# Lesson 13

Problemas-historia y ecuaciones

## Warm-up: Cuál es diferente: Diagramas (10 minutes)

### Narrative

This warm-up prompts students to carefully analyze and compare features of tape diagrams and equations. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear the terminologies students know and how they talk about characteristics of tape diagrams and connect them to equations (MP2, MP7).

### Launch

• Groups of 2
• Display image.
• “Escojan uno que sea diferente. Prepárense para compartir por qué es diferente” //  “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

### Activity

• “Discutan con su pareja cómo pensaron” //  “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

### Student Facing

¿Cuál es diferente?

1. $$27 + \underline{\phantom{\hspace{1.05cm}}} = 40$$

### Activity Synthesis

• “Encontremos al menos una razón por la que cada uno es diferente” //  Let’s find at least one reason why each one doesn’t belong.”
• “¿Cuál diagrama corresponde mejor a la ecuación de C? Expliquen” //  “Which diagram best matches the equation in C? Explain.”

## Activity 1: Clasificación de tarjetas: Problemas-historia y ecuaciones (15 minutes)

### Narrative

The purpose of this activity is for students to connect story problems to the equations that represent them and to solve different types of story problems. Students identify equations with a symbol for the unknown that match a story problem and justify their decisions by describing how the equations represent the quantities and any actions in the story problem (MP4). When students analyze and connect the quantities and structures in the story problems and equations, they are thinking abstractly and quantitatively (MP2) and making use of structure (MP7).

MLR8 Discussion Supports. Display sentence frames to support discussion as students explain their reasoning to their partner: “Observé ___, así que emparejé. . . ” // “I noticed ___ , so I matched . . .” Encourage students to challenge each other when they disagree.

### Required Materials

Materials to Gather

Materials to Copy

• Equations for Different Types of Word Problems

### Required Preparation

• Create a set of cards from the blackline master for each group of 24.
• Each group of 24 needs a set of cards from the previous lesson.

### Launch

• Groups of 24
• Give each group the story problems (Cards A–I) from the Story Problem and Diagram Cards.
• Give one set of Equation Cards to each group of students.
• “Por turnos, lean los problemas-historia. Después de que una persona lea, encuentren juntos la ecuación que corresponda. Cuando piensen que encontraron una correspondencia, explíquenle a su grupo por qué las tarjetas corresponden” //  “Take turns reading the story problems. After one person reads, work together to find an equation that matches. When you think you have found a match, explain to your group why the cards match.”
• “Si creen que más de una tarjeta podría corresponder a la historia, expliquen la correspondencia a su grupo” //  “If you think that more than one card could match the story, explain the match to your group.”
• As needed, demonstrate the activity with a student volunteer.
• “Cuando el grupo termine, escojan 2 problemas-historia de las tarjetas F, G, H o I y resuélvanlos” //  “When your group finishes, choose 2 story problems from Cards F, G, H, or I and solve them.”

### Activity

• 6 minutes: partner work time
• Monitor for students who explain why more than one equation may match a story and how the equations match the quantities in the context of the story problem.
• 4 minutes: independent work time

### Student Facing

1. Empareja cada problema-historia con una ecuación. Explica por qué las tarjetas corresponden.
2. Escoge 2 problemas-historia y resuélvelos. Muestra cómo pensaste.

### Student Response

Students may believe that only one equation could match each story. Encourage students to describe how equations match any actions in the story and whether any other equations show the same actions. If there are no actions in the story, ask students to explain why one or more cards shows the relationship between the parts and the whole. Consider providing the tape diagrams from the previous activity to support students in their explanations.

### Activity Synthesis

• Invite students to share a match for each story.
• “¿Cómo corresponde la ecuación al problema-historia?” //  “How does the equation match the story problem?”
• “¿Hay otra ecuación que podría corresponder al problema-historia? Expliquen por qué sí o por qué no” //  “Is there another equation that could match the story problem? Explain why or why not.”

## Activity 2: Representemos y resolvamos problemas-historia (20 minutes)

### Narrative

The purpose of this activity is for students to use tape diagrams and equations to represent different types of story problems within 100. In this activity, students interpret story problems and use diagrams and equations to represent the unknown quantities. Students are encouraged to solve using a method that makes sense to them.

Students may complete the parts of each problem in an order that makes sense to them. In the synthesis, students compare and connect their diagrams, equations, and methods for solving (MP2, MP7). Monitor for students who draw accurate diagrams and create different equations for the problem with Noah and Kiran’s seeds to share in the lesson synthesis.

