# Lesson 4

Problemas-historia con cambio desconocido

## Warm-up: Cuántos ves: Números hasta 20 (10 minutes)

### Narrative

The purpose of this How Many Do You See is to allow students to use subitizing or grouping strategies to describe the images they see.

### Launch

• Groups of 2
• “¿Cuántos ven? ¿Cómo lo saben?, ¿qué ven?” // “How many do you see? How do you see them?”
• Flash the image.
• 30 seconds: quiet think time

### Activity

• Display the image.
• “Discutan con su compañero cómo pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.
• Repeat for each image.

### Student Facing

¿Cuántos ves?
¿Cómo lo sabes?, ¿qué ves?

### Activity Synthesis

• “¿Qué ecuaciones podemos escribir para representar la última imagen?” // “What equations could we write to represent the last image?” ($$10 + 7 = 17$$, $$8 + 2 + 7 = 17$$, $$10 + 5 + 2 = 17$$)

## Activity 1: Excursión al acuario (20 minutes)

### Narrative

The purpose of this activity is for students to make sense of and solve Add To and Take From, Change Unknown story problems in a way that makes sense to them. Students represent the method they used and different methods are discussed during the synthesis. When students connect the quantities and action in each story problem to an equation and then solve the problem, they reason abstractly and quantitatively (MP2).

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.

Representation: Access for Perception. Provide appropriate reading accommodations and supports to ensure student access to word problems and other text-based content.
Supports accessibility for: Language, Visual-Spatial Processing, Attention

### Launch

• Groups of 2
• Give each group access to connecting cubes in towers of 10 and singles.
• “¿Alguna vez han ido a un acuario? ¿Qué ven cuando visitan un acuario?” // “Have you ever been to an aquarium? What do you see when you visit an aquarium?” (fish, sharks, dolphins, stingrays, birds, snakes)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.

### Activity

• “Vamos a resolver problemas-historia sobre lo que vio Clare en su excursión al acuario” // “We are going to solve some story problems about what Clare saw on her field trip to the aquarium.”
• 8 minutes: independent work time
• 4 minutes: partner discussion
• Monitor for students who represent and solve the problem about the penguins in different ways, such as:
• Represent the problem as $$17 - \boxed{\phantom{3}} = 5$$
• Represent the problem as $$5 + \boxed{\phantom{3}} = 17$$
• Count back from 17 to 5
• Add or count on from 5 to 17
• Subtract $$17 - 5$$

### Student Facing

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

1. Clare vio 8 tortugas marinas nadando juntas en el tanque.

Algunas tortugas más se unieron.
Ahora hay 15 tortugas en el tanque.
¿Cuántas tortugas se unieron al grupo?

2. Había 17 pingüinos sentados en las rocas.
Algunos pingüinos volvieron al agua.
Ahora hay 5 pingüinos sentados en las rocas.
¿Cuántos pingüinos volvieron al agua?

3. El entrenador de focas trajo un balde con 20 pescados para alimentar a las focas.
Las focas se comieron algunos de los pescados.
Ahora quedan 3 pescados en el balde.
¿Cuántos pescados se comieron las focas?

4. En las piscinas de tacto, Tyler tocó 6 mantarrayas.
Después tocó algunas estrellas de mar.
En total, Tyler tocó 14 animales.
¿Cuántas estrellas de mar tocó Tyler?

### Activity Synthesis

• Invite previously identified students to share.
• “¿Cómo nos ayuda $$17 - 5$$ a encontrar el número de pingüinos que volvieron al agua?” // “How does $$17 - 5$$ help us find the number of penguins that went back into the water?” (If you start with all the penguins and take away the 5 that are still sitting on the rock, you will find out how many went back into the water.)

## Activity 2: Encontremos el número desconocido (15 minutes)

### Narrative

The purpose of this activity is for students to consider different ways to solve for the unknown in a Take From, Change Unknown problem. Students are presented with an equation that represents the order of the actions in the story. However, students often find that this equation is less intuitive to find the unknown value than an addition equation with an unknown addend. Students may also share the ways they use known sums and differences and how they think of making a 10 to find the unknown number.

In this activity, students show their understanding of the relationship between the quantities in the problem and their understanding of the relationship between addition and subtraction to share ways to solve the problem (MP2, MP7).

MLR8 Discussion Supports. Synthesis: Provide students with the opportunity to rehearse what they will say with a partner before they share with the whole class.

### Launch

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

### Activity

• 5 minutes: independent work time
• 3 minutes: partner discussion
• Monitor for students who:
• make 10 when adding on from 9 ($$9 + 1 + 6 = 16$$).
• use the relationship between the numbers of frogs to explain why they can use $$16 - 9 =7$$ to find the unknown number.

### Student Facing

Clare observó 16 ranas mugidoras en el acuario.
Después, algunas de ellas se fueron nadando.
Ahora Clare puede ver solamente 9 ranas mugidoras.
¿Cuántas ranas mugidoras se fueron nadando?

Andre escribió $$16 - \boxed{\phantom{3}} = 9$$, pero no sabe cómo encontrar el número desconocido.

Muéstrale a Andre cómo podría encontrar el número desconocido.
Muestra cómo pensaste. Usa dibujos, números o palabras.

### Activity Synthesis

• Invite previously identified students to share.
• “¿Cómo deciden si van a sumar o a restar para encontrar el número desconocido de una ecuación?” // “How do you decide if you are going to add or subtract to find the unknown number in an equation?” (I usually subtract because I know what number to subtract, but I don't know what numbers to add. I always add because I like it better. I saw there was a 9, so I just thought about adding because I know I can make a ten and add some more.)

## Lesson Synthesis

### Lesson Synthesis

Display one of the story problems from the lesson.

“Hoy resolvimos problemas-historia en los que sabíamos cuántos había al principio y al final, pero no sabíamos cuánto cambiaba la cantidad en la mitad de la historia. Examinamos métodos de suma y de resta que se pueden usar para darle sentido a estos problemas y resolverlos. Explíquenle a su pareja por qué se puede usar la suma o la resta para resolver estos problemas” // “Today we solved story problems where we knew how many of something there was at the beginning and at the end, but we didn't know how much it changed in the middle of the story. We looked at addition and subtraction methods that can be used to make sense of and solve these problems. Explain to your partner why it works to use addition or subtraction to solve these problems.” (You can use addition to add on to one number until you get to the total. The number you added on is the unknown number. You can use subtraction to start with the total and take away the other number you know. The number you have left is the unknown number.)