# Lesson 1

Problemas-historia y expresiones

## Warm-up: Observa y pregúntate: Una biblioteca (10 minutes)

### Narrative

The purpose of this warm-up is to elicit the idea that math is found everywhere in our world. Students look for mathematical situations in a picture of a library, which will be helpful when students solve story problems about the library in later activities. While students may notice and wonder many things about this image, noticing numbers or quantities in the image are the important discussion points.

### Launch

• Groups of 2
• Display the image.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time

### Activity

• “Discutan con su pareja cómo pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

### Student Facing

¿Qué observas?
¿Qué te preguntas?

### Activity Synthesis

• “Cuenten una historia matemática que se base en la foto” // “Tell a math story based on the picture.” (There were two books on the shelf. Then the librarian put two more books on the shelf. How many books are on the shelf now? There are six pictures hanging from the ceiling. Three pictures fall down. How many pictures are still hanging from the ceiling?)

## Activity 1: La biblioteca (20 minutes)

### Narrative

The purpose of this activity is for students to make sense of the structure of a Take From, Result Unknown story problem. Students have access to connecting cubes or two-color counters and 10-frames, which they may choose to use strategically to represent and solve the problem (MP5). Some students may apply the ideas from the previous unit where they related subtraction to counting back. As students share their methods, the teacher records their thinking. It is important for the teacher to focus attention on the expression during the activity synthesis. Although some students may attempt to write equations and do so accurately, this representation will be the focus in a later lesson.

Students keep their books closed for the launch of the activity, as the teacher displays and reads the problem.

MLR8 Discussion Supports. Synthesis: Display sentence frames to support whole-class discussion: “_____ y _____ se parecen porque . . .” // “_____ and _____ are the same/alike because . . .” and “_____ y _____ son diferentes porque . . .” // “_____ and _____ are different because . . .” Encourage students to use these sentence frames to compare and contrast representations.

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Give students access to 10-frames and connecting cubes or two-color counters.
• Display the image from the warm-up.
• “Esta es una foto de una biblioteca. Hablen con su pareja sobre lo que saben y lo que se preguntan acerca de las bibliotecas” // “This is a picture of a library. Talk to your partner about what you know and what you wonder about libraries.”
• 3 minutes: partner discussion
• Share and record what students know and wonder about libraries.
• “Vamos a resolver muchos problemas-historia sobre bibliotecas” // "We are going to solve a lot of story problems about libraries."
• Display and read the numberless story.
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.
• If not already mentioned, ask, “¿Hay más niños o menos niños en la biblioteca después de que algunos se van a casa?” // “Are there more or fewer kids at the library after some go home?”

### Activity

• Ask students to open their books.
• Read the problem with numbers.
• 2 minutes: independent work time
• “Compartan con su pareja lo que pensaron” // “Share your thinking with your partner.”
• 2 minutes: partner discussion
• Monitor for students who solve or represent the problem in the following ways:
• objects
• drawings
• count back
• an expression ($$9 - 2$$)

### Student Facing

1. Unos niños estaban en la biblioteca.
Después, algunos de los niños se fueron a casa.

¿Qué observas?
¿Qué te preguntas?

2. Había 9 niños en la biblioteca.
Después, 2 de los niños se fueron a casa.
¿Cuántos niños hay ahora en la biblioteca?
Muestra cómo pensaste. Usa dibujos, números o palabras.

### Student Response

If students use more or fewer than nine objects to represent the kids at the library, consider asking:

• “¿Cómo escogiste cuántos cubos encajables sacar?” // “How did you choose how many connecting cubes to take out?”
• “Hay 9 niños en la biblioteca. ¿Cuáles cubos encajables representan a los nueve niños? ¿Cuáles cubos encajables representan a los niños que se fueron a la casa?” // “There are nine kids at the library. Which connecting cubes show the nine kids? Which connecting cubes show the two kids that went home?”

