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Activity 1

20 mins

Relate Pounds to People

Standards Alignment

Building On

Addressing

Instructional Routines

None

First time implementing?

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

Materials

None

Activity Narrative

The purpose of this activity is for students to analyze several different situations about the same context of sharing pounds of blueberries and generalize what they have learned about the relationship between fractions and quotients. Students rely on their understanding of the relationship between division and fractions to choose numbers that make sense based on the constraints listed in the table. During the Activity Synthesis, students generalize their understanding of the relationship between division situations and fractions greater than 1, less than 1, and equal to one whole.

Launch

Groups of 2
Display table from student book. Refer to the corresponding parts of the table and read, “each person gets exactly 1 pound of blueberries” and “ _____ people share ______ pounds of blueberries equally.”
“What numbers can we write in the blanks so that each person will get exactly 1 pound of blueberries?” (3 and 3, 4 and 4, etc.)
Record responses for all to see.
“What is true about all of the pairs of numbers we used?” (Each blank has the same number in it.)
“Why do the numbers in the blanks have to be the same?” (In order for each person to get exactly one pound of blueberries, the number of people sharing has to be the same as the number of pounds of fruit.)
“We are going to solve more problems like this one. For each row in the table, write numbers in the blanks to fit the rule that is checked.”

Activity

5 minutes: partner work time
“As you walk, notice how the numbers in the tables are the same and different.”
5 minutes: gallery walk
Match each group of 2 with another group of 2 so there are groups of 4.
“Work with your group to make a poster about the numbers that were used in the tables.”
5 minute: group work time
Monitor for groups who:
- Show or explain why the number of people is always less than the number of pounds of blueberries when each person gets more than one pound of blueberries.
- Explain or show why the number of people is always more than the number of pounds of blueberries when each person gets less than one pound of blueberries.
- Explain or show why the number of people is always the number of pounds of blueberries when each person gets pound of blueberries.

Activity Synthesis

Ask previously selected groups to share their posters.
“What is the same about the pairs of numbers that represent each person getting more than one pound of blueberries?” (There are always more pounds of blueberries than there are people sharing the blueberries.)
“What is the same about the pairs of numbers that represent each person getting less than one pound of blueberries?” (There are always less pounds of blueberries than there are people.)
“What is the same about the pairs of numbers that represent each person getting exactly pound of blueberries?” (The number of people sharing the blueberries is always double the number of pounds of blueberries.)
“We are going to think more about these ideas in the next activity.”

Activity 2

15 mins

Why Does It Work?

Standards Alignment

Building On

Addressing

Instructional Routines

MLR7 Compare and Connect

First time implementing?

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

Materials

None

Activity Narrative

The purpose of this activity is for students to explain why for any whole numbers and when is not 0. Students may use words, equations, or diagrams to explain why this is true. In order to see a wide variety of interpretations, students take a Gallery Walk to observe their classmates’ work. Then they discuss how words and diagrams help show the equation for different values of and .

Constructing an argument that works for any pair of numbers requires thinking carefully about the meaning of the dividend, , and the divisor, . Students may use diagrams or situations to help communicate their thinking but will need to explain why these make sense for any numbers and (MP3).

This activity uses MLR7 Compare and Connect. Advances: Representing, Conversing.

Engagement: Provide Access by Recruiting Interest. Synthesis: Optimize meaning and value. Invite students to share why every division expression can be written as a fraction with another teacher.
Supports accessibility for: Attention, Conceptual Processing

Launch

Groups of 2

Activity

“Complete the first problem on your own.”
1–2 minutes: independent work time
2–3 minutes: partner discussion for the first problem

MLR7 Compare and Connect

“Create a visual display that shows your thinking about why every division expression can be interpreted as a fraction. You may want to include details such as words, diagrams, expressions, etc. to help others understand your thinking.”
3–5 minutes: partner work time
5 minutes: gallery walk
“What is the same and what is different between the different explanations?”
30 seconds quiet think time
1 minute: partner discussion

Student Task Statement

What numbers can replace the question marks in each equation? Explain your reasoning.

(Pause for teacher directions.)
Work with your partner to explain why any division expression can be interpreted as a fraction. You can use diagrams, expressions, equations, and words.

Activity Synthesis

Display the image from the first problem in Student Responses or use student work.
“How do diagrams help you see that ?” (They show a set of objects divided in half and also show the same number of halves as there are objects.)
“How do the diagrams help you see that ?” (They show 2 things divided into equal parts and that’s the same as 2 of those equal parts.)
Invite students to share contexts that they used to help understand the relationship between division and fractions.

Student Task Statement

	more than 1	exactly 1	less than 1
	Each person gets ________ pound(s) of blueberries.
__________ people share 7 pounds of blueberries equally.
_________ people share __________ pounds of blueberries equally.
Three people share __________ pounds of blueberries equally.
__________ people share __________ pounds of blueberries equally.

Fill in the blanks to match the rules in the table.
How many pounds of blueberries does each person get when they get more than 1 pound?
How many pounds of blueberries does each person get when they get less than 1 pound of blueberries?

(Pause your work after you answer the 2 questions.)
Work with your group to make a poster that explains or shows your thinking about the following questions.
- What is true about all the pairs of numbers that are used when each person gets less than 1 pound of blueberries?
- What is true about all the pairs of numbers that are used when each person gets more than 1 pound of blueberries?
- What is true about all the pairs of numbers that are used when each person gets exactly pound of blueberries?

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Lesson 5

Relate Division and Fractions

Warm-up

True or False: Interpret Fractions

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

Relate Pounds to People

Standards Alignment

5.NF.B.3

Instructional Routines

First time implementing?

Materials

Activity Narrative

Launch

Activity

Activity Synthesis

Activity 2

Why Does It Work?

Standards Alignment

5.NF.B.3

Instructional Routines

First time implementing?

Materials

Activity Narrative

Launch

Activity

Student Task Statement

Activity Synthesis

Lesson Synthesis

Student Section Summary

Have a correction or suggestion?

Standards Alignment

5.NF.B.3

Student Task Statement

Student Response

Advancing Student Thinking

Are You Ready for More?

Student Response

Advancing Student Thinking

Are You Ready for More?