# Lesson 12

Historias de seda para sari: Pulseras de la amistad

## Warm-up: Verdadero o falso: Comparaciones del valor posicional (10 minutes)

### Narrative

The purpose of this True or False is to elicit strategies and understandings students have for using place value to compare numbers and determine if an equation is true. When students share how they know an equation is true or false based on looking at the total number of tens or total number of ones on each side, they look for and make use of the base-ten structure of numbers and the properties of operations (MP7).

### Launch

•  Display one statement.
• “Hagan una señal cuando sepan si la afirmación es verdadera o no, y puedan explicar cómo lo saben” // “Give me a signal when you know whether the statement is true and can explain how you know.”
• 1 minute: quiet think time.

### Activity

• Share and record answers and strategy.
• Repeat with each statement.

### Student Facing

Decide si cada afirmación es verdadera o falsa. Prepárate para explicar tu razonamiento.

• $$24 = 10 + 14$$
• $$15 + 12 = 27$$
• $$26 = 10 + 6 + 10$$
• $$58 = 20 + 20 + 8$$

### Activity Synthesis

• “¿Cómo pueden usar lo que saben sobre decenas y unidades para explicar su respuesta a la última pregunta?” // “How can you explain your answer for the last equation using what you know about tens and ones?” (There are only 4 tens on the right.)

## Activity 1: Compartamos cintas con amigos (20 minutes)

### Narrative

The purpose of this activity is for students to interpret and solve two-step problems involving length. After reading each story problem, students consider what questions could be asked and what information will be needed in the second part of the problem. Students read each story with a partner, and then solve each story problem independently and compare their solutions.

Students begin the activity by looking at the first problem displayed, rather than in their books. Students represent the problem in a way that makes sense to them and share different representations during the synthesis, explaining how these representations helped solve the problem (MP1, MP2, MP3).

Representation: Access for Perception. Offer strips of colored paper to demonstrate the length of the ribbons, as well as the tape diagrams students create. Encourage students to cut the “ribbon” and label the parts to represent the story. Reiterate the context and connect to the idea of subtraction.
Supports accessibility for: Conceptual Processing, Organization, Memory

### Launch

• Groups of 2
• “Los estudiantes de la clase de Priya están compartiendo cintas para hacer collares y pulseras para sus amigos y familiares” // “The students in Priya’s class are sharing ribbons to make necklaces and bracelets for their friends and family members.”

• Display both parts of the story, but only the problem stems, without revealing the questions.
• “Vamos a leer este problema 3 veces” // “We are going to read this problem 3 times.”
• 1st Read: “Lin encontró un pedazo de cinta que medía 92 cm de largo. Ella le dio a Noah un pedazo que medía 35 cm. Luego, Lin cortó 28 cm de cinta para Jada” // “Lin found a piece of ribbon that is 92 cm long. She gave Noah a piece that is 35 cm. Then, Lin cut off 28 cm of ribbon for Jada.”
• “¿De qué se trata esta historia?” // “What is this story about?”
• 1 minute: partner discussion
• Listen for and clarify any questions about the context.
• 2nd Read: “Lin encontró un pedazo de cinta que medía 92 cm de largo. Ella le dio a Noah un pedazo que medía 35 cm. Luego, Lin cortó 28 cm de cinta para Jada” // “Lin found a piece of ribbon that is 92 cm long. She gave Noah a piece that is 35 cm. Then, Lin cut off 28 cm of ribbon for Jada.”
• “En esta historia, ¿a cuáles longitudes de cinta es importante prestarles atención?” // “Which lengths of ribbon are important to pay attention to in the story?” (length of ribbon Lin started with, length of ribbon given to Noah, length of ribbon given to Jada, length of ribbon Lin has in the end)
• 30 seconds: quiet think time
• 1–2 minutes: partner discussion
• Share and record all quantities.
• Reveal the questions.
• “¿De qué formas diferentes podemos representar este problema?” // “What are different ways we could represent this problem?” (tape diagram, equations)
• 30 seconds: quiet think time
• 1–2 minutes: partner discussion

### Activity

• “Con su compañero, lean la historia nuevamente. Luego, decidan cómo representarla y resuélvanla solos” // “Read the story again with your partner. Then decide how to represent and solve it on your own.”
• “Cuando ambos hayan respondido las preguntas, comparen para ver si están de acuerdo” // “When you have both answered the questions, compare to see if you agree.”
• 10 minutes: partner work time
• Monitor for students who represent each part of the story with:
• tape diagrams
• base-ten diagrams
• other clearly-labeled drawings or diagrams
• equations

### Student Facing

1. Resuelve. Muestra cómo pensaste. Si te ayuda, usa un diagrama. No olvides las unidades.

1. Lin encontró un pedazo de cinta que medía 92 cm de largo. Ella le dio a Noah un pedazo que medía 35 cm. ¿Cuánta cinta le quedó a Lin?
2. Luego, Lin cortó 28 cm de cinta para Jada. ¿Cuánta cinta le queda a Lin ahora?

