# Lesson 14

¿Cuál ecuación corresponde?

## Warm-up: Cuál es diferente: Ecuaciones (10 minutes)

### Narrative

This warm-up prompts students to carefully analyze and compare equations. In addition to calculating the value of each expression, students also think about the structure of each equation, including both the operations and the numbers (MP7).

### Launch

• Groups of 2
• Display the image.
• “Escojan una que sea diferente. Prepárense para compartir por qué es diferente” // “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

### Activity

• “Discutan con su compañero lo que pensaron” // “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

### Student Facing

¿Cuál es diferente?

1. $$10 = 6 + 4$$
2. $$16 - 5 = 11$$
3. $$11 = 6 + 4 + 1$$
4. $$3 + \boxed{\phantom{8}} = 11$$

### Activity Synthesis

• “Encontremos por lo menos una razón por la que cada una es diferente” // “Let’s find at least one reason why each one doesn’t belong.”

## Activity 1: Clasifiquemos problemas-historia (15 minutes)

### Narrative

The purpose of this activity is to sort story problems with unknowns in all positions. Students sort the story problems by whether they are addition or subtraction problems. Some stories include actions that would be represented by one operation, but may be solved using the opposite operation. Students may sort these problems into either category as long they can explain how they sort.

For example, consider this Take From, Start Unknown story problem:

Clare has some stickers.

She gives 9 of them to her friends.

She has 5 stickers left.

In the last lesson, students related this type of problem to a subtraction equation ($$? - 9 = 5$$). This equation shows a way to use equations to represent the actions in the story. However, students may also think of an equation that shows how they would solve the problem ($$5 + 9 = ?$$). This is discussed in the activity synthesis to prepare students to identify more than one equation to match these story problems in the next activity.

Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. Give students a subset of the cards to start with and introduce the remaining cards once students have sorted the initial set of cards.
Supports accessibility for: Organization, Attention

### Required Materials

Materials to Gather

Materials to Copy

• Story Problem Cards, Unknowns in All Positions, Spanish

### Required Preparation

• Create a set of cards from the blackline master for each group of 2.

### Launch

• Groups of 2
• Give each group a set of cards and access to connecting cubes in towers of 10 and singles.
• “Hemos resuelto problemas-historia sobre personas que hacen diferentes artes y manualidades. Hacer collages es otra manualidad popular” // “We have been solving stories about people doing different arts and crafts. Making collages is another popular craft.”
• Display the word “collage” // “collage” for all to see and invite students to share what they know about making a collage.
• If needed ask, “¿Qué materiales pueden usar para hacer un collage?” // “What materials can you use to make a collage?” (stickers, pictures, stamps, markers, glitter, glue)

### Activity

• “Hoy vamos a estudiar muchas historias sobre estudiantes que hicieron collages. Clasifiquen los problemas-historia dependiendo de si son de suma o de resta. Prepárense para explicar cómo lo saben de manera que los demás puedan entender” // “Today we are going to look at lots of stories about students who made collages. Sort the story problems by whether they are addition or subtraction. Be ready to explain how you know so that others can understand.”
• 10 minutes: partner work time
• Monitor for two groups who put the same story problem in different categories.

### Activity Synthesis

• Display the problems that students sorted into different groups (for example, A1, A5 or A6).
• “¿De qué manera es este un problema-historia de suma? ¿De qué manera es este un problema-historia de resta?” // “How is this an addition story problem? How is this a subtraction story problem?” (To solve card A1, I can think about how many pictures to add to 8 to get to 11, or I can think $$11 - 8$$ to find how many pictures there are.)
• Repeat with other problems as time permits.

## Activity 2: Historias y ecuaciones (20 minutes)

### Narrative

The purpose of this activity is to match equations to the story problems from the previous activity. Each story has several equations listed, two of which match the story. Students are encouraged to find both equations; however, it is more important that students can explain how an equation represents what is happening in the story, or how it is used to solve the story. In the launch, students make sense of a familiar diagram to encourage them to use objects or drawings to represent the story if it will help them find the matching equations.

In order to match stories with equations, students reason abstractly and quantitatively (MP2) as they interpret both the numbers and the operations in the equations in terms of a context.

