# Lesson 15

Diagramas con todo tipo de problemas de comparación

## Warm-up: Conversación numérica: 10 y algo más (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for making 10 when adding. These understandings help students develop fluency with operations within 20.
When students look for ways to rearrange and decompose numbers to make 10, they notice and make use of structure of expressions and whole numbers (MP7).

### 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: think time

### Activity

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

### Student Facing

Encuentra mentalmente el valor de cada suma.

• $$4 + 8 + 2$$
• $$4 + 5 + 3 + 2$$
• $$9 + 3 + 1$$
• $$9 + 5$$

### Activity Synthesis

• “¿Cómo les ayudó formar una decena a encontrar las sumas?” // “How did making a ten help when finding the sums?”

## Activity 1: Colecciones de conchas marinas (15 minutes)

### Narrative

The purpose of this activity is for students to interpret a Compare problem with the smaller value unknown and connect the problem to a tape diagram. The launch of the activity is an opportunity for students to share their experiences and ask questions about a beach to ensure each student has access into the context. If it is helpful, display a few images from beaches from different areas around the world. The story problem is introduced without numbers in order to allow students to consider the relationship between quantities. Students consider who has more or less, which supports their interpretation of the tape diagram. If needed to help students connect the tape diagram to the subtraction equation, show students that if you look at Diego’s rectangle and cover up the portion below that part that shows 20, it will be the same as Lin’s rectangle.

At the beginning of this activity, make sure students do not have their workbook open yet.

Action and Expression: Develop Expression and Communication. Give students access to  connecting cubes to build the comparison with a concrete manipulative. The numbers from the problem are shown exactly, with the difference very apparent as well. This supports the pictorial images of the tape diagrams.
Supports accessibility for: Conceptual Processing, Organization

### Launch

• Groups of 2
• “Voy a contarles una historia corta sobre dos estudiantes que fueron a la playa. Pero antes, cuéntenle a su pareja algo que sepan o háganle preguntas que tengan sobre las playas” // “I am going to tell you a quick story about two students who visited a beach. But before I do, tell your partner something you know or questions you have about a beach.”
• Share responses.
• “Ahora sí, nuestra historia: Diego tiene algunas conchas marinas. Lin tiene menos conchas marinas” // “Now, our story: Diego has some shells. Lin has fewer shells.”
• “Hablen con su pareja sobre cuántas conchas marinas podría tener Diego y cuántas conchas marinas podría tener Lin” // "Talk to your partner about how many shells Diego could have and how many shells Lin could have."
• Share responses. Highlight that Diego has more and ask how they know he should have more.
• 1 minute: partner discussion
• Record responses.

### Activity

• “Diego tiene 55 conchas marinas y Lin tiene 20 conchas marinas menos que Diego” // “Diego has 55 shells and Lin has 20 fewer shells than Diego.”
• Display the partially-labeled diagram.
• “Este diagrama muestra algunas partes del problema-historia que acaban de leer, pero le hacen falta algunas palabras” // “This diagram shows some parts of the story problem you just read, but it is missing some labels.”
• “Marquen el diagrama para que muestre cuántas conchas marinas tiene Diego y cuántas tiene Lin. Después, escriban una ecuación para mostrar cómo encontraron la parte desconocida. Usen un signo de interrogación mara mostrar el número desconocido” // “Label the diagram so that it shows how many shells Diego has and how many Lin has. Then write an equation to show how you could find the unknown part. Use a question mark to show the unknown.”
• 2 minutes: independent work time
• 3 minutes: partner discussion
• Monitor for students who explain how each part of the diagram and equation connects to the story problem.

### Student Facing

Diego tiene 55 conchas marinas. Lin tiene 20 conchas marinas menos que Diego.

1. Usa el problema-historia para completar el diagrama.
2. Escribe una ecuación para mostrar cómo puedes encontrar el número desconocido de conchas marinas. Usa un signo de interrogación para representar el número desconocido.

### Activity Synthesis

• Invite previously identified student(s) to explain how they labeled the tape diagram.
• “¿Qué parte representa las conchas marinas de Diego? ¿Cómo lo saben?” // “Which part represents Diego’s shells? How do you know?”
• “¿Qué parte representa las conchas marinas de Lin? ¿Cómo lo saben?” // “Which part represents Lin’s shells? How do you know?”
• “¿Qué parte muestra la diferencia entre la cantidad de conchas marinas que tiene cada estudiante?” // “Which part shows the difference between the amount of shells each student has?”
• “¿Alguien podría explicar con sus propias palabras cómo _____ decidió marcar el diagrama?” // “Could someone explain how _____ decided to label the diagram in their own words?”
• Invite previously identified student(s) to share the equation they used to represent the story problem.
• “¿Cómo usaron el diagrama para escribir su ecuación?” // “How did you use the diagram to write your equation?” (The diagram helped me see I could start with 55 and take away 20 to find Lin’s shells. The diagram helped me see that Lin’s shells and 20 more would be the same as 55.)
• Consider having student(s) describe what the numbers and symbols in the equation represent, as they did for the diagram.

