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The purpose of this Number Talk is for students to mentally calculate a product, with which students will work in context in this lesson. The first two products students may know from memory but if not, the idea of doubling to find can be helpful both for finding the value of and for starting a pattern that continues with the next product, , which is double . 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.
Encuentra mentalmente el valor de cada expresión.
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.
Estima el valor de cada cantidad.
Indica, aproximadamente, cuántos pies cúbicos de materiales reciclables se producen en tu escuela en cada uno de estos periodos de tiempo.
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 with 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 also is 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 also is possible that they will use their place-value understanding and their understanding of single-digit multiplication facts.
Estima si es posible que entre todas las escuelas de primaria del país se produzca suficiente plástico reciclable para llenar los contenedores que Estados Unidos envía cada año a otros países.
“Hoy estimamos la cantidad de plástico reciclable que las escuelas de primaria pueden producir y la comparamos con la cantidad de plástico reciclable 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 recyclable 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 plastic we put in the bins each day, the number of schools and the 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 which operation to use. But the round numbers are easier to calculate.)
“Si supieran que hay 68,372 escuelas, en vez de 70,000, y que Estados Unidos envió 207,364 contenedores llenos 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 of whether the schools could fill all of the containers? Why?” (No, I don't think I could find the value of the quotient but, it still should 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 because we sometimes don't need an exact calculation to answer a question.”
Aprendimos a usar la multiplicación y la división de números enteros para estimar cantidades grandes y para resolver problemas de la vida real. Primero, estimamos el volumen de leche que tomábamos en un día. Usamos esa estimación para encontrar el volumen de leche que tomaban las personas de nuestra clase, de nuestro grado, de nuestra escuela y de 10 escuelas. Después, averiguamos cuántos días tardaría cada grupo en tomar 10,000,000 de centímetros cúbicos de leche.
Luego, resolvimos problemas sobre el área de la Isla de basura del Pacífico. Calculamos las áreas de varios estados de los Estados Unidos y las comparamos con el área de la Isla de basura del Pacífico. ¡Descubrimos que el área de la Isla de basura del Pacífico es mucho mayor que la mayoría de los estados de los Estados Unidos!
Por último, reconocimos la cantidad de basura reciclable que Estados Unidos produce y envía a otros países. Estimamos el volumen de basura reciclable que produce nuestra escuela en un día, una semana, un mes y un año. Después, usamos la estimación para determinar si es posible que entre todas las escuelas de primaria del país se produzca suficiente plástico reciclable para llenar los contenedores que Estados Unidos exporta cada año.