This Number Talk helps students develop strategies to find multiples of 12 mentally, using place value and the distributive property. This work prepares students for converting measurements in feet to measurements in inches.
Launch
Display the first 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
Record students’ answers and strategies.
Keep the expressions and the work displayed.
Repeat with each expression.
Encuentra mentalmente el valor de cada expresión.
Student Response
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Advancing Student Thinking
Activity Synthesis
“¿Cómo se relacionan los valores de los productos y ?” // “How are the values of the products and related?” (There is one more 12 in .)
Activity 1
Standards Alignment
Building On
Addressing
5.MD.A.1
Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.
The purpose of this activity is to compare measurements in inches, feet, and yards. Four different lengths are used and each length is presented in inches, feet, and yards. Students sort these measurements in three different ways. First they sort the measurements in a way that makes sense to them. Then students find equivalent lengths. Finally, they organize lengths that use the same unit in increasing order. The Activity Synthesis highlights why expressing all the measurements, with one unit, is a convenient way to communicate and compare measurements (MP6).
MLR8 Discussion Supports. Students should take turns finding a match and explaining their reasoning to their partner. Display the following sentence frame for all to see: “Observé _____, entonces agrupé . . .” // “I noticed _____, so I matched . . . .” Encourage students to challenge each other when they disagree. Advances: Conversing, Representing
Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. Give students a subset of the cards to start, and introduce the remaining cards once students have completed their initial set of matches. Supports accessibility for: Conceptual Processing; Memory
Launch
Groups of 2
Give each group a set of cards and access to a yardstick.
Display a yardstick.
“¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?” (It shows feet and inches. It shows 36 inches. I wonder if it’s the same length as a meter stick.)
Activity
“Con su compañero, clasifiquen sus tarjetas en categorías que tengan sentido para ustedes” // “Work with your partner to sort your cards into categories in a way that makes sense to you.”
2 minutes: partner work time
Monitor for students who sort by:
The unit of measure.
The way the quantity is written (whole number, mixed number, fraction).
Invite 1–2 previously selected groups to share their categories and how they sorted their cards.
“Clasifiquen las tarjetas en grupos que representen longitudes iguales. Con su compañero, expliquen cómo razonaron” // “Sort the cards into groups that represent equal lengths. Work with your partner to explain your reasoning.”
“Luego, para cada unidad de medida, ordenen las longitudes de la más corta a la más larga” // “Then order the lengths, from shortest to longest, for each unit of measure.”
Monitor for students who:
Use the yardstick to check or explain their reasoning.
Use equivalent lengths they know (1 yard is the same length as 3 feet, so 50 yards is feet).
Group measurements that use the same unit before ordering them from shortest to longest.
6 minutes: partner work time
Activity Synthesis
Invite 2–3 previously selected groups to share a set of equivalent lengths.
Consider asking: “¿Cómo decidieron que esas tarjetas muestran la misma longitud?” // “How did you decide that these cards show the same length?”
Attend to the language that students use to describe their matches, giving them opportunities to describe how they know the measurements are equal.
“¿Cómo ordenaron las medidas? ¿Por qué?” // “How did you order the measurements? Why?” (I chose one of the units, feet, and compared all of the measurements in that unit.)
“¿Por qué fue importante que todas las medidas estuvieran en la misma unidad para poder compararlas?” // “Why was it important for all of the measurements to be in the same unit in order to compare?” (That way I can just compare the numbers because they all have the same unit of measure.)
Activity 2
Standards Alignment
Building On
Addressing
5.MD.A.1
Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.
The goal of this activity is to solve multi-step conversion problems, using customary length units. The given information for both problems is in fraction form. Students need to find the perimeter of the different fields and then investigate how many times around each field is a given number of miles. The first problem involves 3 steps:
Find the perimeter of the rectangular field.
Find the total distance of 6 laps around the field.
Convert from yards to feet or feet to yards.
The second problem has only two steps, but the number of laps is unknown and students need to find how many laps make at least 2 miles.
When students critically analyze Priya's claim that six laps of the soccer field is more than a mile, they critique the reasoning of others (MP3).
Launch
Groups of 2
“¿Aproximadamente cuánta distancia es una milla?” // “About how far is a mile?”
1–2 minutes: quiet think time
Record responses for all to see.
Describe to students a location that is about a mile away from the school.
“¿Aproximadamente cuántos pies hay en una milla?” // “About how many feet are in a mile?”
