# Lesson 20

Envíos de basura

## Warm-up: Conversación numérica: Tres factores (10 minutes)

### Narrative

The purpose of this Number Talk is for students to mentally calculate a product which students will work with in context in this lesson. The first two products students may know from memory but if not, the idea of doubling $$8 \times 4$$ to find $$8 \times 8$$ can be helpful both for finding the value of $$8 \times 8$$ and for starting a pattern that continues with the next product, $$8 \times 8 \times 2$$, which is double $$8 \times 8$$. The factors 8, 8, and 20 turn out to be the side lengths, in feet, of a standard container used on cargo ships. Students will examine these containers and the ships that carry them throughout the lesson.

### 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.”
• 1 minute: quiet think time

### Activity

• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Encuentra mentalmente el valor de cada expresión.

• $$8 \times 4$$
• $$8 \times 8$$
• $$8 \times 8 \times 2$$
• $$8 \times 8 \times 20$$

### Activity Synthesis

• “¿Cómo encontraron el valor de $$8 \times 8 \times 20$$?” // “How did you find the value of $$8 \times 8 \times 20$$?” (I multiplied $$8 \times 8 \times 2$$ by 10 because 20 is $$10 \times 2$$.)

## Activity 1: Qué desperdicio (15 minutes)

### Narrative

The purpose of this activity is for students to make reasoned estimates about the volume of recyclable goods a school produces in a day, a week, a month, and a year. Students have seen cubic feet and cubic meters briefly in an earlier unit and it may be helpful to build a cubic foot to enable them to visualize this unit of measure and improve their estimates.

Answers to the questions here will vary widely based on the size of the school, the size of the recycling bins, and the exact estimates students make. Mathematically, the important point is that students use multiplication appropriately in their estimates and develop a sense for the staggering size of the waste that they will consider in the second activity.

Engagement: Provide Access by Recruiting Interest. Optimize meaning and value. Invite students to share how they contribute to the recyclable materials in the classroom.
Supports accessibility for: Social-Emotional Functioning, Language

### Required Preparation

• Gather a small recycle bin or trash can and a large recycle bin or trash can.

### Launch

• “Estados Unidos envía a otros países materiales reciclables, como el plástico, para que sean procesados. Vamos a estimar el volumen de los materiales reciclables que se producen en nuestra escuela” // “The United States ships recyclable goods like plastic to other countries for processing. We are going to estimate the volume of recyclable materials our school produces.”
• Show a recycling bin or trash can from class.
• Show a large recycling bin or large trash can from school (if possible).
• “¿Cómo podemos estimar el número de pies cúbicos que caben en el contenedor de reciclaje del salón?” // “How can we estimate the number of cubic feet the class recycling bin holds?” (We can measure the length, width, and height. We can build a cubic foot and put it inside the recycling bin to see how much space it takes up.)
• 1 minute: small-group discussion

### Activity

• 5 minutes: individual think time
• 5 minutes: partner discussion time
• Monitor for students who
• make different estimates for the size of the recycling bins and how often they are filled
• make round estimates for the volume of recyclables the school produces and for the classroom

### Student Facing

1. El número de pies cúbicos que caben en el contenedor de reciclaje del salón.
2. El número de pies cúbicos que caben en los contenedores de reciclaje de la escuela.
2. ¿Aproximadamente cuántos pies cúbicos de materiales reciclables crees que se producen en tu escuela en cada uno de estos periodos de tiempo? Explica o muestra tu razonamiento.

1. un día
2. una semana
3. un mes
4. un año
3. ¿Crees que todos los materiales reciclables que se producen en tu escuela en un año cabrían en tu salón? Muestra o explica tu razonamiento.

### Activity Synthesis

• Invite students to share their estimates for the volume of the different recycling bins.
• “¿Cómo estimaron el volumen de los contenedores de reciclaje pequeños?” // “How did you estimate the volume of the small bins?” (It looks like it’s about 2 feet tall and I think the base is maybe a square foot. So that’s 2 cubic feet.)
• “¿Cómo estimaron el volumen de los contenedores de reciclaje grandes?” // “How did you estimate the volume of the large recycling bins?” (I think they’re about 3 feet tall with a base of about 4 square feet so that would be 12 cubic feet.)

## Activity 2: Plástico y más plástico (20 minutes)

### Narrative

The purpose of this activity is to use estimation to compare the amount of recyclable plastic produced by all elementary schools in the United States to the amount of recyclable plastics the United States exports every year for processing. In this task, an estimate for each school is provided. The new parts of this activity are considering all of the schools in the country, for which an estimate is provided, and the total amount of plastics exported by the United States each year, for which an estimate is also provided.

The numbers in this activity go beyond those expected for the grade 5 division standard but they are friendly and the quotient is small enough that students could find it by repeated subtraction or addition. It is also possible that they will use their place value understanding and their understanding of single-digit multiplication facts.

