# Lesson 15

Fraction Division Situations

## Warm-up: Number Talk (10 minutes)

### Narrative

The purpose of this Number Talk is for students to demonstrate strategies and understandings they have for dividing a whole number by a unit fraction and a unit fraction by a whole number. These understandings help students develop fluency and will be helpful later in this lesson when students solve division problems.

### Launch

• Display one expression.
• “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

### Activity

• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Find the value of each expression mentally.

• $$6 \div 3$$
• $$6 \div \frac{1}{3}$$
• $$\frac{1}{3} \div 6$$
• $$\frac{1}{3} \div 12$$

### Activity Synthesis

• “How are the expressions $$6\div\frac{1}{3}$$ and $$\frac{1}{3} \div 6$$ the same? How are they different?” (They both have a 6 and a $$\frac{1}{3}$$ but $$6 \div \frac{1}{3}$$ is greater than 1 and $$\frac{1}{3} \div 6$$ is less than 1.)

## Activity 1: Card Sort: Fraction Division Problem Sort (20 minutes)

### Narrative

The purpose of this activity is for students to match situations and expressions and then answer the questions asked about the situations. The numbers used in the problems are deliberately chosen so that students cannot make the matches just by looking at the numbers. Considering expressions that represent situations will help students as they write their own situations in the next activity. A sorting task gives students opportunities to analyze representations, statements, and structures closely and make connections (MP2, MP7).

MLR8 Discussion Supports. Students should take turns finding a match and explaining their reasoning to their partner. Display the following sentence frames for all to see: “I noticed _____, so I matched . . . .” Encourage students to challenge each other when they disagree. Advances: Conversing, Representing
Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. Give students a subset of the cards to start with and introduce the remaining cards once students have completed their initial set of matches. Supports accessibility for: Attention; Organization

### Required Materials

Materials to Copy

• Fraction Division Problem Sort

### Required Preparation

• Create a set of cards from the blackline master for each group of 2.

### Launch

• Groups of 2
• Give each group a set of pre-cut cards.

### Activity

• “This set of cards includes situations and expressions. Match each situation to an expression. Work with your partner to justify your choices.”
• 8 minutes: partner work time
• “Work together to answer the question in each situation.”
• 8 minutes: partner work time
• If students do not have enough time to answer all of the questions, use the problems as a center.

### Student Facing

1. Your teacher will give you a set of cards. Match each expression with a situation. Some expressions do not have a matching situation.

### Student Response

If students do not correctly match situations to expressions, have students draw a diagram for each situation. Consider asking, “Do any of the expressions match the diagram you drew?” and ask students to explain why the match makes sense.

### Activity Synthesis

• Ask students to share the matches they made and how they know those cards go together.
• Attend to the language that students use to describe their matches, giving them opportunities to describe the kind of division happening in the situation more precisely.
• Highlight the use of terms that reference the number of groups and the size of the group.

## Activity 2: Division Story Situations (15 minutes)

### Narrative

The purpose of this activity is for students to write situations involving division of a whole number by a unit fraction and division of a unit fraction by a whole number. They may use one of the contexts from the stories in the previous activity, changing the quantities suitably, or they may make up their own. Consider having a gallery walk for students to see the variety of story problems.

### Launch

• Groups of 2-4

### Activity

• 3–5 minutes: partner work time
• 3–5 minutes: small-group work time
• Monitor for students who write “how many in each group” stories and “how many groups” stories and invite them to share, highlighting the differences in the situations.

### Student Facing

1. Choose one of the expressions from the card sort that didn't have a match. Write a situation that matches the expression.

### Student Response

If students don’t think of a situation that makes sense, ask them to think about one of the contexts from earlier in the unit and describe the equation using that context. For example, the paper strips or the macaroni and cheese.

### Activity Synthesis

• Invite students to share problems (or have a gallery walk).

## Lesson Synthesis

### Lesson Synthesis

Display chart from a previous lesson.

“What can we add to our chart to show what we learned about division in this section?”