# Lesson 15

Diferentes tipos de problemas-historia

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

### Narrative

This warm-up prompts students to compare four equations. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another. During the synthesis, ask students to explain the meaning of the equal sign in their reasoning.

### 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

• 2–3 minutes: partner discussion
• Record responses.

### Student Facing

¿Cuál es diferente?

1. $$7 = \boxed7$$

2. $$\boxed7 = 3 + 4$$

3. $$4 + 3 = \boxed8$$

4. $$7 - 3 = \boxed4$$

### Activity Synthesis

• “¿Qué nos enseña cada ecuación sobre el signo igual?” // “What does each equation help us know about the equal sign?” (It shows us that the equal sign means the amount on either side is the same.)

## Activity 1: ¿Qué preguntas podemos hacer? (10 minutes)

### Narrative

The purpose of this activity is for students to make sense of a problem before solving it by familiarizing themselves with a context and the mathematics that might be involved (MP1). Students are asked to tell a story about an image in order to generate observations that lead them to ask mathematical questions about the context. This sets them up for Activity 2 in which students will be solving story problems in the given context.

MLR8 Discussion Supports. Display sentence frames to support partner discussion: “La imagen muestra . . .” // "The picture shows. . . ." and “Puedo contar . . .” // “I can count. . . .”

### Launch

• Groups of 2
• “Usen números para describir la imagen” // “Use numbers to describe the image.”
• 1 minute: quiet think time
• 2 minutes: partner discussion
• Share responses.

### Activity

• “Piensen en las matemáticas que hay en esta imagen. ¿Qué preguntas matemáticas se pueden hacer acerca de esta imagen?” // “Think about the mathematics in this image. What mathematical questions could be asked about this picture?”
• 3 minutes: independent work time
• 2 minutes: partner discussion
• Monitor for students who are asking questions about how many altogether or how many more or fewer.

### Student Facing

¿Qué preguntas matemáticas puedes hacer acerca de esta imagen?

### Activity Synthesis

• Invite several students to share one question with the class.
• Record responses.
• If needed, ask, “¿Se puede responder esta pregunta con la imagen? ¿Cómo lo saben?” // “Can this question be answered by the image? How do you know?”
• “¿En qué se parecen estas preguntas? ¿En qué son diferentes?” // “What do these questions have in common? How are they different?” (Some of them use the same numbers. Some ask to find the total and others ask to find the difference.)

## Activity 2: Diferentes tipos de problemas (15 minutes)

### Narrative

The purpose of this activity is for students to solve a variety of story problems and write addition and subtraction equations that match those problems. Students solve Put Together/Take Apart, Total or Addend Unknown problems and Compare, Difference Unknown problems. Students may solve in any way they want and write equations to match the story problem, putting a box around the number that represents the answer (MP2).

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

• Groups of 2

### Activity

• “Van a resolver problemas sobre la imagen del calentamiento. Las preguntas pueden incluir algunas de las que ustedes hicieron. Muestren cómo pensaron. Usen dibujos, números o palabras. Escriban una ecuación que corresponda al problema-historia. Si pueden, escriban dos ecuaciones diferentes que correspondan al problema" // “You will solve problems about the picture from the warm up. The questions may include some of the questions you asked. Show your thinking using drawings, numbers, or words. Write an equation to match the story problem. If you can, write two different equations that match the problem.”
• 6 minutes: independent work time
• 4 minutes: partner discussion
• Monitor for students who solved using drawings, can clearly explain how they solved, and wrote an equation.

### Student Facing

1. Hay 8 personas en la mesa.
6 de ellas son estudiantes.
¿Cuántas son profesores?
Muestra cómo pensaste. Usa dibujos, números o palabras.

Ecuación: ________________________________

Ecuación: ________________________________

2. Elena tiene 4 fichas geométricas.
Tyler tiene 6 fichas geométricas.
¿Cuántas fichas geométricas menos tiene Elena que Tyler?
Muestra cómo pensaste. Usa dibujos, números o palabras.

Ecuación: ________________________________

Ecuación: ________________________________

3. Tyler tiene 6 fichas geométricas.
Elena tiene 4 fichas geométricas.
¿Cuántas fichas geométricas tienen en total?
Muestra cómo pensaste. Usa dibujos, números o palabras.

Ecuación: ________________________________

Ecuación: ________________________________

Muestra cómo pensaste. Usa dibujos, números o palabras.

Ecuación: ________________________________

Ecuación: ________________________________

### Activity Synthesis

• Display: Elena has 4 pattern blocks. Tyler has 6 pattern blocks. How many fewer patterns blocks does Elena have than Tyler?
• “¿Cómo resolvieron este problema? ¿Qué ecuación escribieron?” // “How did you solve this problem? What equation did you write?”
• Record student methods and equations.
• Repeat for the other problems with the same numbers.
• “¿En qué se parecen estos problemas? ¿En qué son diferentes?” // “How are these problems the same? How are they different?” (They both have Elena and Tyler. They both have 4 and 6. In one we find the difference and in the other one we find the total. The answers are different.)
• If needed, ask, “¿El total es importante para resolver el primer problema? ¿Por qué sí o por qué no?” // “Is the total important to solving the first problem? Why or why not?” (No, because we are comparing the students.)

## Activity 3: Centros: Momento de escoger (15 minutes)

### Narrative

The purpose of this activity is for students to choose from activities that offer practice adding and subtracting within 10. Students choose from any stage of previously introduced centers.

• Capture Squares
• Shake and Spill
• What’s Behind My Back

### Required Materials

Materials to Gather

### Required Preparation

• Gather materials from previous centers:
• Capture Squares, Stage 1
• Shake and Spill, Stages 3 and 4
• What's Behind My Back, Stage 2

### Launch

• Groups of 2
• “Ahora van a escoger un centro de los que ya conocemos” // “Now you are going to choose from centers we have already learned.”
• Display the center choices in the student book.
• “Piensen qué les gustaría hacer” // “Think about what you would like to do.”
• 30 seconds: quiet think time

### Activity

• Invite students to work at the center of their choice.
• 10 minutes: center work time

### Student Facing

Escoge un centro.

Revuelve y saca

Qué hay a mis espaldas

### Activity Synthesis

• Using a tower of 8 cubes, break the tower and hide one part behind your back.
• “¿Qué hay a mis espaldas? ¿Cómo lo saben?” // “What’s behind my back? How do you know?”
• Write equations to match student methods.

## Lesson Synthesis

### Lesson Synthesis

Display $$7 - 2 = \boxed{5}$$ and $$2 + \boxed{5} = 7$$.

“Hoy escribimos diferentes ecuaciones que corresponden a la misma historia. Cuenten una historia que pueda corresponder a ambas ecuaciones” // “Today we wrote different equations to match the same story. Tell a story that could match both of these equations.” (I have 7 balloons. My friend has 2 balloons. How many more balloons do I have than my friend?)

## Student Section Summary

### Student Facing

• Construimos torres de cubos que tienen el mismo número de cubos.

Podemos agregar 7 cubos azules más.
Podemos quitar 7 cubos rojos.

• Resolvimos problemas-historia sobre “¿cuántos más” y “¿cuántos menos”.

Elena tiene 4 fichas geométricas.
Tyler tiene 6 fichas geométricas.
¿Cuántas fichas geométricas menos tiene Elena que Tyler?

$$4 + \boxed{2} = 6$$

o

$$6 - 4 = \boxed{2}$$

• Aprendimos que estos problemas se pueden resolver con una suma o una resta.