MLR1 Stronger and Clearer Each Time. Synthesis: Before the whole-class discussion, give students time to meet with 2–3 partners to share and get feedback on their response to the final question. Invite listeners to ask questions, to press for details and to suggest mathematical language. Give students 2–3 minutes to revise their written explanation based on the feedback they receive.

### Launch

• Groups of 2
• “Van a comparar una estimación de la cantidad de plástico reciclable que se produce en todas las escuelas primarias del país y la cantidad de plástico que Estados Unidos envió en el 2018 a otros países para que fuera reciclada” // “You are going to compare an estimate for the amount of recyclable plastic produced by all elementary schools in the country with the amount of plastic the United States shipped in 2018 to other countries where it is recycled.”

### Activity

• 5 minutes: individual work time
• 10 minutes: partner work time
• Monitor for students who
• recall that the they made the calculation for the first problem in the warm-up
• use the division algorithm to find the number of days it takes a school to fill one cargo container
• use the fact that $$3 \times 7 = 21$$ and place value to find the value of $$210,\!000 \div 70,\!000$$

### Student Facing

Tu meta es responder la siguiente pregunta haciendo estimaciones: ¿Entre todas las escuelas de primaria del país se podría producir suficiente plástico reciclable para llenar los contenedores que Estados Unidos envía cada año a otros países?

1. Un contenedor estándar de un barco de carga mide 20 pies de largo, 8 pies de ancho y 8 pies de alto. ¿Cuál es el volumen del contenedor?
2. Cada escuela produce aproximadamente 40 pies cúbicos de plástico reciclable cada día. ¿Cuántos días tardaría una escuela en llenar un contenedor estándar?
3. En el 2018, Estados Unidos exportó aproximadamente 210,000 contenedores llenos de plástico. Hay aproximadamente 70,000 escuelas de primaria en Estados Unidos. ¿Cuántos contenedores debe llenar cada escuela para llenar todos esos contenedores?
4. ¿Crees que entre todas las escuelas de primaria del país se produce suficiente plástico reciclable para llenar todos los contenedores que Estados Unidos exporta? Muestra o explica tu razonamiento.

### Activity Synthesis

• Invite students to share their solutions for finding the number of days it would take a school to fill one of the cargo containers with plastic.
• “¿Cómo pueden usar la ecuación $$128 \div 4 = 32$$ para encontrar el valor de $$1,\!280 \div 40$$?” // “How can you use the equation $$128 \div 4 = 32$$ to find the value of $$1,\!280 \div 40$$?” (They have the same value because if 32 groups of 4 is 128, putting ten times as many in each group will give 10 times as much for the total.)
• Invite students to share their response for how many cargo containers each school will fill.
• “¿Cómo encontraron el valor de $$210,\!000 \div 70,\!000$$?” // “How did you find the value of $$210,\!000 \div 70,\!000$$?” (I know that $$3 \times 70 = 210$$ and so this is also true for thousands.)
• Invite students to share their reasoning for the last question about all elementary school plastic recyclables.
• “Gran parte de la basura que hay en la Isla de basura del Pacífico es plástico. Hoy nos hicimos una idea de cuánto plástico reciclable se produce en todas las escuelas de nuestro país” // “Much of the debris that is in the Great Pacific Garbage Patch is plastic. Today, we got a sense of how much recyclable plastic all of the schools in our country produce.”

## Lesson Synthesis

### Lesson Synthesis

“Hoy estimamos la cantidad de plástico reciclable que las escuelas de primaria pueden producir y la comparamos con la cantidad de plástico que Estados Unidos envía a otros países” // “Today we made estimates for the amount of recyclable plastic elementary schools might produce and compared this with the amount of plastic that the United States ships abroad.”

“¿Cuáles son algunas de las estimaciones que hicieron o usaron hoy?” // “What are some of the different estimates you made or worked with today?” (the volume of recycling bins, the amount of things we put in the bins each day, the number of schools and amount of recyclable plastics shipped)

“¿En qué se parecen calcular usando estimaciones y calcular usando valores exactos? ¿En qué se diferencian?” // “How is calculating with estimates the same as using exact values? How is it different?” (I still need to know what operation to use. But the round numbers are easier to calculate with.)

“Si supieran que hay 68,372 escuelas en vez de 70,000 y que Estados Unidos envió 207,364 contenedores de plástico a otros países, ¿cambiarían su respuesta a la pregunta de si las escuelas podrían llenar todos los contenedores? ¿Por qué?” // “If you knew that there were 68,372 schools rather than 70,000 and the U.S. shipped 207,364 cargo containers of plastic, would that change your answer to the question whether the schools could fill all of those containers? Why?” (No. I don't think I could find the value of the quotient but it should still be close to 3.)

“Estimar no solo es importante para comprobar si las respuestas son razonables, sino también porque a veces no necesitamos un cálculo exacto para responder una pregunta” // “Estimation is important not only to check the reasonableness of answers but also we sometimes don't need an exact calculation to answer a question.”