# Lesson 9

Inventemos problemas en palabras

## Warm-up: Conversación numérica: Diferencia y miles (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for subtracting multi-digit numbers when the minuend is a multiple of 100. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to interpret student work and solve word problems that involve multi-digit numbers.

### Launch

• Display one expression.
• “Hagan una señal cuando tengan una respuesta y puedan explicar cómo la obtuvieron” // “Give me a signal when you have an answer and can explain how you got it.”

### Activity

• 1 minute: quiet think time
• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Encuentra mentalmente el valor de cada expresión.

• $$5,\!000 - 403$$
• $$5,\!300 - 473$$
• $$25,\!300 - 493$$
• $$26,\!000 - 1,\!493$$

### Activity Synthesis

• “¿Siempre usaron una de las primeras expresiones como ayuda para encontrar el valor de una nueva expresión? ¿En algunos casos cambiaron de estrategia?” // “Did you find yourself always using an earlier expression to help you find the value of a new expression? Did you find yourself switching strategies at times?”
• “¿Sobre cuál expresión les pareció más retador razonar?” // “Which expression did you find most challenging to reason about?” (Sample response: $$26,\!000-1,\!493$$ because there were many zeros in the number being subtracted from.)

## Activity 1: ¿Cuál es la pregunta? (15 minutes)

### Narrative

In this activity, students analyze a situation and given solutions and think about what questions were asked. They also write their own question that can be answered with the quantities in the situation. As they connect equations to a context, students reason quantitatively and abstractly (MP2) and engage in aspects of modeling (MP4).

MLR8 Discussion Supports: Display sentence frames to support small-group discussion: “Primero, yo _____ porque . . .” // “First, I _____ because . . .” or “¿Por qué tú . . . ?” // “Why did you . . . ?”
Representation: Develop Language and Symbols. Help students make sense of the situation by seeing it represented in multiple ways. For example, before showing students Kiran’s answers and reasoning, invite them to draw labeled tape diagrams, number lines, or comic strips to represent the situation. Give students the opportunity to see their classmates’ representations before working independently on the task.
Supports accessibility for: Conceptual Processing, Organization, Memory

### Launch

• Groups of 2
• “¿Alguna vez han hecho una caminata larga? ¿Cuál es la mayor distancia que han recorrido caminando?” // “Have you ever gone on a long hike? What is the longest distance you ever traveled just by walking?”
• “Examinemos el trabajo que hizo un estudiante para responder unas preguntas sobre dos hombres que establecieron récords mundiales de viajes a pie” // “Let’s look at the work a student did to answer questions about two men who set world records for traveling by walking.”

### Activity

• 5 minutes: independent work time
• 5 minutes: partner work
• “Compartan sus soluciones con su compañero y compartan estrategias para resolver la tarea” // “Share solutions with your partner and share strategies for solving the task.”
• 5 minutes: Trade problems with a partner, solve, and review strategies for solving.

### Student Facing

George Meegan caminó 19,019 millas entre 1977 y 1983. Terminó a la edad de 31. Gastó 12 pares de botas de montaña.

Jean Beliveau caminó 46,900 millas entre 2000 y 2011. Terminó a la edad de 56.

Estas son las respuestas de Kiran a algunas preguntas sobre la situación.

Escribe la pregunta que podría estar respondiendo Kiran. En la última fila, escribe una nueva pregunta sobre la situación, muestra la respuesta y muestra cómo razonaste.

pregunta respuesta y razonamiento
1.

$$1983 - 1977 = 6$$
$$12 \div 6 = 2$$
2 pares de botas de montaña
2.

$$56 - 31 = 23$$
23 años
3.

$$2011 - 2000 = 11$$
11 años

$$11 \times \underline{\hspace{1 cm}} = 46,\!900$$
$$11 \times 4,\!000 = 44,\!000$$
$$11 \times 200 = 2,\!200$$
$$11 \times 70 = 770$$

$$44,\!000 + 2,\!200 + 770 = 46,\!970$$
$$4,\!000 + 200 + 70 = 4,\!270$$
4,270 millas

4.

### Activity Synthesis

• “Con solo mirar las ecuaciones, ¿cómo averiguaron cuál era la pregunta que se estaba haciendo?” // “How did you figure out the question that was asked just by looking at the equations?” (We can look at the numbers they used and look back at the story to see what they meant. For example, subtracting the years lets us know something about the difference between the years. Dividing 12 by 6 lets us know that the years and the pairs of boots were used to find an answer.)

## Activity 2: ¿Cuál es el problema? (20 minutes)

### Narrative

In this task, students create their own word problems that must have a specific answer and follow additional constraints involving the type of operations that could be used to solve the problem or the size of the numbers they can use (MP2, MP4).

• Groups of 2

### Activity

• 5 minutes: independent work time
• 10 minutes: partner work time

### Student Facing

Elena, Noah y Han escribieron cada uno un problema que tenía como respuesta 1,564.

• Elena usó la multiplicación.
• Noah usó números de varios dígitos y solo usó la suma.
• Han usó la multiplicación y la resta.

En cada caso, escribe un problema que el estudiante podría haber escrito. Muestra que la respuesta a la pregunta es 1,564.

• Problema de Elena:

Solución:

• Problema de Noah:

Solución:

• Problema de Han:

Solución:

### Activity Synthesis

• Select 1–2 students to share the problem they created for each constraint.
• “¿Cómo empezaron?” // “How did you start?”
• “¿Cómo se aseguraron de que la respuesta fuera 1,564? ¿Cómo se aseguraron de que su problema coincidiera con lo que usó cada estudiante?” // “How did you make sure 1,564 would be the answer? How did you make sure your problem would match what each student used?”

## Lesson Synthesis

### Lesson Synthesis

“Hoy averiguamos cuáles eran las preguntas de varios problemas e inventamos nuevos problemas que involucraban distintas operaciones” // “Today we determined the questions for different problems and created new problems that involve different operations.“

“¿En qué fueron diferentes sus procesos de pensamiento al inventarse preguntas y al responderlas?” // “How was the thinking process different when coming up with questions than when answering questions?”

“¿Qué les pareció retador acerca de inventarse preguntas cuando les daban una situación y alguna información sobre esta? ¿Y cuando la única información que se les daba era la respuesta?” // “What was challenging about creating questions when a situation and some information about it are given? What about when no information other than the answer was given?”