### Activity Synthesis

• Invite previously identified students to share in the order listed above.
• “¿En qué se parecen estas representaciones? ¿En qué son diferentes?” // “How are these representations the same? How are they different?”
• If needed, display $$9 - 2$$.
• “¿Cómo corresponde esta expresión al problema-historia?” // “How does this expression match the story problem?”

## Activity 2: Problemas-historia sobre la biblioteca (20 minutes)

### Narrative

The purpose of this activity is for students to solve Add To and Take From, Result Unknown problems in a way that makes sense to them (MP1). The problems use the same numbers in order to encourage students to think about the action in the problem and how it relates to operations. Students may represent the problems with objects or drawings, and count all, count on, or count back to solve the problems. Students write expressions and some may attempt to write equations.

During the lesson synthesis, students are re-introduced to equations. They notice how the answer to the question is represented in the equation. The teacher draws a box around the answer to signify that this part of the equation is the answer to the question.

Action and Expression: Internalize Executive Functions. Invite students to plan a method, including the tools they will use, for solving the story problems. If time allows, invite students to share their plan with a partner before they begin.
Supports accessibility for: Conceptual Processing, Organization

### Required Materials

Materials to Gather

• Groups of 2

### Activity

• 6 minutes: independent work time
• “Compartan con su pareja cómo pensaron. Asegúrense de que ambos estén de acuerdo en la respuesta” // “Share your thinking with your partner. Be sure that you both agree on the answer.”
• 4 minutes: partner discussion

### Student Facing

1. Había 5 libros en una repisa.
Clare puso 2 libros más en la repisa.
¿Cuántos libros hay ahora en la repisa?
Muestra cómo pensaste. Usa dibujos, números o palabras.

Expresión: ________________________________

2. Había 6 libros apilados sobre la mesa.
4 de los libros se cayeron al piso.
¿Cuántos libros quedan sobre la mesa?

Muestra cómo pensaste. Usa dibujos, números o palabras.

Expresión: ________________________________

3. 6 niños estaban escuchando una historia.
4 niños más se unieron al grupo.
¿Cuántos niños están ahora escuchando la historia?
Muestra cómo pensaste. Usa dibujos, números o palabras.

Expresión: ________________________________

4. Había 5 computadoras encendidas. La bibliotecaria apagó 2 de las computadoras.
Muestra cómo pensaste. Usa dibujos, números o palabras.

Expresión: ________________________________

### Activity Synthesis

• Review solutions and expressions for both story problems with the numbers 5 and 2.
• “¿Cómo corresponde la expresión a la historia?” // “How does the expression match the story?”
• If needed ask, “¿Qué representa el 5? ¿Qué representa el 2?” // "What does the 5 represent? What does the 2 represent?”
• “¿En qué son iguales estos problemas? ¿En qué son diferentes?” // “How are these problems the same? How are they different?” (They have the same numbers, but different answers. Problem 1 is addition, problem 4 is subtraction.)

## Lesson Synthesis

### Lesson Synthesis

Display the problem about books on a shelf.

“Hoy escribimos expresiones para representar problemas-historia. Para este problema escribimos la expresión 5 + 2. Después resolvimos el problema. Podemos escribir una ecuación que muestre la respuesta. La ecuación '$$5 + 2 = 7$$' nos dice que 5 más 2 es la misma cantidad que 7” // “Today we wrote expressions to represent story problems. For this problem we wrote the expression 5 + 2. Then we solved the problem. We can write an equation that shows the answer. The equation “$$5 + 2 = 7$$” tells us that 5 plus 2 is the same amount as 7.”

“¿Qué representa el 7?” // “What does the 7 represent?” (the total number of books on the shelf, 5 books + 2 books)

“Cuando escribimos una ecuación, podemos dibujar un cuadro alrededor del número que muestra la respuesta a la pregunta. Esto significa que la ecuación se escribiría así: $$5 + 2 = \boxed{7}$$” // “When we write an equation, we can draw a box around the number that shows the answer to the question. That means the equation would be written as $$5 + 2 = \boxed{7}$$.“