standard_description: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., p^(2)). For example, by truncating the decimal expansion of Ö2, show that Ö2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
problem_activity: 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.
Advances: Representing, Speaking, Listening
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
Containers of different sizes
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
Here are three true statements about this jug of milk.
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:
[IMG]
One gallon is __________ times as much as 1 quart.
One gallon is __________ times as much as 1 cup.
One quart is __________ times as much as 1 cup.
For a potluck party, Priya and three other relatives are bringing mango lassi.
[IMG]
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "row", "style": "text-align:center"}, "_value": "guest"}, {"_attributes": {"scope": "col", "style": "text-align:center"}, "_value": "amount of lassi"}]}]}], "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Priya"}, {"_attributes": {"style": "text-align:center"}, "_value": "10 cups"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Uncle"}, {"_attributes": {"style": "text-align:center"}, "_value": "3 quarts"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Cousin"}, {"_attributes": {"style": "text-align:center"}, "_value": "8 cups"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Grandma"}, {"_attributes": {"style": "text-align:center"}, "_value": "2 gallons"}]}]}]}]}
Who prepared the most mango lassi? Explain or show your reasoning.
How many cups of lassi did all the guests bring?
Complete this sentence: Priya’s grandma made __________ times as much lassi as Priya’s cousin. Show how you know.
Student Response
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Advancing Student Thinking
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.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col", "style": "text-align:center"}, "_value": "guest"}, {"_attributes": {"scope": "col", "style": "text-align:center"}, "_value": "amount of lassi"}, {"_attributes": {"scope": "col", "style": "text-align:center"}, "_value": "amount of lassi (cups)"}]}]}], "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Priya"}, {"_attributes": {"style": "text-align:center"}, "_value": "10 cups"}, {"_attributes": {"style": "text-align:center"}, "_value": "10"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Uncle"}, {"_attributes": {"style": "text-align:center"}, "_value": "3 quarts"}, {"_attributes": {"style": "text-align:center"}, "_value": "12"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Cousin"}, {"_attributes": {"style": "text-align:center"}, "_value": "8 cups"}, {"_attributes": {"style": "text-align:center"}, "_value": "8"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Grandma"}, {"_attributes": {"style": "text-align:center"}, "_value": "2 gallons"}, {"_attributes": {"style": "text-align:center"}, "_value": "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.
[IMG]
“How does the diagram show that 1 gallon is 4 times as much as 1 quart and 16 times as much as 1 cup?”


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