Lesson 15
Situaciones de división de fracciones
Warm-up: Conversación numérica (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.
- “Hagan una señal cuando tengan una respuesta y puedan explicar cómo la obtuvieron” // “Give me a signal when you have an answer and can explain how you got it.”
- 1 minute: quiet think time
Activity
- Record answers and strategy.
- Keep expressions and work displayed.
- Repeat with each expression.
Student Facing
Encuentra mentalmente el valor de cada expresión.
- \(6 \div 3\)
- \(6 \div \frac{1}{3}\)
- \(\frac{1}{3} \div 6\)
- \(\frac{1}{3} \div 12\)
Student Response
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Activity Synthesis
- “¿En qué se parecen las expresiones \(6\div\frac{1}{3}\) y \(\frac{1}{3} \div 6\)? ¿En qué son diferentes?” // “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: Clasificación de tarjetas: Clasifiquemos problemas de división de fracciones (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).
Required Materials
Materials to Copy
- Fraction Division Problem Sort, Spanish
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
- “Este grupo de tarjetas tiene situaciones y expresiones. Emparejen cada situación con una expresión. Con su compañero, justifiquen sus elecciones” // “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
- “Respondan juntos la pregunta de cada situación” // “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
- Tu profesor te dará un grupo de tarjetas. Empareja cada expresión con una situación. Algunas expresiones no tienen una situación que les corresponda.
- Responde cada pregunta. Prepárate para compartir cómo razonaste.
Student Response
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Advancing Student Thinking
If students do not correctly match situations to expressions, have students draw a diagram for each situation. Consider asking, “¿Alguna de las expresiones le corresponde al diagrama que dibujaste?” // “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: Situaciones-historia de división (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
- Escojan una de las expresiones de la clasificación de tarjetas que no haya tenido pareja y escriban una situación que le corresponda.
- Intercambien la situación con otro grupo y respondan la pregunta de ellos.
Student Response
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Advancing Student Thinking
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.
“¿Qué podemos agregar a nuestro póster para mostrar lo que aprendimos en esta sección sobre la división?” // “What can we add to our chart to show what we learned about division in this section?”
Cool-down: Empareja y resuelve (5 minutes)
Cool-Down
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