# Lesson 9

Multiplicación como grupos iguales

## Warm-up: Conversación numérica: Más suma (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for addition within 100. It also provides an opportunity to observe student strategies as they work toward becoming fluent in addition within 1,000.

When students use strategies based on place value to add they look for and make use of structure (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: quiet think time

### Activity

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

### Student Facing

Encuentra mentalmente el valor de cada expresión.

• $$40+35$$
• $$45+35$$
• $$45+36$$
• $$34+58$$

### Activity Synthesis

• “¿Cómo hicieron para componer nuevas decenas mientras resolvían estos problemas?” // “How did you compose new tens as you solved these problems?” (In the second problem I composed a ten from the 2 fives. In the third problem I composed a new ten from the 5 and the 6 and still had 1 leftover.)
• “¿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: De gráficas con escala a grupos iguales (15 minutes)

### Narrative

The purpose of this activity is for students to connect scaled picture graphs to situations involving equal groups. The scale of the picture graph will be used to help students think about a category of the graph as a situation involving equal groups.

The launch of the activity is an opportunity for students to share their experiences and ask questions about the graph to ensure each student has access to the context. If it is helpful, display a few images of different types of signs students may see in their community.

Representation: Internalize Comprehension. Synthesis: Invite students to identify which details were important or most useful to solve the problem. Display the sentence frame, “La próxima vez que lea una gráfica con escala, prestaré atención a . . .” //  “The next time I read a scaled picture graph, I will pay attention to . . . “
Supports accessibility for: Visual-Spatial Processing

### Required Materials

Materials to Gather

### Required Preparation

Each student needs 20 connecting cubes or counters.

### Launch

• Groups of 2
• “Vamos a mirar una gráfica de dibujos con escala sobre las señales que Elena vio camino a casa. ¿Qué tipos de señales ven en su barrio?” // “We’re going to look at a scaled picture graph about signs that Elena saw on the way home. What types of signs do you see in the community?” (stop signs, speed limit signs, street signs, billboards)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.
• Display the graph.

### Activity

• “Trabajen individualmente para representar el número de señales de límite de velocidad que Elena vio camino a casa” // “Work independently to represent the number of speed limit signs that Elena saw on the way home.”
• 1 minute: independent work time.
• Monitor for students who create drawings of equal groups similar to the one shown in the last problem to display during the synthesis.
• 1 minute: partner discussion
• “Completen el siguiente problema con su pareja” // “Work with your partner to complete the next problem.”
• 1 minute: quiet think time
• 2 minutes: partner discussion
• “¿Cómo supieron cuál afirmación describió las señales de límite de velocidad que Elena vio camino a casa?” // “How did you know which statement described the speed limit signs that Elena saw on the way home?” (There were 3 pictures on the graph. Each picture represents 2 signs.)
• Share responses.
• “Tómense unos minutos para completar el último problema individualmente” // “Take a few minutes to complete the last problem on your own.”
• 3 minutes: independent work time
• “Compartan sus respuestas con su pareja” // “Share your responses with your partner.”
• 1 minute: partner discussion

### Student Facing

Elena recolectó datos sobre los tipos de señales que vio camino a casa. Los datos se muestran en esta gráfica de dibujos:

1. Representa el número de señales de límite de velocidad que Elena vio camino a casa.
2. ¿Cuál de estas afirmaciones describe el número de señales de límite de velocidad que vio Elena? Explica tu razonamiento.

1. Hay 3 dibujos y cada dibujo representa 1 señal de límite de velocidad.
2. Hay 3 dibujos y cada dibujo representa 2 señales de límite de velocidad.
3. Hay 2 dibujos y cada dibujo representa 2 señales de límite de velocidad.
3. ¿Cómo puede este dibujo representar las señales de tránsito que Elena vio camino a casa?

### Activity Synthesis

• Display a student-created drawing of equal groups that represents the speed limit signs that Elena saw on the way home and the drawing in the last problem.
• “En estos dibujos se muestran grupos iguales. ¿Cómo les ayudaron estos dibujos a representar los datos de la gráfica de dibujos?” // “These drawings show equal groups. How did these drawings help you represent the data in the picture graph?” (The key told us that each picture represented 2 signs and the drawings helped us see the 2 signs. Each group showed 2 signs.)

## Activity 2: Situaciones de grupos iguales (20 minutes)

### Narrative

The purpose of this activity is for students to represent situations involving equal groups in a way that makes sense to them. Have connecting cubes available for students to use to represent the situation, if they would like. Students may also draw a picture. One partner could use the objects while one draws and then switch for each problem. The focus of the discussion is on the important quantities of each situation and how students used their representation to model each quantity (MP4).

In the launch of the activity, it may be helpful to ask students to tell their partner a quick story or ask any questions about the focus of each of the three contexts to ensure each student has access. It may also be helpful to display images for students to reference.

MLR8 Discussion Supports. Synthesis: Involve both partners in sharing their response with the whole class. While one student speaks, invite the other student to follow along and point to where the numbers are in their representations.

### Required Materials

Materials to Gather

### Required Preparation

Each student needs 20 connecting cubes or counters.

### Launch

• Groups of 2
• “¿En qué lugares del barrio ven grupos de 2?, ¿grupos de 5?, ¿grupos de 10?” // “What are some places you see groups of 2 in the community? Groups of 5? Groups of 10?” (Shoes. Socks. Wings. Hands have 5 fingers. Flowers can have 5 petals. Markers come in packs of 10. Ten people on a bus.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share and record responses.
• Choose a student-generated example with small numbers or display this situation: “Hay 3 flores. Cada flor tiene 5 pétalos” // “There are 3 flowers. Each flower has 5 petals.”
• “¿Cómo podrían representar esta situación?” // “How could you represent this situation?”
• 30 seconds: quiet think time
• 1-2 minutes: partner work time
• Share and record responses. Focus on how the representation connects to the problem.
• “¿Cómo representaron las 3 flores?” // “How did you represent the 3 flowers?”
• “¿Cómo representaron los 5 pétalos de cada flor?” // “How did you represent the 5 petals on each flower?”
• “¿Alguien representó esto de otra manera?” // “Did someone represent this differently?”

### Activity

• “Ahora, con su pareja, van a representar más situaciones de grupos iguales” // “Now you are going to represent some more situations involving equal groups with your partner.”
• 5–7 minutes: partner work time
• If some students finish earlier than others, encourage them to write their own situation and trade with their partner.

### Student Facing

1. Hay 4 personas con zapatos. Cada persona tiene 2 zapatos.

### Activity Synthesis

• Ask 2-3 students to share their work for each problem. Be sure to share a variety of different representations.
• In each, ask how the numbers in the situation are represented in their work.
• “¿Cómo les ayudan las representaciones a imaginarse la situación?” // “How do the representations help you picture the situation?” (I can pretend the objects are the things in the story like the shoes. The drawing is like a picture of what’s happening in the story.)

## Lesson Synthesis

### Lesson Synthesis

Display a representation of equal groups from the lesson.

“Todas las situaciones que observamos hoy son de multiplicación. La multiplicación es la forma como representamos el número total de objetos cuando se tiene cierto número de grupos iguales. Por ejemplo, podemos decir que en esta imagen hay 5 grupos de 2” // “The situations we looked at today were all multiplication. Multiplication is how we represent the total number of objects when you have a certain number of equal groups. For example, in this picture, we would say we have 5 groups of 2.”

“Describan una situación de grupos iguales que se pueda representar como una multiplicación” // “Describe a situation with equal groups that you could represent as multiplication.” (Packs of pencils, bins or baskets with the same number of things in each one, pairs of shoes, rows of seats on the bus.)