### Activity Synthesis

• Invite 2–3 previously identified students to display their work side-by-side for all to see.
• “¿Cómo les ayuda cada representación a entender el problema?” // “How does each representation help you understand the problem?” (In the diagrams, they used labels to show what each part means. I can see how they used Lin's length of ribbon in both parts. In the equations, I can see the same numbers, but it's a little harder to tell what each part means. I can make sense of them by looking at the other diagrams people made.)

## Activity 2: Pulseras de la amistad y regalos (15 minutes)

### Narrative

The purpose of this activity is for students to represent and solve two-step story problems. The story problems are presented in parts, and students are encouraged to represent each part in a way that makes sense to them. In the synthesis, students compare different ways they represent and solve the problem.

• Groups of 2

### Activity

• “Lean cada problema con su compañero, pero resuélvanlo solos. Muestren cómo pensaron. Usen diagramas, ecuaciones o palabras” // “Read each problem with your partner and solve it on your own. Show your thinking using diagrams, equations, or words.”
• 5 minutes: independent work time
• 5 minutes: partner discussion
• Monitor for students who use tape diagrams, base-ten diagrams, and equations to represent each part of the last problem.

### Student Facing

1. Resuelve. Muestra cómo pensaste. No olvides las unidades. Si te ayuda, usa un diagrama.

1. Han tiene 82 pulgadas de cinta. Él sólo necesita 48 pulgadas. ¿Cuánto debería quitarle?

2. Han le dio a Clare la cinta que él no necesitaba. Clare la usó para alargar su cinta. La cinta de Clare medía 27 pulgadas. ¿Cuánto mide la cinta de Clare ahora?

2. Resuelve. Muestra cómo pensaste. No olvides las unidades. Si te ayuda, usa un diagrama.

1. La cinta de Andre es demasiado corta. Él tiene 28 pulgadas de cinta, pero necesita que mida 50 pulgadas de largo. ¿Cuánta cinta más necesita?

2. Mai le regaló a Andre la cinta que necesitaba. Ahora a Mai le quedan 49 pulgadas de cinta. ¿Con cuánta cinta empezó Mai?

### Student Response

Students may represent and solve the first part of each problem accurately, but see the second part as a problem with two unknowns. Consider asking:

• “¿Qué información nueva te da la segunda parte del problema? ¿Qué necesitas averiguar? ¿Qué sabes ya?” // “What new information does the second part of the problem give you? What do you need to figure out? What do you already know?”
• “¿Qué ocurrió en la primera parte de la historia? ¿Qué descubriste? ¿Cómo puedes usarlo en la segunda parte del problema?” // “What happened in the first part of the story? What did you figure out? How could you use that in the second part of the problem?”

### Activity Synthesis

• Invite previously identified students to share their diagrams and equations for each part of the problem.
• “¿Cómo representó _____ el problema? ¿De qué manera cada representación muestra el problema-historia?” // “How did _____ represent the problem? How does each representation show the story problem?”

## Lesson Synthesis

### Lesson Synthesis

“Hoy resolvieron diferentes tipos de problemas-historia que tenían dos partes” // “Today you solved different kinds of story problems that had two parts.”

“¿Cómo representaron lo que pensaron? ¿Cómo llevaron la cuenta de sus cálculos? ¿Cómo hicieron para tener presentes las longitudes que conocían y las que necesitaban descubrir?” // “How did you represent your thinking and keep track of your calculations? How did you keep up with the lengths you knew and what you needed to find out?” (I used diagrams to make sense of the story. I drew base-ten diagrams to help me solve. I put a circle around my answer so I could use it for the next problem.)

“¿Qué ideas para resolver problemas-historia han aprendido de los demás?” // “What ideas for solving story problems have you learned from others?”

Share and record responses.