# Lesson 12

Representemos y resolvamos problemas de multiplicación

## Warm-up: Cuántos ves: Muchos puntos (10 minutes)

### Narrative

The purpose of this warm-up is for students to subitize or use grouping strategies to describe the images they see. When students decompose the images into groups of 10 to count efficiently, they are looking for and making use of structure (MP7). For these images, students may need them displayed for a longer amount of time in order to see the structure.

### Launch

• Groups of 2
• “¿Cuántos ven? ¿Cómo lo saben?, ¿qué ven?” // “How many do you see? How do you see them?”
• Flash image.
• 30 seconds: quiet think time

### Activity

• Display image.
• “Discutan con su compañero cómo pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses. Use multiplication expressions when students share explanations involving equal groups.
• Repeat for each image.

### Student Facing

¿Cuántos ves? ¿Cómo lo sabes?, ¿qué ves?

### Activity Synthesis

• “¿Qué patrón les ayudó a encontrar el número total de puntos?” // “What pattern was helpful in finding the total number of dots?”
• “¿Alguien puede expresar con otras palabras la forma en la que ______ vio los puntos?” // “Who can restate the way _____ saw the dots in different words?”
• “¿Alguien vio los puntos de la misma manera, pero lo explicaría de otra forma?” // “Did anyone see the dots the same way but would explain it differently?”
• “¿Alguien quiere compartir otra observación sobre la manera en la que _____ vio los puntos?” // “Does anyone want to add an observation to the way ______ saw the dots?”

## Activity 1: Las cajas de Tyler (15 minutes)

### Narrative

The purpose of this activity is for students to use the Co-craft Questions math language routine to make sense of a multiplication situation before solving. Students are first asked to generate questions they could ask about part of a problem. Then, students are given the full problem and asked to solve it. The activity concludes with students reflecting on the representations they used. In this activity, students will need to see the full problem to solve. Before the lesson, record the problem and have it hidden until the appropriate time in the lesson or write it for all to see at that point during the activity.

### Launch

• Groups of 2

MLR5 Co-Craft Questions

• Display only the problem stem, “Tyler has 3 boxes.” without revealing the question.
• “Escriban una lista de preguntas matemáticas que se podrían hacer sobre esta situación” // “Write a list of mathematical questions that could be asked about this situation.” (What’s in the boxes? How many things are in the boxes? How many things does he have altogether?)
• 2 minutes: independent work time
• 2–3 minutes: partner discussion
• Invite several students to share one question with the class. Record responses.
• “¿Qué tienen en común estas preguntas? ¿En qué son diferentes?” // “What do these questions have in common? How are they different?”

### Activity

• “Piensen cómo van a resolver el problema” // ”Think about how you’ll solve the problem.”
• 30 seconds: quiet think time
• 2–3 minutes: partner work time

### Student Facing

Tyler tiene 3 cajas. En cada caja hay 5 pelotas de béisbol. ¿Cuántas pelotas de béisbol tiene en total? Muestra cómo pensaste. Usa diagramas, símbolos u otras representaciones.

### Activity Synthesis

• Display student work with different representations of the problem one at a time (drawings of equal groups, tape diagrams, and expressions). If no student writes an expression, write one for students to analyze.
• “¿Cómo nos ayuda cada representación a entender lo que ocurre en el problema?” // “How does each representation help us see what’s happening in the problem?”

## Activity 2: Resolvamos problemas de grupos iguales (20 minutes)

### Narrative

The purpose of this activity is for students to use what they’ve learned about multiplication to solve and represent situations that involve equal groups. Students now have experience with multiple representations and have the opportunity to choose which representation is most helpful to represent multiplication situations.

The launch of the activity is an opportunity for students to share their experiences and ask questions about the objects to ensure each student has access to the context. If it is helpful, display images of the items for students to reference.

MLR8 Discussion Supports. Synthesis: As students describe their representations of the problems, use gestures to emphasize the number of groups and how many are in each group. For example, trace with your finger around each group, and point to each object in each group to show how many there are.
Representation: Access for Perception. Provide access to connecting cubes. Ask students to identify correspondences between the concrete and visual representation used.
Supports accessibility for: Conceptual Processing

### Launch

• Groups of 2
• Write the list of objects (“equipos, aretes, lápices, pedazos de vidrio, zanahorias” // “teams, earrings, pencils, pieces of glass, carrots”) on a display for all students to see.
• “Tómense un minuto para leer esta lista. Después, discutan sobre los objetos que conocen o sobre los objetos de los que tienen preguntas” // “Take a minute to read this list. When you are done, discuss the objects you know or have questions about.”
• 3 minutes: partner discussion
• Share a few responses.
• “Ahora vamos a representar y resolver más problemas en los que hay grupos iguales. Tómense unos minutos para empezar a trabajar en los problemas antes de trabajar en parejas” // “Now we’re going to represent and solve more problems with equal groups. Take a couple of minutes to begin working on the problems before you work in partners.”
• 2–3 minutes: independent work time

### Activity

• “Resuelvan cada problema con su pareja” // “Work with your partner to solve each problem.”
• 5–7 minutes: partner work
• Identify students who use different representations like drawings of equal groups or tape diagrams as they solve the problems.

### Student Facing

Resuelve cada problema. Muestra cómo pensaste. Usa diagramas, símbolos u otras representaciones.

1. Hay 4 campos de fútbol. Hay 2 equipos en cada campo. ¿Cuántos equipos hay en total?
2. Hay 7 ventanas. Cada ventana tiene 2 piezas de vidrio. En total, ¿cuántas piezas de vidrio hay en las ventanas?
4. Kiran tiene 4 cajas. En cada caja hay 5 lápices. ¿Cuántos lápices tiene Kiran?
5. Andre tiene 3 bolsas de zanahorias. En cada bolsa hay 10 zanahorias. ¿Cuántas zanahorias tiene Andre?

### Student Response

• “Cuéntame cómo resolviste este problema” // “Tell me about how you solved this problem.”
• “¿Cómo sabes que este problema es sobre grupos iguales?” // “How does the problem involve equal groups?”

### Activity Synthesis

• For each problem, display different representations, one at a time.
• “¿Cómo nos ayuda esta representación a entender lo que ocurre en el problema?” // “How does this representation help us see what’s happening in the problem?” (You can see there are 4 groups for the fields and 2 dots in each group for the teams. The diagram is split into 5 parts for the 5 bags, and each section has a 10 in it for the number of earrings.)
• “¿Cómo puede ayudarnos cada representación a resolver el problema?” // “How could each representation help us solve the problem?” (Counting the dots. Counting by 10.)
• If needed, “¿Qué expresión podríamos escribir para representar esta situación?” // “What expression could we write to represent this situation?”

## Lesson Synthesis

### Lesson Synthesis

Display samples of student work with different representations (drawings of equal groups, tape diagrams, and equations).

“¿Cuál representación les ayudó más hoy y por qué?” // “Which representation did you find most helpful today and why?” (Drawings of equal groups because I could see what was happening in the problem. Diagrams because it helped me understand the problem, but I didn’t have to draw all the dots.)