
2
3
4
5

Which fractions are less than ? Circle each of them. Then complete this sentence:

I know a fraction is less than when . . .
Which fractions are greater than but less than 1? Circle each of them with a pencil of a different color. (Or draw a triangle around each one.) Then complete this sentence:

I know a fraction is greater than but less than 1 when . . .
Circle the remaining fractions with a pencil of a third color. (Or draw a square around each one.) How would you describe the size of these fractions?
Next to the table, create a legend or key to show what each color (or each shape) represents.
Here are some pairs of fractions from the table. In each pair, which fraction is greater?
1. or
2. or
3. or
4. or

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Lesson 12

Ways to Compare Fractions

Warm-up

Estimation Exploration: What’s That Point?

Instructional Routines

First time implementing?

Materials

Activity Narrative

Launch

Activity

Student Task Statement

Student Response

Advancing Student Thinking

Are You Ready for More?

Activity Synthesis

Activity 1

The Greatest of Them All

Standards Alignment

4.NF.A

Instructional Routines

First time implementing?

Materials

Activity Narrative

Launch

Activity

Student Task Statement

Activity Synthesis

Activity 2

Relative to and 1

Instructional Routines

First time implementing?

Materials

Activity Narrative

Launch

Activity

Activity Synthesis

Lesson Synthesis

Have a correction or suggestion?

Standards Alignment

3.NF.A.1

4.NF.A.2

Student Response

Advancing Student Thinking

Are You Ready for More?

Student Task Statement

Student Response

Advancing Student Thinking

Are You Ready for More?

Standards Alignment

4.NF.A.2