Lesson 14

This Number Talk encourages students to rely on the structure of numbers in base ten and what they know about the place-value relationship between the digits to mentally solve problems (MP7). The strategies elicited here help students develop fluency in adding multi-digit whole numbers. While students may use counting on or compensation to find sums, the student responses focus on using the relationship between the expressions to find the sum. Both approaches are valid and should be honored.

• 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

• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

• “¿En qué se pareció la manera de encontrar la primera suma a la manera de encontrar la última suma?” // “How was finding the first sum like finding the last sum?” (Each could be done by adding a multiple of 1,000 or 10,000 to the first number—instead of the second given number—and then subtracting a value.)

In this activity, students work with customary units of capacity for liquids (gallon, quart, and cup). The task prompts them to discern the relationship between the units, express the relationships with multiplicative comparison statements, and perform conversions to solve problems. When they identify the relationship between gallons, quarts, and cups students reason abstractly and quantitatively (MP2).

To compare quantities given in different units, students choose which unit to use for comparison and consider the implications of their choice. Students are likely to convert a value in a larger unit to to a smaller unit (from gallons and quarts to cups), but some may reason the other way around (from cups and quarts to gallons, ending up with fractional amounts). In grade 4, students are expected only to convert from a larger unit to a smaller one.

• Gather a one-gallon jug (with or without milk), a one-quart container, and a one-cup container for display during the launch.
• On chart paper, create the table in the activity with an extra column for showing the amounts of lassi in cups, to be displayed during synthesis.

• Groups of 2
• Read the first sentence and the bullet points in the first problem.
• Display a one-gallon jug (with or without milk), a one-quart container, and a one-cup container. Tell students that, when filled up, the jug holds 1 gallon.
• “Este es un recipiente al que le cabe 1 cuarto de galón de líquido. ¿Cómo se relaciona esa cantidad con la cantidad de la jarra?” // “Here is a container that holds 1 quart of liquid. How is that amount related to the amount in the jug?” (It takes 4 of these to fill up the jug.)
• “Este es un recipiente al que le caben 16 tazas. ¿Cómo se relaciona esa cantidad con la cantidad de la jarra?” // “Here is a container that holds 16 cups. How is that amount related to the amount in the jug?” (It takes 16 of these to fill up the jug.)
• “Completen las afirmaciones del primer problema. Después, compartan sus respuestas con su compañero” // “Complete the statements in the first problem. Then, share your responses with your partner.“
• 1 minute: quiet think time
• 1 minute: partner discussion
• “Resolvamos algunos problemas usando lo que sabemos sobre estas unidades con las que se miden líquidos” // “Let’s use what we know about these units for measuring liquids to solve some problems.”
• Explain to students that mango lassi is an Indian drink, a smoothie made of mango and yogurt or milk.

• 5 minutes: independent work time
• 5 minutes: partner discussion
• Monitor for:
  • which unit(s) students use to compare the amounts
  • the representations students use to reason about the quantities

Students may compare only the numbers in the table and not the units. Encourage them to compare two amounts at a time—for instance, 8 cups and 2 gallons. Ask them how they would know which of the two is greater. To draw their attention to the units, consider asking them to illustrate or describe those two amounts using actual containers (if available) or using drawings.

• Poll the class on the unit they used to compare the amounts of lassi.
• Select a student who chose each option to share the rationale behind their decision.
• Display the table with an extra column for showing the amounts in cups.
• Invite students to share their responses to the questions about lassi and their reasoning, completing the table along the way.

  guest	amount of lassi	amount of lassi (cups)
  Priya	10 cups	10
  Uncle	3 quarts	12
  Cousin	8 cups	8
  Grandma	2 gallons	32

• Highlight that converting the amounts into the same unit helped us: see the greatest amount, find the total amount, and see how many times as much lassi one guest made compared to another guest.
• To reinforce students' understanding of the relationship between the units of capacity used here, consider creating a diagram such as shown.

  

  

• “¿Cómo muestra el diagrama que 1 galón es 4 veces 1 cuarto de galón y es 16 veces 1 taza?” // “How does the diagram show that 1 gallon is 4 times as much as 1 quart and 16 times as much as 1 cup?”

In this activity, students convert units of weight measurements—pounds and ounces—and use multiplicative reasoning to solve problems about weight. As in the prior activity, students can choose to reason in either of the two units, but the given quantities encourage conversion from pounds to ounces.

This activity uses MLR6 Three Reads. Advances: reading, listening, representing

• Groups of 2
• “¿Han usado plastilina para hacer un objeto o construir una figura?” // “Have you used clay to make an object or build a figure?”
• If students are unfamiliar with modeling clay, consider displaying some and showing how it can be used for making shapes and objects.

• Display only the problem stem, without revealing the question(s).
• “Vamos a leer este problema 3 veces” // “We are going to read this problem 3 times.”
• 1st Read: “En un almacén de manualidades, la plastilina se vende en paquetes de diferentes tamaños: 1 libra, 24 onzas, 3 libras y 5 libras. Un profesora de arte necesita 120 onzas de plastilina para su clase” // “At a craft store, clay is sold in packs of different sizes: 1 pound, 24 ounces, 3 pounds, and 5 pounds. An art teacher needs 120 ounces of clay for her class.”
• “¿De qué se trata esta situación?” // “What is this situation about?”
• 1 minute: partner discussion
• Listen for and clarify any questions about the context.
• 2nd Read: “En un almacén de manualidades, la plastilina se vende en paquetes de . . .” // “At a craft store, modeling clay is sold in packages of . . .”
• “Nombren las cantidades. ¿Qué cosas de esta situación podemos contar o medir?” // “Name the quantities. What can we count or measure in this situation?”
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share and record all quantities.
• Reveal the question(s).
• 3rd Read: Read the entire problem aloud, including the questions.
• “¿Qué estrategias podemos usar para resolver este problema?” // “What are some strategies we can use to solve this problem?”
• 30 seconds: quiet think time
• 1 minute: partner discussion
• “¿Alguien nos puede recordar cuál es la relación que hay entre las libras y las onzas?” // “Who can remind us of the relationship between pounds and ounces?” (One pound is equivalent to 16 ounces. One pound is 16 times as heavy as 1 ounce.)

• 5 minutes: independent work time
• 3 minutes: partner discussion
• Monitor for students who use ounces to solve the first set of problems and those who use pounds (by first finding out that 120 ounces is 7 pounds and 8 ounces or \(7\frac12\) pounds).

• Select students to briefly share their responses and reasoning.
• “¿Alguien llegó a la misma conclusión, pero razonó de otra forma?” // “Did anyone reach the same conclusion but reasoned in a different way?”