# Lesson 5

Problemas-historia de juntar y separar

## Warm-up: Verdadero o falso: Más o menos (10 minutes)

### Narrative

The purpose of this True or False is to elicit strategies and understandings students have for place value and the operations of addition and subtraction (MP7). Students may use these understandings to reason about whether each equation is true or false without finding the value of the expressions.

### 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 strategies.
• Repeat with each statement.

### Student Facing

Prepárate para explicar tu razonamiento.

• $$57 + 20 = 59$$
• $$66 - 4 = 62$$
• $$17 + 76 = 59$$

### Activity Synthesis

• “¿Cómo pueden explicar su respuesta sin encontrar el valor de la expresión?” // “How can you explain your answer without finding the value of the expression?”

## Activity 1: En el planetario (20 minutes)

### Narrative

The purpose of this activity is for students to make sense of and solve Put Together/Take Apart, Addend Unknown story problems (MP2). In the synthesis, students discuss different methods used to solve these problems, including using addition and subtraction.

The teacher may want to incorporate movement into this activity by writing each problem on a piece of chart paper and placing each one in a different location around the classroom. Students can solve the problem at one location, discuss the problem with their partner, then move on to a new problem at a new location.

Engagement: Provide Access by Recruiting Interest. Provide choice. Invite students to decide which problem to start with.
Supports accessibility for: Attention, Social-Emotional Functioning

### Launch

• Groups of 2
• Give each group access to connecting cubes in towers of 10 and singles.
• Display the image in the student book.
• “¿Qué observan en esta imagen? ¿Qué se preguntan?” // “What do you notice in this picture? What do you wonder?” (There are bright colors. This looks like stars in the sky. Why is there red in the sky? Where is this?)
• “Esta es una imagen de algo que se llama la nebulosa de la Hélice. Es una de muchas cosas interesantes que se pueden ver en nuestro cielo. Las personas que están interesadas en aprender más sobre las estrellas, los planetas o cualquier otra cosa que hay en el cielo pueden visitar un planetario para aprender sobre todas estas cosas. Vamos a resolver algunos problemas sobre una excursión al planetario” // “This is a picture of something called the Helix Nebula. It is one of many interesting things that can be seen in our sky. People who are interested in learning more about stars, planets, or anything else that is found in the sky, can visit a planetarium to learn all about these things. We are going to solve some problems about a field trip to the planetarium.”

### Activity

• 8 minutes: independent work time
• 4 minutes: partner discussion
• Monitor for students who solve the problem about bright and dim stars with addition and for students who solve the same problem with subtraction.

### Student Facing

Resuelve todos los problemas.
Muestra cómo pensaste. Usa dibujos, números o palabras.

1. En el planetario hay 7 estudiantes de primer grado y algunos estudiantes de segundo grado.
En el planetario hay 18 estudiantes.
¿Cuántos estudiantes de segundo grado hay en el planetario?

2. Cuando la función empezó, 18 estrellas iluminaron el cielo.
13 estrellas eran brillantes.
Algunas estrellas eran tenues.
¿Cuántas estrellas eran tenues?

3. Durante la función, Diego y Tyler vieron 15 estrellas fugaces en total.
Diego vio 6 estrellas fugaces. Tyler vio las demás.
¿Cuántas estrellas fugaces vio Tyler?

4. En la tienda del planetario, Elena compró 12 calcomanías de estrellas.
También compró algunas calcomanías de planetas.
Elena compró 20 calcomanías.
¿Cuántas calcomanías de planetas compró?

### Student Response

If students attempt to solve each problem by adding the known quantities, consider asking:

• “¿De qué se trata el problema-historia? ¿Qué sabes? ¿Qué necesitas averiguar?” // “What is the story problem about? What do you know? What do you need to figure out?”
• “¿Qué hiciste para resolver el problema?” // “What did you do to solve the problem?”
• “¿Qué significa tu respuesta en la historia? ¿Tiene sentido?” // “What does your answer mean in the story? Does it make sense?”