Representation: Develop Language and Symbols. Provide students with access to a chart that shows an example of a completed tape diagram so that students can refer to it as they work on the activity. Supports accessibility for: Visual-Spatial Processing, Memory, Attention

### Required Materials

Materials to Gather

• Groups of 2

### Activity

• “Ahora pueden dibujar diagramas y y escribir ecuaciones que representen problemas-historia” // “Now you get a chance to draw diagrams and write equations that represent story problems.”
• “Lean la historia cuidadosamente. Después, resuelvan cada problema y muestren cómo pensaron” // “Read the story carefully. Then solve each problem and show your thinking.”
• 8 minutes: independent work time
• 5 minutes: partner discussion
• Monitor for students who:
• use an addition equation to represent Andre’s seeds
• subtract to find the number of seeds Andre won using a base-ten diagram or equations.

### Student Facing

1. Lin jugó un juego con semillas. Empezó el juego con algunas semillas. Después ganó 36 semillas. Ahora tiene 64 semillas. ¿Cuántas semillas tenía Lin al principio?

1. Escribe una ecuación con un signo de interrogación para representar el valor desconocido.

2. Resuelve la ecuación. Muestra cómo pensaste. Usa dibujos, números o palabras.

2. Andre empezó un juego con 32 semillas. Después ganó más semillas. Ahora tiene 57 semillas. ¿Cuántas semillas ganó Andre?

1. Marca el diagrama para representar la historia.

2. Escribe una ecuación con un signo de interrogación para representar el valor desconocido.

3. Resuelve la ecuación. Muestra cómo pensaste. Usa dibujos, números o palabras.

3. Diego recolectó 22 semillas de flores amarillas y 48 semillas de flores azules. ¿Cuántas semillas recolectó en total?

1. Marca el diagrama para representar la historia.

2. Escribe una ecuación con un signo de interrogación para representar el valor desconocido.

3. Resuelve la ecuación. Muestra cómo pensaste. Usa dibujos, números o palabras.

4. Noah y Kiran recolectaron 92 semillas de calabaza. Noah recolectó 53 semillas de calabaza. ¿Cuántas semillas recolectó Kiran?

1. Dibuja un diagrama para representar la historia.

2. Escribe una ecuación con un signo de interrogación para representar el valor desconocido.

3. Resuelve la ecuación. Muestra cómo pensaste. Usa dibujos, números o palabras.

### Student Response

If students draw their own diagrams, but do not label the quantities, consider asking:

• “¿Cuáles son las diferentes cosas de esta historia que puedes contar? ¿Cómo muestra tu diagrama estas cosas?” // “What are the different things that you can count in the story? How does your diagram show these things?”
• “¿Qué podrías agregarle a tu diagrama para ayudarle a alguien a hacer conexiones con la historia?” // “What could you add to your diagram to help someone make connections to the story?”

### Activity Synthesis

• Invite a previously identified student to share their completed tape diagram and the addition equation for Andre's seeds.
• Invite a previously identified student to share the way they used subtraction to find how many seeds Andre won.
• “¿En qué se parecen la ecuación de ______ y el método de _____? ¿En qué son diferentes?” //  “How are _____’s equation and _____’s method the same? How are they different?” (They both use the same numbers. _____’s method is a way to find the unknown value in the equation. They are different because the equation is addition, but the method shows subtraction).
• “¿El método de ______ que usa resta corresponde a las acciones del problema-historia? Explica por qué sí o por qué no” //  “Does _____’s method using subtraction match the actions in the story problem? Explain why or why not.” (No. The story tells about starting with some seeds and getting more seeds. That is addition. But you can use subtraction to find the value, since there is an unknown addend.)
• “A veces puede ser mejor usar ecuaciones de suma o de resta para representar las acciones que ocurren en una historia. Pero siempre pueden usar suma o resta para encontrar un sumando desconocido” //  “Sometimes it might be better to use addition or subtraction equations to represent the actions that are happening in a story. But you can always use addition or subtraction to find an unknown addend.”

## Lesson Synthesis

### Lesson Synthesis

Display student work samples for the story about Noah and Kiran’s seeds that show an accurate diagram, an addition equation that represents the story, and a subtraction equation that represents the story.

“¿Las dos ecuaciones corresponden a la historia y al diagrama? Expliquen” //  “Do both equations match the story and the diagram? Explain.” (Yes. Each equation shows the total amount of seeds and Noah’s seeds. The question mark shows Kiran’s seeds. You could show how Noah’s seeds and Kiran’s seeds are related with addition or subtraction.)

“¿Cuál les ayuda a darle sentido a una historia: un diagrama, una ecuación o ambos?” //  “Which helps you make sense of a story—a diagram, an equation, or both?”