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Launch

Groups of 2
Display the image.
“What is an estimate that’s too high? Too low? About right?”

Activity

1 minute: quiet think time
1 minute: partner discussion
Record responses.

Record an estimate that is:

too low	about right	too high

Student Response

to access Student Response.

Advancing Student Thinking

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 apply what they have learned about multiplication and division of fractions to strategically write expressions with the greatest value. Students notice and explain patterns (MP7) such as:

To make a product as large as possible, the two factors should be chosen as large as possible.
To make a quotient or fraction as large as possible, the dividend should be as large as possible and the divisor as small as possible.

MLR8 Discussion Supports. Synthesis: Before inviting students to share their strategies for making the expression as large as possible, give groups time to rehearse what they might say if selected.
Advances: Speaking

Engagement: Provide Access by Recruiting Interest. Synthesis: Invite students to generate a list of additional examples of problems that can be solved using multiplication or division that connect to their personal backgrounds and interests.
Supports accessibility for: Attention, Conceptual Processing

Launch

Groups of 2

Activity

15 minutes: partner work time
Monitor for students who reason about the size of the product or quotient based on the location of the digits.

For each expression, find the greatest product or quotient you can make with the numbers 1, 2, 3, 4, 5, and 6. You can only write each number once in each expression. You do not need to use all the numbers. Explain or show your reasoning.

Student Response

to access Student Response.

Advancing Student Thinking

Activity Synthesis

Invite previously selected students to share their responses.
Display the second expression.
Invite students to share their strategies for making the expression as large as possible.
“Why is a good choice for making this expression as large as possible?” (When I find the value, I multiply 6 and 5. Those are the two biggest numbers so I know that will give me the biggest value.)
“Is there another choice for filling in the blanks that gives the same value?” (Yes, I can also do .)

Activity 2

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

None

Activity Narrative

In the previous activity, students chose digits to create expressions whose value was as large as possible. The purpose of this activity is for students to create expressions with the smallest possible value. The expressions and digits that students use are the same. The patterns that they identified in the previous activity will apply here as well but they lead to a different choice of expressions.

Launch

Groups of 2

Activity

7–8 minutes: independent work time
2–3 minutes: partner work time
Monitor for students who reason about the size of the product or quotient based on the location of the digits.

For each expression, find the smallest product or quotient you can make with the numbers 1, 2, 3, 4, 5, and 6. You can only write each number once in each expression. You do not need to use all the numbers. Explain or show your reasoning.

Student Response

to access Student Response.

Advancing Student Thinking

Activity Synthesis

Display the last expression.
“Why is a good choice for making the expression as small as possible?” (The numerator is 1 so I want the denominator to be as large as possible. That’s why putting in the 6 and 5 is a good strategy.)
“Is there another choice for filling in the blanks that gives the same value?” (Yes, I can also do .)
“What is the value of and ? How do you know?” ( because I am either cutting into 5 equal pieces or into 6 equal pieces. Either way there are or 30 of those pieces in a whole.)

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Lesson 19

Fraction Games

Warm-up

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Activity 1

Standards Alignment

Building On

Addressing

5.NF.B.4

5.NF.B.7

Building Toward

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Activity 2

Standards Alignment

Building On

Addressing

5.NF.B.4

5.NF.B.7

Building Toward

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Lesson Synthesis

Student Section Summary

Standards Alignment

Building On

Addressing

5.NF.B.4

Building Toward