This Number Talk encourages students to use place-value structure to mentally solve problems. The strategies elicited here will be helpful later in the lesson when students convert from milliliters to liters. When they divide by powers of 10, students look for and make use of place-value structure (MP7).
Launch
Display the first problem.
“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 problems and the work displayed.
Repeat with each problem.
Encuentra mentalmente el valor de cada expresión.
Student Response
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Advancing Student Thinking
Activity Synthesis
Display: 1,401 and 1.401
“¿En qué se parecen estos números?” // “How are these numbers the same?” (They both have a 1, then a 4, then a 0, then a 1.)
“¿En qué son diferentes?” // “How are they different?” (The place values of the digits are different. The value of each digit in 1.401 is the value of the same digit in 1,401.)
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.
Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
The purpose of this activity is for students to convert between measurements in milliliters and liters, providing practice multiplying and dividing by 1,000. Students work with numbers in many forms, including whole numbers, decimals, fractions, and numbers in exponential form.
Engagement: Internalize Self-Regulation. Synthesis: Provide students an opportunity to self-assess and reflect on their own progress. For example, provide students with a partially completed chart so they can compare their answers and talk about the similarities and the differences with their partners. Supports accessibility for: Attention; Memory; Social-Emotional Functioning
Launch
Groups of 2
Display the image.
“¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?” (There are different sizes of water bottles. There are numbers underneath the water bottles. How much more water does the big bottle hold than the little bottle? How many milliliters are in a liter?)
Display the table:
L
mL
1
1,000
10
0.1
100,000
10
“¿Qué números van en las casillas vacías de la tabla?” // “What numbers go in the empty boxes in the table?”
30 seconds quiet think time
“Explíquenle a su compañero cómo pensaron” // “Explain your thinking to a partner.”
Fill in the table and leave it displayed for students to refer to during the lesson.
L
mL
1
1,000
10
10,000
0.1
100
100
100,000
0.01
10
Activity
3–5 minutes: independent work time
1–2 minutes: partner discussion
Monitor for students who compare the quantities by converting:
Milliliters to liters.
Liters to milliliters.
Completa la tabla.
L
mL
5
6.3
0.95
800,000
65
En cada caso, decide si las dos medidas son iguales. Si no lo son, escoge la medida que es mayor. Explica o muestra cómo razonaste.
15 mL y 0.15 L
2,500 mL y 2.5 L
200 mL y de L
1 mL y L
15,600 mL y 15.5 L
Student Response
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Advancing Student Thinking
If students only use multiplication or division to convert the units in the table, consider asking:
Refer to the completed table from the Launch and ask students: “¿Qué patrones observas?” // “What patterns do you notice?”
Add rows to the table. “¿Cómo puedes usar la multiplicación para averiguar el número de mililitros que hay en 2 litros de agua? ¿Cómo puedes usar la división para averiguar el número de litros que hay en 1 mililitro de agua?” // “How can you use multiplication to figure out the number of milliliters in 2 liters of water? How can you use division to figure out the number of liters in 1 milliliter of water?”
Activity Synthesis
Invite selected students to share how they compared the measurements.
Display: 15,600 mL and 15.5L
“¿Cuántos litros es 15,600 mililitros? ¿Cómo lo saben?” // “How many liters are 15,600 milliliters? How do you know?” (15.6 liters, because I divide by 1,000)
“¿Cuántos mililitros es 15.5 litros? ¿Cómo lo saben?” // “How many milliliters are 15.5 liters? How do you know?” (15,500 milliliters, because there are 1,000 milliliters in each liter so that’s 15,000 and half of 1 thousand, which is 500.)
“¿Cuál es mayor: 15,600 mililitros o 15.5 litros? ¿Cómo lo saben?” // “Which is greater? 15,600 milliliters or 15.5 liters? How do you know?” (15,600 milliliters, because I can compare, them using either liters or milliliters.)
“Cuando resolvieron este problema, ¿convirtieron de mililitros a litros o de litros a mililitros? ¿Por qué?” // “When you solved this problem, did you convert from milliliters to liters or from liters to milliliters? Why?” (I converted from liters to milliliters because multiplying by 1,000 is more comfortable than dividing by 1,000.)
