# Lesson 20

Más práctica en representar y resolver

## Warm-up: Conversación numérica: Dos pasos (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies students have for multiplying single-digit factors and adding two-digit numbers. The expressions involve two operations. They encourage students to look for and make use of structure as they use their understanding of equal-size groups and properties of operations to find products and sums (MP7). The reasoning here will be helpful later when students solve two-step word 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

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

### Student Facing

Encuentra mentalmente el valor de cada expresión.

• $$20 + (2 \times 3)$$
• $$30 + (4 \times 3)$$
• $$50 + (8 \times 3)$$
• $$99 + (8 \times 3)$$

### Activity Synthesis

• “¿Cómo les ayudaron las primeras dos expresiones a encontrar el valor de las últimas dos expresiones?” // “How did the first two expressions help you find the value of the last two expressions?”
• “¿Alguien puede expresar el razonamiento de ___ de otra forma?” // “Who can restate ___ 's reasoning in a different way?”
• “¿Alguien usó la misma estrategia, pero la explicaría de otra forma?” // “Did anyone have the same strategy but would explain it differently?”
• “¿Alguien pensó en el problema de otra forma?” // “Did anyone approach the problem in a different way?”
• “¿Alguien quiere agregar algo a la estrategia de _____?” // “Does anyone want to add on to _____’s strategy?”

## Activity 1: Falta de información: Introducción (15 minutes)

### Narrative

The purpose of this activity is to introduce students to the structure of the MLR4 Information Gap routine. This routine facilitates meaningful interactions by positioning some students as holders of information that is needed by other students.

Tell students that first, a demonstration will be conducted with the whole class, in which they are playing the role of the person with the problem card. Explain to students that it is the job of the person with the problem card (in this case, the whole class) to think about what information they need to answer the question.

For each question that is asked, students are expected to explain what they will do with the information, by responding to the question, “¿Por qué necesitas saber ______?” // “Why do you need to know (that piece of information)?” If the problem card person asks for information that is not on the data card (including the answer!), then the data card person must respond with, “No tengo esa información” // “I don’t have that information.” In explaining their answers, students need to be precise in their word choice and use of language (MP6).

Once the students have enough information to solve the problem, they solve the problem independently.

The info gap routine requires students to make sense of problems by determining what information is necessary and then ask for information they need to solve them. This may take several rounds of discussion if their first requests do not yield the information they need (MP1).

### Launch

• Groups of 2
• “En los problemas de esta lección se explora la organización de un evento especial en la escuela. ¿Cuál es su evento favorito de la escuela o de su barrio?” // “The problems in this lesson are about setting up for a special event at a school. What’s your favorite special event at school or in your community?”
• Share responses.

### Activity

MLR4 Information Gap

• Display the Sample Problem Card.
• Listen for and clarify any questions about the context.
• “Parte de la información que necesitan para resolver este problema hace falta y yo la tengo aquí. ¿Qué información específica necesitan?” // “Some of the information you need to solve this problem is missing, and I have it here. What specific information do you need?”
• 1–2 minutes: quiet think time
• “Con su compañero, decidan qué información necesitan para resolver el problema y hagan una lista de preguntas que pueden hacer para averiguarla” // “With your partner, decide what information you need to solve the problem, and create a list of questions you can ask to find out.”
• 2–3 minutes: partner discussion
• Invite students to share 1 question at a time.
• Record each question on a display, and respond with: “¿Por qué necesitan saber ______?” // “Why do you need to know ______ [the information requested]?” Students should provide a justification for how they will use the information before the information is revealed.
• Answer questions using only information stated on the Sample Data Card (do not reveal).
• Record information that is shared on the display. Give students time to decide whether they have enough information to solve the problem.
• Repeat until students decide they have enough information to solve, then ask students to solve.
• 2–4 minutes: independent work time

### Activity Synthesis

• Invite 1–2 students to share how they solved the problem.
• “¿Cuáles preguntas les ayudaron a encontrar cuántas sillas había en la habitación?” // “Which questions helped you find out how many chairs were in the room?” (How many chairs were in the corner? How many chairs were in each row? How many rows were there?)
• If there were any questions that the data card cannot answer, discuss them here.

