# Lesson 10

¿Cuál es la pregunta?

## Warm-up: Observa y pregúntate: Un día en el parque (10 minutes)

### Narrative

The purpose of this Notice and Wonder is to elicit different questions from students about a story to prepare them for writing their own questions for a math story in an upcoming activity. Although students may notice and wonder many things, the most important discussion point will be the types of mathematical questions that can be asked about the story.

### Launch

• Groups of 2
• Display the questionless story problem.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time

### Activity

• “Discutan con su compañero lo que pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

### Student Facing

En el parque, hay 37 niños en el campo de fútbol, 18 niños en las canchas de tenis y 25 niños en las mesas de pícnic.

¿Qué observas? ¿Qué te preguntas?

### Activity Synthesis

• “¿Qué preguntas matemáticas se pueden hacer sobre esta situación?” // “What are some mathematical questions that could be asked about this situation?”
• Record responses.
• “¿Qué tienen en común estas preguntas? ¿En qué son diferentes?” // “What do these questions have in common? How are they different?”

## Activity 1: Preguntemos y respondamos (20 minutes)

### Narrative

The purpose of this activity is for students to ask a question that can be answered with the given information and then answer the question. There are many different questions students can ask including:

• Who picked the most apples?
• How many apples did they pick together?
• Did Elena or Diego pick more apples?
• How many apples did Diego pick?

These questions require all the given information to solve. Students may also ask questions which require only some of the information to solve, such as, “How many apples did Han pick?” The activity synthesis focuses on sharing different questions students asked and how they found the answer, with a focus on the multi-step problem “How many apples did they pick altogether?” Images are provided for display, however, student work should be used as much as possible in the synthesis.

### Launch

• Groups of 2
• “A veces las personas compran manzanas en el mercado agrícola o en el supermercado, pero a veces van a un huerto de manzanas a recolectarlas” // “Sometimes people buy apples at the market or grocery store, but sometimes people go to an apple orchard to pick apples.”
• “Cada persona lleva una cesta para recoger las manzanas que recolectó y luego las paga” // “Each person gets a basket to collect the apples they pick, and then they pay for the apples.”
• “Recolectar manzanas es un plan divertido para hacer en familia o con amigos” // “Apple picking can be a fun outing for families and friends.”
• “Van a leer una historia y a hacer preguntas sobre unos amigos que fueron juntos a recolectar manzanas” // “You will be reading a story and asking questions about friends who went apple picking together.”

### Activity

• “Piensen en las preguntas que pueden hacerle a alguien y que esta historia puede ayudarle a responder” // “Think about the questions you could ask someone that this story could help them answer.”
• 5 minutes: independent work time
• “Intercambien las preguntas con su compañero y encuentren la respuesta” // “Switch questions with your partner and find the answer.”
• “Compartan cómo pensaron y revisen si están de acuerdo en la respuesta” // “Share your thinking and check to see if you agree about the answer.”
• 5 minutes: partner work time
• Monitor for students who represent how many apples Han picked and students who represent how many apples Diego picked compared to Han to share in the synthesis as shown.

### Student Facing

Elena recolectó 29 manzanas. Elena recolectó 14 manzanas menos que Han. Han recolectó 15 manzanas más que Diego.

1. Escribe una pregunta que alguien podría responder basándose en esta información.
2. Responde tu pregunta. Muestra cómo pensaste. Usa diagramas, símbolos u otras representaciones.

### Student Response

If students write a question that can’t be answered with the information given, consider asking:
• “¿De qué se trata la historia?” // “What is the story about?”
• “¿Qué se puede contar en la historia?” // “What can be counted in the story?”
• “¿Qué cantidades conoces? ¿Qué es desconocido?” // “What quantities do you know? What is unknown?”

### Activity Synthesis

• Invite students to share their questions.
• Display a diagram that represents the number of apples Han picked, such as:
• “¿Qué representa el diagrama?” // “What does the diagram represent?” (The number of apples Han picked since he picked 14 more than Elena.)
• “¿Cómo encontraron cuántas manzanas recolectó Han?” // “How did you find how many apples Han picked?” (I added 30 to 14 to get 44 and then took away 1 to get 43.)
• Display a diagram that represents the number of apples Diego picked compared to Han, such as:
• “¿Qué representa el diagrama?” // “What does the diagram represent?” (How many apples Diego picked compared to Han.)
• “¿Cómo encontraron cuántas manzanas recolectó Diego?” // “How did you find how many apples Diego picked?” (I took 15 away from 43.)
• “¿Cómo encontraron cuántas manzanas recolectaron en total Elena, Han y Diego?” // “How did you find how many apples Elena, Han, and Diego picked altogether?” (I added 29, 43, and 28. I put all the tens together to get 80 and all the ones together to get 20 then added 80 and 20.)