## Activity 2: Clasificación de tarjetas: En la playa (20 minutes)

### Narrative

The purpose of this activity is for students to connect Compare problems, tape diagrams, and equations with unknowns in all positions. Support students with interpreting “more” or “fewer” in the context of the story problem by encouraging them to explain which quantity should be the bigger quantity and which should be the smaller quantity. Ask them to describe what they look for in a diagram or equation to make sure it matches a story problem. When students analyze and connect the quantities and structures in the story problems, diagrams, and equations, they think abstractly and quantitatively (MP2) and make use of structure (MP7).

If students are not yet reading independently, consider reading one story problem at a time and giving students time to independently find their matches. It is recommended to read the story problems in order beginning with story problem A if facilitated in this way.

MLR8 Discussion Supports. To support students as they take turns finding a match and explaining their reasoning, display the following sentence frames for all to see: “Yo observé ___ , entonces emparejé . . .” // “I noticed ___ , so I matched . . .” Encourage students to challenge each other when they disagree.

### Required Materials

Materials to Copy

• Card Sort: At the Beach, 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 cards from the blackline master.
• “Lin y Diego quieren comparar otras cosas que recolectaron e hicieron en la playa” // “Lin and Diego want to compare other things they collected and did at the beach.”
• “Encuentren un diagrama y una ecuación que corresponda al problema-historia. Puede que haya más de una ecuación que corresponda a cada problema-historia” // “Find one diagram and one equation that match a story problem. There may be more than one equation that matches each story problem.”
• “Tomen turnos para leer un problema-historia. Después de que uno de ustedes lo lea, encuentren juntos otras tarjetas que correspondan. Cuando crean que han encontrado una tarjeta que corresponde, explíquenle a su pareja por qué” // “Take turns reading a story problem. After one partner reads, work together to find other cards that match. When you think you have found a match, explain to your partner why the cards match.”
• “Si les ayuda, pueden marcar los diagramas para explicar cómo corresponden” // “If it helps, you may label the diagrams to explain your matches.”
• As needed, demonstrate the activity with a student volunteer.

### Activity

• 8 minutes: partner work time
• Monitor for students who explain how each diagram and equation matches the quantities in the context of the story problem.
• “Comparen sus correspondencias con las de otro grupo. Si tienen correspondencias distintas, trabajen juntos para explicar cuáles tarjetas sí corresponden o por qué una tarjeta podría corresponder a problemas-historia diferentes” // “Compare your matches with the matches of another group. If you have different matches, work together to explain which cards belong or why a card could belong to different groups.”
• 4 minutes: small-group work time

### Student Facing

1. Lee una tarjeta que tenga un problema-historia.
2. Encuentra tarjetas que corresponden al problema-historia.
3. Explica por qué las tarjetas corresponden.

### Student Response

If students match story problems with equations or diagrams that do not accurately show the quantities or their relationships, consider asking:

• “¿Cómo decidiste cuál ecuación o diagrama corresponde a la historia?” // "How did you choose which equation or diagram matches the story?"
• “¿Puedes explicar cómo corresponde el problema-historia a este diagrama o ecuación?” // "Can you explain how the story problem matches this diagram or equation?"

### Activity Synthesis

• Invite 2–3 student groups to share their matches. Consider selecting groups to share their matches for story problems A, B, and C.
• “¿Cómo saben que el diagrama corresponde al problema-historia?” // “How do you know the diagram matches the story problem?”
• “¿Cómo corresponde su ecuación al problema-historia?” // “How does your equation match the story problem?”
• “¿Hay otra ecuación que puede corresponder a su problema-historia? ¿Cómo lo saben?” // “Is there another equation that could match your story problem? How do you know?”

## Lesson Synthesis

### Lesson Synthesis

“Hoy seguimos trabajando con diagramas para representar problemas-historia de comparación. Los diagramas pueden ayudar a mostrar si debemos encontrar el número más grande, el número más pequeño o la diferencia” // “Today, we worked more with diagrams to represent Compare story problems. Diagrams can help show if we need to find the bigger number, the smaller number, or the difference.”

Display: Card H, J, and L from Activity 2.

“¿Cuál diagrama muestra que se está buscando el número más grande? ¿Cómo lo saben?” // “Which diagram shows that you are looking for the bigger number? How do you know?” (L because the bigger bar has a question mark.)

“¿Cuál diagrama muestra que se está buscando el número más pequeño? ¿Cómo lo saben?” // “Which diagram shows that you are looking for the smaller number? How do you know?” (Diagram J,  because the smaller bar has a question mark.)