Activity 2
Standards Alignment
Building On
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.
Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
The purpose of this activity is for students to solve multi-step problems involving metric units of liquid volume (MP2). The given quantities involve fractions. One of the quantities involves the fraction , which students may convert to a decimal, or they may perform the needed arithmetic with fractions. Students also have a choice of converting to milliliters or liters, and there are different points in the calculations when they may choose to make the conversion.
Different approaches students may use to solve the problems include:
Convert the volume of the bottle to liters (as a decimal or a fraction) and work in liters.
Find out how much each dancer drinks in milliliters, and then convert to liters.
Find out how much all the dancers drink in milliliters and then convert to liters.
Find out how much all the dancers drink in milliliters, and then convert the cooler volume to milliliters.
The purpose of the Lesson Synthesis is to compare some of these different approaches.
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 “How many liters of water did the dancers drink?” 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. Advances: Writing, Speaking, Listening
Launch
Groups of 2
Display the image.
“¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?” (The orange thing is a lot bigger than the water bottle. What is that orange thing? How many bottles of water will fill up the orange thing?)
“Este es un dibujo de una botella de agua y un dispensador de agua. Al dispensador de agua anaranjado le cabe mucha agua. Vamos a resolver algunos problemas sobre el agua del dispensador” // “This is an illustration of a water bottle and a water cooler. The orange water cooler can hold a lot of water. We are going to solve some problems about the water in the cooler.”
Activity
5–8 minutes partner work time
Monitor for students who convert from:
Milliliters to liters at different steps in the calculations for the first problem.
Liters to milliliters at different steps in the calculations for the first problem.
En el grupo artístico hay 25 bailarines. Durante el ensayo, cada bailarín se toma botellas de agua.
Cada botella contiene 500 mL de agua. ¿Cuántos litros de agua en total se toman los bailarines? Explica o muestra cómo razonaste.
Cada dispensador contiene 15 L de agua. ¿Cuántos dispensadores necesita el grupo? ¿Cuántos litros de agua quedan después del ensayo si todos los dispensadores estaban llenos al principio? Explica o muestra cómo razonaste.
Los bailarines preparan una bebida hidratante disolviendo 30 mL de mezcla para bebida en 500 mL de agua. ¿Cuántos litros de mezcla para bebida se necesitan para el ensayo del grupo? Explica o muestra cómo razonaste.
Activity Synthesis
Invite a student, who found the number of milliliters all of the dancers drank, to share their reasoning.
“¿Cómo averiguaron cuántos mililitros de agua toma un bailarín?” // “How did you figure out how many milliliters of water one dancer drinks?” (I took 500 and then half of 500, or 250, more.)
“¿Cómo averiguaron cuántos mililitros de agua toman todos los bailarines?” // “How did you figure out how many milliliters all of the dancers drink?” (I multiplied 750 by 25.)
“¿Cómo averiguaron cuántos dispensadores necesitan los bailarines?” // “How did you find how many coolers the dancers need?” (I multiplied the number of liters in the cooler by 1,000.)
Invite a student, who found the number of liters all of the dancers drank, to share their reasoning.
“¿En qué son diferentes estos métodos?” // “How are the methods different?” (One method calculates in milliliters and the other method calculates in liters. The numbers with milliliters are much bigger. The numbers with liters are smaller. They are decimals or fractions.)
Lesson Synthesis
“Convertimos litros a mililitros y mililitros a litros, y usamos estas conversiones para resolver problemas. Para esto, multiplicamos o dividimos” // “Today we converted between liters and milliliters and used these conversions to solve problems. We multiplied or divided.”
“Vimos dos formas de resolver el problema del dispensador de agua” // “We saw two ways to solve the water-cooler problem.”
Display student work from the lesson that shows multiplication and division.
“¿Cuál estrategia prefieren? ¿Por qué?” // “Which strategy do you prefer? Why?” (I liked working in milliliters because then I could use whole numbers. I like using liters because I can visualize a liter and that helps me make sense of the calculations.)
Standards Alignment
Building On
Addressing
5.NBT.A.1
Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
