Lesson 6

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 need to look for and make use of place value structure (MP7).

• Display one 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

• Record answers and strategy.
• Keep problems and work displayed.
• Repeat with each problem.

• 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 \(\frac{1}{1,000}\) the value of that digit in 1,401.)

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.

• Groups of 2
• Display the image.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?” (There are different sized water bottles. There are numbers underneath the water bottles. How much more water does the big one hold than the little one? How many milliliters are in a liter?)
• Display a table like this one:

  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

• 3–5 minutes: independent work time
• 1–2 minutes: partner discussion
• Monitor for students who:
  • compare the quantities by converting milliliters to liters
  • compare by converting liters to milliliters

If students confuse the operations they need to use to convert milliliters to liters or liters to milliliters, refer to the table from the launch and ask, “¿Qué patrones observas?” // “What patterns do you notice?”

If necessary, add rows to the table and ask them to explain how many milliliters of water are in 2 liters of water and 3 liters of water, and 0.001 liter of water.

• Invite selected students to share how they compared the measurements. 
• Display: 15,600 mL and 15.5 L
• “¿Cuántos litros es 15,600 mililitros? ¿Cómo lo saben?” // “How many liters are 15,600 milliliters? How do you know?” (15.6 since 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 since there are 1,000 milliliters in each liter so that’s 15,000 and half of a 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 mL 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.)

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 \(\frac{1}{2}\) 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 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.

• 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.”

• 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
  • convert from liters to milliliters at different steps in the calculations for the first problem

If a student mixes up the units as they are solving the problem, display a table like the one from the previous activity and ask them to use it to record the number of liters and milliliters of water in a bottle and a cooler.

• Invite a student who found how many 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 how many liters all of the dancers drank to share their reasoning.
• “¿En qué son diferentes estos métodos?” // “How are the methods different?” (One calculates in milliliters and the other one in liters. The numbers with milliliters are much bigger. The numbers with liters are smaller. They are decimals or fractions.)