### Activity Synthesis

• Display $$15 - 6 = \boxed{\phantom{3}}$$ and $$6 + \boxed{\phantom{3}} = 15$$
• “¿Cómo les ayudan estas dos ecuaciones a encontrar el número de estrellas fugaces que vio Tyler?” // “How do both of these equations help you find the number of shooting stars Tyler saw?”
• Invite previously identified students to share. As needed, ask students to connect the numbers they use to the story problem.
• “¿En qué se parecen estos métodos? ¿En qué son diferentes?” // “How are these methods the same? How are they different?” (They both find the same number of dim stars. Both show that there’s some bright stars, some dim stars, and a total number. One way uses addition to count on from the number of bright stars. One uses subtraction to take away the number of bright stars from the total.)

## Activity 2: ¿Cuáles ecuaciones corresponden? (15 minutes)

### Narrative

The purpose of this activity is for students to identify different equations that can be used to represent the same problem. Students explain why each equation does or does not represent the story. This helps students understand that Put Together/Take Apart story problems can be represented and solved with either addition or subtraction when an addend is unknown (MP2).

MLR8 Discussion Supports. Students should take turns finding a match and explaining their reasoning to their partner. Display the following sentence frames for all to see: “Observé ______, entonces asocié . . .” // “I noticed _____, so I matched . . . .” Encourage students to challenge each other when they disagree.

### Launch

• Groups of 2
• Give each group access to connecting cubes in towers of 10 and singles.

### Activity

• 10 minutes: partner work time

### Student Facing

En cada caso, marca 2 ecuaciones que se puedan usar para resolver el problema. Prepárate para explicar por qué las ecuaciones representan la historia y por qué la otra ecuación no.

1. Noah pintó 9 estrellas blancas.
También pintó algunas estrellas amarillas.
Noah pintó 17 estrellas en total.
¿Cuántas estrellas amarillas pintó?

1. $$17 - 9 = \boxed{\phantom{3}}$$
2. $$9 + 17 = \boxed{\phantom{3}}$$
3. $$9 + \boxed{\phantom{3}} = 17$$
2. Kiran vio 16 objetos en el cielo.
11 de los objetos eran estrellas.
El resto de los objetos eran planetas.
¿Cuántos objetos eran planetas?

1. $$16 + 11 = \boxed{\phantom{3}}$$
2. $$11 + \boxed{\phantom{3}} = 16$$
3. $$16 - 11 = \boxed{\phantom{3}}$$
Si te queda tiempo: resuelve cada problema usando las dos ecuaciones.

### Activity Synthesis

• For each problem:
• Invite students to share how each equation they chose represents the problem.
• Invite students to share why one of the equations does not represent the problem.

## Lesson Synthesis

### Lesson Synthesis

“Hoy resolvimos problemas-historia en los que había un número total de objetos y dos partes distintas. Conocíamos el número total y el número de una de las partes. Usamos sumas y restas para representar el problema y encontrar el número desconocido” // “Today we solved story problems where there was a total number of objects and two different parts. We knew the total number and the number of one of the parts. We used addition and subtraction to represent the problem and find the unknown number.”

“¿Por qué pueden usar una suma o una resta para encontrar el número desconocido?” // “Why can you use either addition or subtraction to find the unknown number?” (You can use addition because you know one part, so you can think of what to add to get to the total. It’s like when we use addition to find the answer to subtraction. You can use subtraction because if you take away the number of one of the parts, the unknown number is what is left.)

“Cuando asociamos ecuaciones a los problemas-historia, ¿qué observaron acerca de las ecuaciones que no le correspondían a las historias? ¿Pueden sumar los números del problema de cualquier forma que ustedes quieran?” // “When we matched equations to the story problems, what did you notice about the equations that did not match? Can you add the numbers in the problem anyway you want?” (You can’t just add the numbers in the problem. You have to make sure they match what the story is about.)