## Activity 2: Falta de información: Feria de pastelería (20 minutes)

### Narrative

This Info Gap activity gives students an opportunity to determine and request information needed to solve a two-step problem that involves multiplication.

The Info Gap structure requires students to make sense of problems by determining what information is necessary, and then to ask for information they need to solve it. This may take several rounds of discussion if their first requests do not yield the information they need (MP1). It also allows them to refine the language they use and ask increasingly more precise questions until they get the information they need (MP6).

Here is an image of the cards for reference:

Representation: Access for Perception. Begin by giving a physical demonstration of the activity’s procedure to support understanding of the activity and understanding of the context.
Supports accessibility for: Social-Emotional Functioning, Memory

### Required Materials

Materials to Copy

• Info Gap: Bake Sale, Spanish

### Required Preparation

• Create a set of cards from the blackline master for each group of 2.
• Keep set 1 separate from set 2.

### Launch

• Groups of 2

MLR4 Information Gap

• Display the task statement, which shows a diagram of the Info Gap structure.
• 1–2 minutes: quiet think time
• Read the steps of the routine aloud.
• “Les voy a dar una tarjeta de problema o una tarjeta de datos. Lean su tarjeta en silencio. No se la muestren ni se la lean a su compañero.” // “I will give you either a problem card or a data card. Silently read your card. Do not read or show your card to your partner.”
• Distribute the cards.
• 1–2 minutes: quiet think time
• Remind students that after the person with the problem card asks for a piece of information the person with the data card should respond with “¿Por qué necesitas saber _____?” // “Why do you need to know ______ [the information requested]?”

### Activity

• 3–5 minutes: partner work time
• After students solve the first problem, distribute the next set of cards. Students switch roles and repeat the process with Problem Card 2 and Data Card 2.

### Student Facing

Tu profesor te dará una tarjeta de problema o una tarjeta de datos. No se la muestres ni se la leas a tu compañero.

Haz una pausa aquí para que tu profesor pueda revisar tu trabajo.

Pídele al profesor un nuevo grupo de tarjetas. Intercambia roles con tu compañero y repite la actividad.

### Activity Synthesis

• “De las clases de preguntas que hicieron, ¿cuáles fueron las más útiles?” // “What kinds of questions were the most useful to ask?”
• Select 1–2 students to share different strategies used to solve one of the problems. Try to feature a student-drawn tape diagram.
• “¿Alguien resolvió el problema de otra forma?” // “Did anyone solve the problem in a different way?”
• “¿Alguien usó un diagrama de cinta?” // “Did anyone use a tape diagram?”
• “¿Cómo supieron si su respuesta tenía sentido?” // “How did you know if your answer made sense?”
• “¿Cómo podríamos representar el segundo problema con una ecuación en la que se use una letra para representar la cantidad desconocida?” // “How could we represent the second problem with an equation with a letter for the unknown quantity?” ($$230 - (7 \times 10) = {d}$$)

## Lesson Synthesis

### Lesson Synthesis

“Hoy aprendimos la rutina ‘Falta de información’. ¿Cómo les ayudó esta rutina a darle sentido a los problemas que resolvieron?” // “Today we learned the Information Gap routine. How did this routine help you make sense of the problems you solved?” (The routine gave me a chance to focus on what was important in the problem. I had to think about what I needed to know to solve the problem. I had to think about why some information was needed to solve the problem. It helped me make sense of what was happening in the problem.)

## Student Section Summary

### Student Facing

En esta sección, redondeamos números para estimar las respuestas a los problemas. Esto nos ayudó a decidir si nuestras respuestas a los problemas tenían sentido basándonos en la situación y en los números de la situación.

También escribimos ecuaciones que tenían un número desconocido y usamos diagramas para hallar la respuesta exacta a los problemas.

Situación:

Mai tenía 104 chaquiras. Ella compró 2 paquetes más de chaquiras. Cada paquete trae 10 chaquiras. ¿Cuántas chaquiras tiene ahora?

Diagrama:

Ecuación con un número desconocido:

$$104+(2\times10)=n$$