# Lesson 11

¿Cómo resolvemos problemas-historia?

## Warm-up: ¿Qué sabes sobre los problemas-historia? (10 minutes)

### Narrative

The purpose of this What Do You Know About _____? is to invite students to share what they know about story problems. Monitor for student comments regarding the types of story problems they know about and the methods they use to understand and represent story problems.

### Launch

• Display the question.
• “¿Qué saben sobre los problemas-historia?” // “What do you know about story problems?”
• 1 minute: quiet think time

### Activity

• Record responses.
• “¿Cuáles son algunas formas en las que pueden mostrar lo que pasa en un problema-historia?” // “What are some ways you can show what happens in a story problem?”

### Student Facing

¿Qué sabes sobre los problemas-historia?

### Activity Synthesis

• “Hoy vamos a resolver diferentes tipos de problemas-historia y a compartir las diferentes formas en las que los representamos y resolvemos” // “Today we are going to solve different types of story problems and share the different ways we represent and solve them.”

## Activity 1: ¿Cuántas semillas? (20 minutes)

### Narrative

The purpose of this activity is for students to solve a story problem in a way that makes sense to them. Students solve a Compare, Difference Unknown problem within 50 that requires composing or decomposing a ten if students add or subtract by place. During the synthesis, students describe and compare how they used tools, diagrams, and equations in different ways to make sense of and solve the problem (MP2, MP3, MP5).

Students may represent or solve the problem with any method that makes sense to them. Monitor and select students with the following methods to share during the synthesis:

• use connecting cubes or base-ten blocks to represent the problem as a comparison
• use a tape diagram to represent the problem
• use base-ten blocks to show adding or subtracting by place
• use a base-ten diagram to show adding or subtracting by place
• use an equation(s) to show adding or subtracting by place
MLR2 Collect and Display. Synthesis: Direct attention to words collected and displayed from the previous lessons to compare representations. Invite students to borrow language from the display as needed, and update it throughout the lesson.

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• “¿Alguien ha visto semillas alguna vez? ¿Dónde las han visto? ¿Dónde se pueden encontrar?” // “Has anyone ever seen seeds? Where have you seen them? Where can they be found?”
• Share responses.

### Activity

• “Diego y Jada recolectaron semillas para sembrar. Pueden usar los cubos encajables, los bloques en base diez u otras representaciones para entender el problema y resolverlo. Prepárense para explicar cómo pensaron” // “Diego and Jada gathered seeds to plant. You can use the connecting cubes, base-ten blocks, or other representations to help make sense of the problem and solve it. Be prepared to explain your thinking.”
• 6 minutes: independent work time
• As students work, consider asking:
• “¿Qué necesitan encontrar para responder la pregunta? ¿Cómo lo saben?” // “What do you need to find to answer the question? How do you know?”
• “¿Cómo mostraron las semillas de Diego?” // “How did you show Diego’s seeds?”
• “¿Cómo mostraron las semillas de Jada?” // “How did you show Jada’s seeds?”
• “¿Cómo van a encontrar la diferencia?” // “How will you find the difference?”
• “Ahora, comparen el método que ustedes usaron con el de su compañero. ¿En qué se parecen los métodos? ¿En qué son diferentes?” // “Now compare your method with your partner. How are your methods the same? How are they different?”
• 2 minutes: partner discussion

### Student Facing

1. Diego recolectó 42 semillas de naranja. Jada recolectó 16 semillas de manzana. ¿Cuántas semillas más recolectó Diego que Jada? Muestra cómo pensaste.

### Student Response

If students find the sum of Diego and Jada’s seeds, consider asking:

• “¿Qué te pide encontrar el problema-historia?” // “What does the story problem ask you to find?”
• “¿Cómo muestra tu trabajo cuántas semillas más usó Diego?” // “How does your work show how many more seeds Diego used?”
• “¿Cómo podrías usar tus herramientas o un diagrama para comparar las semillas de Diego y las de Jada?” // “How could you use your tools or a diagram to compare Diego and Jada’s seeds?”