## Activity 2: ¿Cuál es la pregunta? (15 minutes)

### Narrative

The purpose of this activity is to interpret student work with given numbers and use a story context to determine what question was answered. The first problem shows a tape diagram which puts together the three quantities in the story. The second problem shows a compare tape diagram with the three given quantities and an unknown. In each case, students need to reason about the representations and the given given information to determine what question the work could answer (MP2). Determining the relationships between quantities and using them to ask questions and solve problems is an aspect of modeling with mathematics (MP4).

The goal of the activity synthesis is to identify questions, especially for the second problem, and discuss strategies for performing the calculations.

MLR8 Discussion Supports. Display sentence frames to answer the questions during the synthesis. “Observé _____, entonces yo . . .” // “I noticed _____ so I . . . .”
Representation: Access for Perception. Invite students to act out the scenario of what is happening in the story problem. Have the students pretend to combine the photographs to see the action in the problem. This helps students make the connection to addition.
Supports accessibility for: Conceptual Processing, Attention

• Groups of 2

### Activity

• “Van a examinar el trabajo de un estudiante y a descifrar cuál es la pregunta que el estudiante está tratando de responder” // “You are going to look at some student work and figure out what question the student is trying to answer.”
• 5 minutes: independent work time
• 5 minutes: partner discussion

### Student Facing

Clare recolectó 51 manzanas. Lin recolectó 18 manzanas y Andre recolectó 19 manzanas.

Este es el trabajo que hizo un estudiante para encontrar la respuesta a una pregunta sobre las manzanas.

1.

$$51 + 19 = 70$$

$$70 + 18 = 88$$

¿Cuál es la pregunta?

Explica cómo lo sabes.

2.

$$19 + 18 = 37$$

$$51 - 37 = 14$$

¿Cuál es la pregunta?

Explica cómo lo sabes.

### Student Response

If students write a question that doesn’t match the context and the diagram, consider asking:
• “¿Qué observas acerca del trabajo del estudiante?” // “What do you notice about the student work?”
• “¿Cómo crees que se relaciona el trabajo del estudiante con la historia?” // “How do you think the student work connects to the story?”

### Activity Synthesis

• Invite 12 students to share questions for the first problem.
• “¿Cómo supieron que el estudiante estaba tratando de encontrar una cantidad total?” // “How did you know the student was trying to find a total amount?” (The tape diagram and student work shows addition.)
• “¿Por qué piensan que el estudiante sumó 51 y 19 en vez de 51 y 18?” // “Why do you think the student added 51 and 19 rather than 51 and 18?” (They make 70 together. That way, there is no need to make a ten when you add the third number.)
• Invite 12 students to share questions for the second problem.
• “¿Cómo supieron que la pregunta podría ser sobre comparar? ¿Por qué no podía ser una pregunta sobre quitar?” // “How did you know the question might be about comparing? Why not a question about taking away?” (The operation is subtraction but Lin’s apples and Andre’s apples aren’t taken away from Clare’s apples. The diagram helps see that it is a comparison.)
• “¿Qué estrategias pueden usar para calcular $$51 - 19 - 18$$?”// “What strategies can you use to calculate $$51 - 19 - 18$$?” (Use the number line. Make a drawing. Subtract 20 and add 1, subtract 20 more and add 2.)

## Lesson Synthesis

### Lesson Synthesis

“Hoy escribimos preguntas para algunos problemas-historia. También usamos diagramas y ecuaciones para averiguar qué preguntas podrían haberse respondido” // “Today we wrote questions for story problems and used diagrams and equations to figure out what questions might have been answered.”

“¿Qué necesitan saber para poder escribir una pregunta matemática sobre una historia?” // “What do you need to know to be able to write a math question for a story?” (You need to know some numbers or amounts of things. You need something you can count or measure. You might need to know what people are doing, like putting things together or taking things away.)

“¿Qué pistas hay en los diagramas o ecuaciones que les pueden ayudar a averiguar cuál es la pregunta matemática que alguien está tratando de resolver sobre una historia?” // “What clues in diagrams or equations can help you figure out what math question someone might be trying to figure out for a story?” (It helped to see what kind of diagram people were using. The question mark to show what was unknown was a good clue. We needed to know some parts of the story, like what was being counted or measured.)