# Lesson 19

Resolvamos problemas que incluyen arreglos

## Warm-up: Conversación numérica: Un grupo menos (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have about equal groups in multiplication expressions and see a pattern as one factor is decreased. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to use multiplication to answer questions about array situations.

When students notice that as the number being multiplied by 2 decreases the product decreases by a group of 2, they look for and express regularity in repeated reasoning (MP8).

### 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.

• $$10\times2$$
• $$9\times2$$
• $$8\times2$$
• $$7\times2$$

### Activity Synthesis

• “¿Qué observaron sobre los productos a medida que trabajamos en esta serie de problemas?” // “What do you notice about the products as we worked through this series of problems?” (They decrease by 2.)
• “¿Por qué el producto disminuye de 2 en 2?” // “Why does the product decrease by 2 each time?” (The number of groups decreased by 1.)

## Activity 1: Arreglo de colores (25 minutes)

### Narrative

The purpose of this activity is for students to use the Co-craft math language routine to write questions that can be asked about array situations and to relate array situations to equations. Students should be encouraged to use whatever strategy or representation feels appropriate to them. Given their prior experiences, they may represent the situation with an array and skip-count or consider equal groups in other ways to find the total.

### Launch

• Groups of 2

MLR5 Co-craft Questions

• Display: “Hay 7 filas” // “There are 7 rows.”
• “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 rows? How many things are in each row? How many things are there 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?” (They all have to do with rows. They have to do with more detail about the rows, like what’s in the rows and how many are in each row.)

### Activity

• “Para completar el primer problema, resuelvan esta situación de cualquier manera que tenga sentido para ustedes” // “Complete the first problem by solving this situation in any way that makes sense to you.”
• 3–4 minutes: independent work time
• 1–2 minutes: partner discussion
• Share a variety of student representations and solution strategies.
• “Piensen en la situación que hemos considerado. ¿Cómo podrían representar la situación con una ecuación que tenga un símbolo para representar el número desconocido?” // “Think about the situation we have been considering. How could you represent the situation using an equation with a symbol for the unknown?”
• 2 minutes: quiet think time
• “Compartan su ecuación con su compañero. Juntos, reescriban la ecuación con la solución que encontraron en lugar del símbolo” // “Share your equation with your partner. Together, rewrite the equation with the solution you found in place of the symbol.”
• 2 minutes: partner work

### Student Facing

Hay 7 filas. Cada fila tiene 5 crayones. ¿Cuántos crayones hay?

1. Resuelve este problema. Explica o muestra tu razonamiento.
2. Representa la situación con un arreglo y con una ecuación. Usa un símbolo para representar el número desconocido en la ecuación.

### Activity Synthesis

• “¿Qué ecuación o ecuaciones escribieron?” // “What equation(s) did you write?”
• Display an equation with a symbol and one with the solution.
• “¿Cómo se conecta cada parte de la ecuación con la situación?” // “How does each part of the equation connect to the situation?" (The 7 is the number of rows. The 5 is the number of crayons in each row. The 35 represents the total number of crayons, but it was a question mark when we didn't know how many there were.)

## Activity 2: Las palmeras de Tyler (10 minutes)

### Narrative

The purpose of this activity is for students to write an equation with a symbol for the unknown to represent an array situation. Then, they answer the question in the multiplication situation. Encourage students to use whatever strategy or representation feels appropriate to them. Given their prior experiences, they might represent the situation with an array and skip-count or consider equal groups in other ways to find the total.

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 context of the first problem. To ensure all students have access, it may also be helpful to display images for students to reference about coconut trees or Mexico.

MLR8 Discussion Supports. Synthesis: If necessary, invite students to repeat their question using mathematical language. For example, “¿Puedes decir eso de nuevo, pero usando la palabra arreglo?” // “Can you say that again, using the word array?”
Action and Expression: Develop Expression and Communication. Activity: Invite students to show thinking using connecting cubes or counters.
Supports accessibility for: Conceptual Processing

### Launch

• Groups of 2
• Display the image.
• “Las palmeras cocoteras se cultivan en climas cálidos y tienen muchos usos. A veces se siembran en filas. ¿Qué otros cultivos se siembran en filas?” //  “Coconut trees are grown as a crop in warm climates and have lots of uses. Sometimes they are grown in rows. What are some other crops that are grown in rows?” (Corn. Strawberries. Carrots.)

### Activity

• “Ahora van a practicar lo que acabamos de aprender sobre resolver situaciones que incluyen un arreglo y a escribir una ecuación que tenga un símbolo para representar el número desconocido” // “Now you are going to practice what we just learned about solving array situations and writing an equation with a symbol for the unknown.”
• 5–7 minutes: independent work time
• As you circulate, consider asking:
• “¿Cómo se conecta cada número o símbolo de su ecuación con la situación?” //  “How does each number or symbol in your equation connect to the situation?”
• “¿Cómo usan grupos iguales para encontrar la solución del problema?” // “How are you using equal groups to find the solution to the problem?”
• “Compartan su estrategia con su compañero. Hagan todas las preguntas que tengan sobre las ideas de su compañero” // “Share your strategy with your partner. Ask any questions you have about your partner’s ideas.”
• 2 minutes: partner discussion

### Student Facing

• Escribe una ecuación que represente la situación. Usa un símbolo para representar el número desconocido.
• Resuelve el problema. Muestra cómo pensaste.
1. En México, un campo de palmeras cocoteras tiene 5 filas de palmeras. Cada fila tiene 9 palmeras. ¿Cuántas palmeras hay?

2. Después de aprender sobre los cultivos de coco en México, Tyler quiere sembrar palmeras cocoteras en su patio, en Florida. Su mamá solo le dejará sembrar 2 filas de 4 palmeras en su patio.

¿Cuántas palmeras sembrará Tyler?

### Activity Synthesis

• “¿Qué dudas tienen todavía sobre resolver problemas que incluyen arreglos o escribir una ecuación que tenga un símbolo para representar el número desconocido?” // “What questions do you still have about solving array problems or writing an equation with a symbol for the unknown?”

## Lesson Synthesis

### Lesson Synthesis

Display the information from the first problem in Activity 2.

A field of coconut trees in Mexico has 5 rows of trees.
Each row has 9 trees. How many trees are there?

$$5\times9=?$$

$$5\times9=45$$

“¿Cómo representan estas ecuaciones la situación que incluye un arreglo?” // “How do each of these equations represent the array situation?” (The equation with the symbol represents the 5 rows of trees and the 9 trees in each row in the situation before we knew there were 45 trees. The equation with the 45 includes the solution to the problem because there were 45 trees.)

Consider asking: “En la primera ecuación, ¿qué representa el signo de interrogación? En la segunda ecuación, ¿qué representa el 45 en la situación?” // “What does the question mark in the first equation represent in the situation? What does the 45 in the second equation represent in the situation?”