### Activity Synthesis

• Invite previously identified students to share their methods in the given order.
• “¿En qué se parecen los diagramas? ¿En qué son diferentes?” // “How are the diagrams the same? How are they different?” (The diagrams all show Diego’s and Jada’s seeds. Some diagrams show the problem and help you see the bigger amount, the smaller amount, and the difference. Some diagrams show how we added and subtracted tens and ones.)

## Activity 2: Las semillas de la grandeza (15 minutes)

### Narrative

The purpose of this activity is for students to solve different types of story problems within 50 that may require composing or decomposing a ten when adding or subtracting by place. Students are encouraged to solve the story problems in a way that makes sense to them. The synthesis focuses on sharing the ways students made sense of and solve a Compare, Smaller Unknown problem.

Monitor for a variety of different ways students use drawings, diagrams, or equations to make sense of or solve the problems for sharing in the lesson synthesis. Look and listen for examples of ways students make sense of what they need to find, such as a tape diagram or base-ten blocks, before they use methods to calculate unknown values (MP1).

Engagement: Provide Access by Recruiting Interest. Provide choice. Invite students to decide which story problem to start with and what strategy they are going to use to show their thinking.
Supports Accessibility for: Organization, Attention

### Required Materials

Materials to Gather

• Groups of 2

### Activity

• “Trabajen con su compañero para darle sentido a cada problema-historia y resolverlo. Muestren cómo pensaron. Usen dibujos, números o palabras” // “Work with your partner to make sense of each story problem and solve it. Show your thinking using drawings, numbers, or words.”
• 8 minutes: partner work time
• Monitor for different ways students use labels and diagrams to make sense of the last problem.

### Student Facing

Resuelve cada problema-historia. Muestra cómo pensaste.

1. Lin tenía 31 semillas de girasol. Le dio 15 semillas a Priya. ¿Cuántas semillas tiene Lin ahora?
2. Noah usó semillas de maíz amarillo y de maíz azul para hacer un diseño. Usó 37 semillas en total. Usó 28 semillas amarillas. ¿Cuántas semillas azules usó?
3. Elena recolectó 50 semillas de calabaza. Andre recolectó 23 semillas de calabaza menos que Elena. ¿Cuántas semillas recolectó Andre?

### Student Response

If students attempt to compare the quantities in every problem or use representations that do not match the situation, consider asking:

• “¿Qué pasa en esta historia?” //“What is happening in this story?”
• “¿Cómo pueden trabajar juntos para actuar la historia?” //“How could you work together to act out the story?”

### Activity Synthesis

• Invite previously identified students to share their diagrams and labels.
• If students do not use tape diagrams to show the last problem, but represent their thinking using visually similar ways (for example, placing a row of base-ten blocks above another row of base-ten blocks), record these methods using a tape diagram.
• “¿Cómo les ayudó su representación a entender el problema-historia?” // “How did your representation help you understand the story problem?” (It helped me show what was happening with the seeds in the story. It helped me show the different groups of seeds and what I needed to find.)
• “¿Cómo les ayudó su representación a resolver el problema-historia?” // “How did your representation help you solve the story problem?” (It helped me see what I needed to find and helped me think about whether I wanted to add or subtract to find the unknown value.)

## Lesson Synthesis

### Lesson Synthesis

Display a tape diagram, a base-ten diagram, and a student-invented diagram or drawing from the second activity.

“¿En qué se parecen estos diagramas y dibujos? ¿En qué son diferentes?” // “How are these diagrams and drawings the same? How are they different?” (They all show parts of the story problems we solved. The tape diagram shows parts of the story problem, but it doesn’t show how you add or subtract. The base-ten diagram shows the parts of the story and shows how you added or subtracted.)

“¿Cuáles diagramas les parecen de más ayuda cuando tratan de entender una historia? ¿Cuál usan cuando resuelven el problema?” // “Which diagrams do you find most helpful when you are trying to understand a story? Which do you use when you solve the problem?”