# Lesson 10

Exploración de estimación

## Warm-up: Exploración de estimación: No se necesita conductor (10 minutes)

### Narrative

The purpose of an Estimation Exploration is for students to practice the skill of estimating a reasonable answer based on experience and known information. Students are given some information about a parking garage and pictures of the interior and exterior.

Invite students to share the assumptions they used when they make and share their estimates. For example, students may share how they used the photos to estimate how many floors there were and how many cars could fit on each floor. They may share the assumptions they made about whether each floor held the same amount of cars or how the cars were arranged on the floors based on the picture that they used to estimate that there are 10 floors and each floor holds the same amount of cars.

### Launch

• Groups of 2
• Display image.

### Activity

• “¿Qué estimación sería muy alta?, ¿muy baja?, ¿razonable?” // “What is an estimate that’s too high? Too low? About right?”
• 1 minute: quiet think time
• 1 minute: partner discussion
• Record responses.

### Student Facing

En estas imágenes se muestran el exterior y el interior de una torre de estacionamientos en Wolfstadt, Alemania. El estacionamiento es automatizado: cada automóvil se sube en un ascensor y se ubica en un estacionamiento.

¿Cuántos automóviles caben en la torre?

Escribe una estimación que sea:

muy baja razonable muy alta
$$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$ $$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$ $$\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}$$

### Activity Synthesis

• “¿Qué suposiciones hicieron sobre el estacionamiento para hacer su estimación?” // “What assumptions did you make about the parking garage to make your estimate?”
• “¿Qué información les ayudaría a hacer una estimación más precisa?” // “What information would help you make a more accurate estimate?”
• Consider revealing the actual number of cars in the structure, which is 400. The parking structure has 20 stories and 20 cars per story.

## Activity 1: Cuidado dental (10 minutes)

### Narrative

In this activity, students use given descriptions and their knowledge of multiplication to make some estimates of the cost and time associated with brushing teeth. To complete the estimation, students will need to make some assumptions about what constitutes “a lifetime” and the cost of a single toothbrush. The activity gives students another example before they write their own Estimation Exploration activity.

Engagement: Provide Access by Recruiting Interest. Revisit math community norms to prepare students for working with an uncertain situation. Remind students about expectations for handling disagreements and provide sentence frames to support possible ways to come to a resolution.
Supports accessibility for: Social-Emotional Functioning

### Launch

• Groups of 2
• Solicit some ideas from students: “¿Qué tipos de cosas podemos estimar en esta situación?” // “What kinds of things can we estimate in this situation?”

### Activity

• 4–5 minutes: independent work time
• 2 minutes: partner discussion
• Monitor for the different assumptions that students make to answer the questions.

### Student Facing

Jada cepilla sus dientes durante 2 minutos, dos veces al día. Ella cambia su cepillo de dientes cada 3 meses.​​​​​​

Teniendo en cuenta esta información, haz algunas estimaciones y muestra cómo razonaste:

1. Aproximadamente, durante toda su vida:

1. ¿Cuántos cepillos de dientes usará ella?
2. ¿Cuántos dólares gastará en cepillos de dientes?
2. Encuentra aproximadamente cuántos minutos pasará cepillándose sus dientes:

1. en un año
2. durante toda su vida
3. Piensa en otra pregunta de estimación que puedas hacer sobre esta situación.

### Activity Synthesis

• Select students who made different assumptions about cost and the length of a lifetime to share their responses and reasoning. Record their estimates.
• If time permits, invite students to share the new estimation questions they thought of for this situation. “¿Cómo podrían hacer esas estimaciones?” // “How might you make those estimates?”

## Activity 2: Hagan que sus compañeros estimen (15 minutes)

### Narrative

In this activity, students create an Estimation Exploration activity that focuses on multi-digit multiplication. Students may choose to present a situation (as in the toothbrush example), something observed in the classroom (such as a large shelf filled with books), or an image (as in the warm-up). They need to anticipate the reasoning strategies others might use to make an estimate.