“¿Qué estimación sería muy baja?, ¿muy alta?, ¿razonable?” // “What is an estimate that is too low? Too high? About right?”
Record students’ responses in the table:
muy baja
razonable
muy alta
//
too low
about right
too high
Display: There are 5,280 feet in one mile.
Leave the display up throughout the lesson.
“Vamos a resolver algunos problemas sobre millas” // “We are going to solve some problems about miles.”
Activity
7–10 minutes: partner work time
Monitor for students who:
Find the number of yards in a mile.
Convert yards to feet for the first problem.
Un campo rectangular mide 90 yardas de largo y yardas de ancho. Priya dice que 6 vueltas alrededor del campo es una distancia mayor que 1 milla. ¿Estás de acuerdo? Explica o muestra cómo razonaste.
Otro campo rectangular mide pies de largo y pies de ancho. ¿Cuántas vueltas tiene que correr Priya alrededor de este campo para correr al menos 2 millas?
Student Response
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Advancing Student Thinking
If students don’t have a strategy to solve the first problem, consider asking:
“¿Puedes representar una persona que corre una vuelta alrededor del campo?” // “Can you represent a person running one lap around the field?”
“¿Cómo puedes averiguar la distancia que hay en una vuelta alrededor del campo?” // “How can you figure out the distance of one lap around the field?”
Activity Synthesis
Invite students to share their solutions to the first problem.
“¿Cómo encontraron cuánta distancia hay en 1 vuelta alrededor del campo?” // “How did you find how far 1 lap around the field is?” (I multiplied the length and the width by 2 and added them.)
“¿Cuánta distancia hay en una vuelta?” // “How far is one lap?” ( yards)
“¿Cuánta distancia hay en 6 vueltas? ¿Cómo lo saben?” // “How far is 6 laps? How do you know?” (1,587 yards, I multiplied by 6.)
“¿Cómo encontraron el producto ?” // “How did you find the product ?” (I multiplied 264 by 6. I know that is 3 so I added that.)
“¿6 vueltas es más de o menos de una milla?” // “Is 6 laps more than or less than a mile?” (Less, because it’s less than 5,000 feet. Less, because a mile is more than 1,700 yards.)
Lesson Synthesis
“Hoy hicimos conversiones entre distancias que estaban en unidades tradicionales” // “Today we converted between distances in customary units.”
Display: 10 feet
“¿Cuántas pulgadas hay en 10 pies?, ¿cuántas yardas?” // “How many inches are in 10 feet? How many yards?” (120 inches, yards)
Display: 10 meters
“¿Cuántos centímetros hay en 10 metros?, ¿cuántos kilómetros?” // “How many centimeters are in 10 meters? How many kilometers?” (1,000 centimeters, 0.01 kilometer)
“¿En que se parecen hacer conversiones entre unidades métricas de longitud y hacer conversiones entre unidades tradicionales de longitud?” // “How is converting between metric length units the same as converting between customary length units?” (In each case, I multiply by a number when going from a bigger unit to a smaller unit, and I divide by a number when going from a bigger unit to a smaller unit.)
“¿En qué es diferentes hacer conversiones entre unidades métricas de longitud a hacer conversiones entre unidades tradicionales de longitud?” // “How is converting between metric length units different than converting between customary length units?” (When we convert in metric units, we multiply or divide by a power of 10 so the digits in the measurement stay the same. With customary units, the division or multiplication is not by a power of 10 so it takes more work, the digits change, and I may need to use fractions instead of decimals.)
Student Section Summary
Estudiamos potencias de 10 y conversiones de unidades. Aprendimos que podemos escribir productos de varios 10 como una potencia de 10. Por ejemplo, podemos escribir como . El número 4 es un exponente y significa que hay 4 factores de 10.
También hicimos conversiones de distintas unidades de medida. Hay 1,000 milímetros en un metro y hay 1,000 metros en un kilómetro. Esto significa que hay o de milímetros en un kilómetro. También podemos decir que hay milímetros en un kilómetro.
Usamos lo que ya sabemos sobre los números decimales para hacer conversiones. Hay 1,000 metros en un kilómetro. Cada metro es o 0.001 kilómetros. Por eso, 853 metros también se puede escribir como 0.853 kilómetros.
Standards Alignment
Building On
Addressing
Building Toward
5.MD.A.1
Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.
