# Lesson 14

Weight and Capacity Measurements

## Warm-up: Number Talk: Lots of Thousands (10 minutes)

### Narrative

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.

### Launch

• Display one expression.
• “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

### Activity

• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Find the value of each expression mentally.

• $$1,\!200 + 900$$
• $$12,\!500 + 9,\!000$$
• $$13,\!000 + 9,\!900$$
• $$130,\!000 + 99,\!000$$

### Activity Synthesis

• “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.)

## Activity 1: Milk and Mango Lassi (20 minutes)

### Narrative

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.

MLR8 Discussion Supports. To support the transfer of new vocabulary to long term memory, invite students to chorally repeat these words or phrases in unison 1-2 times: gallon, quart, cup.
Representation: Access for Perception. Give students access to connecting cubes. Invite them to use the cubes to support their thinking in a way that makes sense to them. If students need additional support, invite them to use the cubes to first build and label a representation of one cup, one quart, and one gallon.
Supports accessibility for: Conceptual Processing

### Required Materials

Materials to Gather

### Required Preparation

• 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.

### Launch

• 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.
• “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.)
• “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.)
• “Complete the statements in the first problem. Then, share your responses with your partner.“
• 1 minute: quiet think time
• 1 minute: partner discussion
• “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.

### Activity

• 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

### Student Facing

• This jug contains 1 gallon of milk.
• This jug contains 4 quarts of milk.
• This jug contains 16 cups of milk.

Complete each statement so that it is true:

1. One gallon is __________ times as much as 1 quart.
2. One gallon is __________ times as much as 1 cup.
3. One quart is __________ times as much as 1 cup.
2. For a potluck party, Priya and three other relatives are bringing mango lassi.

guest amount of lassi
Priya 10 cups
Uncle 3 quarts
Cousin 8 cups
Grandma 2 gallons
1. Who prepared the most mango lassi? Explain or show your reasoning.
2. How many cups of lassi did all the guests bring?
3. Complete this sentence: Priya’s grandma made __________ times as much lassi as Priya’s cousin. Show how you know.

### Student Response

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.

### Activity Synthesis

• 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.
• “How does the diagram show that 1 gallon is 4 times as much as 1 quart and 16 times as much as 1 cup?”

## Activity 2: Clay for Art Class (15 minutes)

### Narrative

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.

### Launch

• Groups of 2
• “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).
• “We are going to read this problem 3 times.”
• 1st Read: “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.”
• “What is this situation about?”
• 1 minute: partner discussion
• Listen for and clarify any questions about the context.
• 2nd Read: “At a craft store, modeling clay is sold in packages of . . .”
• “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).
• “What are some strategies we can use to solve this problem?”
• 30 seconds: quiet think time
• 1 minute: partner discussion
• “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.)

### Activity

• 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).

### Student Facing

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.

1. Would she have enough clay if she bought each of the following combinations? Explain or show your reasoning.
1-pound pack 24-ounce pack 3-pound pack 5-pound pack
Combo A 1 1
Combo B 1 1 1 1
Combo C 1 2
2. Decide if each statement is true or false. Be prepared to explain or show your reasoning.

1. A 3-pound pack weighs 2 times as much as a 24-ounce pack.
2. If we combine a 1-pound pack, a 3-pound pack, and a 5-pound pack, we’d have 6 times as much clay as what’s in a 24-ounce pack.

### Activity Synthesis

• Select students to briefly share their responses and reasoning.
• “Did anyone reach the same conclusion but reasoned in a different way?”

## Lesson Synthesis

### Lesson Synthesis

“Today we solved problems by converting one unit to another unit—first from gallons to quarts or cups (or the other way around) and then from pounds to ounces (or the other way around). By converting some measurements, we were able to make comparisons, find total amounts, and more.”

Display the two sets of quantities from the two activities:

• 10 cups
• 3 quarts
• 8 cups
• 2 gallons
• 1 pound
• 24 ounces
• 3 pounds
• 5 pounds

“If someone claimed that 3 quarts is greater than 2 gallons because 3 is greater than 2, how would you explain that this is not true? What correction would you offer?” (The units are not the same for those two quantities, so we can’t just compare the numbers. One gallon is 4 times as much as 1 quart, so we are comparing 8 quarts and 3 quarts.)

“If someone claimed that 24 ounces is 8 times as much as 3 pounds, would you agree? Why or why not?” (Disagree. One pound is 16 ounces, so 24 ounces is 1 pound and 8 ounces or $$1\frac{1}{2}$$ pounds, which is half as much as 3 pounds, not 8 times as much. Or we could say that 3 pounds, which is 48 ounces 2 times as much as 24 ounces.)