### Required Preparation

• Gather two magazines or other sources of images for each group of 3–4 students.

### Launch

• Groups of 3–4

### Activity

• “En grupo, creen una actividad tipo ‘Exploración de estimación’ en la que haya un número grande de objetos o una cantidad grande” // “Work with your group to create an Estimation Exploration activity that involves a large number of objects or a large quantity.”
• “Asegúrense de pensar en las distintas estrategias que podrían usar sus compañeros para hacer una estimación” // “Be sure to consider different strategies that others might use to make an estimate.”
• 11–12 minutes: small-group work time

### Student Facing

Es su turno de crear un problema de estimación.

1. Piensen en situaciones o busquen imágenes a su alrededor con las que puedan hacer problemas de estimación interesantes. Escriban 4 o 5 ideas o posibles temas.
2. Escojan su idea favorita. Luego:
• Escriban una pregunta de estimación que motive a sus compañeros a usar la multiplicación de números de varios dígitos para responderla.
• Escriban una estimación que sea:
muy baja razonable muy alta
$$\phantom{\hspace{1.9cm} \\ \hspace{1.9cm}}$$ $$\phantom{\hspace{1.9cm} \\ \hspace{1.9cm}}$$ $$\phantom{\hspace{1.9cm} \\ \hspace{1.9cm}}$$
Prepárense para explicar su razonamiento.

### Activity Synthesis

• Clear up any confusion and allow them a few minutes to revise their design, if needed.

## Activity 3: Dirijan su actividad tipo “Exploración de estimación” (10 minutes)

### Narrative

In this activity, students facilitate the Estimation Exploration activity they created for another group in the class. If time allows, encourage students to run the activity for multiple groups.

MLR8 Discussion Supports. Synthesis: During group presentations, invite the student(s) who are not speaking to follow along and point to the corresponding parts of the display.

### Launch

• Combine every two groups of 3–4.
• Give each group a piece of poster paper to record their written scenario (if they have one) and to record responses.

### Activity

• “Dirijan su actividad de estimación. Háganlo por turnos con el grupo que se hicieron” // “Take turns facilitating your estimation activity with the group you’re partnered with.”
• Remind groups to switch roles halfway through the allotted time.

### Student Facing

Sigan estos pasos para dirigir su actividad tipo “Exploración de estimación” y presentársela a otro grupo:

• Muestren su imagen o presenten su escenario.
• Pregunten a sus compañeros: “¿Qué estimación sería muy alta?, ¿muy baja?, ¿razonable?”.
• Denles 1 minuto para pensar en silencio.
• Denles 1 o 2 minutos para que ellos discutan.
• Pídanles que compartan sus estimaciones y cómo las hicieron. Anoten las ideas de sus compañeros.
• Si saben el número o la cantidad real, consideren revelarlo.

### Activity Synthesis

• See lesson synthesis.

## Lesson Synthesis

### Lesson Synthesis

Invite students to reflect on their process. Discuss questions such as:

“¿Qué diferencia hubo entre el proceso de crear una actividad tipo ‘Exploración de estimación’ y responder una?” // “How was the process of creating an Estimation Exploration activity different from answering one?” (Creating the activity is more involved. It requires researching, thinking of possible ways to estimate, actually making estimates, and maybe revising the question. Doing the activity only involves finding a way to estimate and explaining it.)

“¿Qué aprendieron mientras dirigían su actividad tipo ‘Exploración de estimación’?” // “What did you learn as you facilitated your Estimation Exploration?” (The estimates that others find could be close or far from our estimates or the actual number. Others might use other strategies that we did not think of or make assumptions that are very different than ours.)

“Si tuvieran la oportunidad de ajustar su actividad, ¿cambiarían algo? ¿Qué cambiarían?” // “If you had a chance to revise your activity, would you change anything? What would you change?”