MLR8 Discussion Supports Display sentence frames to support partner discussion: “Pienso que las ecuaciones _____ y _____ corresponden a la historia porque . . .” // “I think the equations _____ and _____ match the story problem because…,” “Estoy de acuerdo porque . . .” // “I agree because…,” and “Estoy en desacuerdo porque . . .” // “I disagree because…”

### Launch

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.
• Display the diagram and read the first story problem. Do not display the equations.
•  “¿De qué manera el diagrama representa el problema-historia?” // “How does the diagram represent the story problem?” (The eight white cubes show the pictures of people. The three blue cubes were added to get to a total of 11. So the three blue cubes show the pictures of animals.)
• 1 minute: quiet think time
• 1 minute: partner discussion
• “¿Cuáles ecuaciones corresponden a la historia?” // “Which equations match the story?”
• Display the equations.
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Monitor for students who chose the second and third equations.
• Invite students to share.
• If needed: “¿De qué manera el diagrama corresponde a la ecuación?” // “How does the diagram match the equation?”
• “Hay una ecuación de suma y una ecuación de resta que pueden corresponder a este problema” // “There is an addition and subtraction equation that can match this problem.”

### Activity

• 10 minutes: partner work time

### Student Facing

En cada problema, marca las 2 ecuaciones que corresponden a la historia.
Si te ayuda, puedes usar objetos o dibujos para representar el problema.

1. Jada usa 8 imágenes de personas.
Ella también usa algunas imágenes de animales.
En total, usa 11 imágenes.
¿Cuántas imágenes de animales usa ella?

• $$8 + 11 = {?}$$
• $$8 + {?} = 11$$
• $$11 - 8 = {?}$$
2. Kiran tenía 19 imágenes.
Él le dio algunas a su hermana.
Ahora le quedan 11 imágenes.
¿Cuántas imágenes le dio Kiran a su hermana?

• $$11 + 19 = {?}$$
• $$19 - {?} = 11$$
• $$19 - 11 = {?}$$
3. El collage de Han tiene 16 sellos.
El collage de Lin tiene 10 sellos menos.
¿Cuántos sellos tiene el collage de Lin?

• $$10 + 16 = {?}$$
• $$10 + {?} = 16$$
• $$16 - 10 = {?}$$
4. Elena usa 9 calcomanías más que Andre.
Andre usa 5 calcomanías.
¿Cuántas calcomanías usa Elena?

• $$9 + 5 = {?}$$
• $$5 + 9 = {?}$$
• $$9 - 5 = {?}$$
5. Noah tiene 6 sellos.
Tyler tiene 16 sellos.
¿Cuántos sellos menos tiene Noah que Tyler?

• $$6 + {?} = 16$$
• $$16 - 6 = {?}$$
• $${?} - 6 = 16$$
6. Clare tenía algunas calcomanías.
Ella les dio 9 de ellas a sus amigos.
Le quedaron 5 calcomanías.
¿Con cuántas calcomanías empezó Clare?

• $$5 + 9 = {?}$$
• $$9 - 5 = {?}$$
• $${?} - 9 = 5$$

Si te queda tiempo, escoge un problema-historia y resuélvelo.
Muestra cómo pensaste. Usa dibujos, números o palabras.

### Activity Synthesis

• Display the problem about Noah and Tyler and a tower of 6 cubes and a tower of 16 cubes.
• “Usen los cubos para explicar cómo podemos usar la suma para resolver este problema” // “Use the cubes to explain how we can use addition to solve this problem.”
• Repeat for subtraction.

## Lesson Synthesis

### Lesson Synthesis

Display story problem A2:

Kiran has 19 pictures.

He gives some to his sister.

Now he has 11 pictures left.

How many pictures did Kiran give to his sister?

• $$11 + ? = 19$$
• $$19 - ? = 11$$
• $$19 - 11 = ?$$

“¿Cuál ecuación corresponde mejor a las acciones de esta historia? ¿Por qué?” // “Which equation best matches the actions in this story? Why?” ($$19 - \underline{\hspace{1 cm}} = 11$$ because in the story Kiran starts with 19 pictures, he gives some away, and the story tells us he has 11 left.)

“¿Cuál ecuación corresponde a la manera en la que resolverían este problema? ¿Por qué?” // “Which equation matches how you would solve this problem? Why?” (I would use $$19 - 11 = \underline{\hspace{1 cm}}$$ because I if I take away the pictures he has left, I will know how many he gave to his sister. I would use $$11 + \underline{\hspace{1 cm}} = 19$$ because I would rather add than subtract. I can add to the 11 pictures he had left until I get to 19 and that will tell me how many he gave to his sister.)