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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, their responses focus on using the relationship between the expressions to find the sum. Both approaches are valid and should be accepted.
Find the value of each expression mentally.
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 likely will convert a value in a larger unit to a value in 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
Here are 3 true statements about this jug of milk.
Complete each statement so that it is true:
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 3 other relatives are bringing mango lassi (MAYNG-goh LAH-see).
Who prepared the most mango lassi? Explain or show your reasoning.
| guest | amount of lassi |
|---|---|
| Priya | 10 cups |
| uncle | 3 quarts |
| cousin | 8 cups |
| grandma | 2 gallons |
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.
| guest | amount of lassi | amount of lassi (cups) |
|---|---|---|
| Priya | 10 cups | 10 |
| Uncle | 3 quarts | 12 |
| Cousin | 8 cups | 8 |
| Grandma | 2 gallons | 32 |
In this activity, students convert units of weight—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.
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-pound pack | 24-ounce pack | 3-pound pack | 5-pound pack | |
|---|---|---|---|---|
| A | 1 | 1 | ||
| B | 1 | 1 | 1 | 1 |
| C | 1 | 2 |
Decide if each statement is true or false. Explain or show your reasoning.
“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:
“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 pounds, which is half as much as 3 pounds, not 8 times as much. Or we could say 3 pounds is 48 ounces or 2 times as much as 24 ounces.)
Invite students to use the containers displayed during the Launch, if available.