Lesson 15

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.

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

• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

• “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.)

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).

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

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

• “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.

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.

• 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.

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.

• Groups of 2-4

• 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.

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.

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