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.
Launch
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
Activity
Record answers and strategies.
Keep expressions and work displayed.
Repeat with each expression.
Student Task Statement
Encuentra mentalmente el valor de cada expresión.
Student Response
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Advancing Student Thinking
Activity Synthesis
“¿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 in the expression—instead of the second number—and then subtracting a value.)
Activity 1
20 mins
Leche y lassi de mango
Standards Alignment
Building On
Addressing
4.MD.1
Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), …
Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
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: “galón” // “gallon,” “cuarto de galón” // “quart,” “taza” // “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 representations of one cup, one quart, and one gallon. Supports accessibility for: Conceptual Processing
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.
“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 quarts 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 cups 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 (MAYNG-goh LAH-see) 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 Task Statement
Estas son 3 afirmaciones verdaderas sobre esta jarra de leche.
Esta jarra contiene 1 galón de leche.
Esta jarra contiene 4 cuartos de galón de leche.
Esta jarra contiene 16 tazas de leche.
Completa cada afirmación para que sea verdadera:
Un galón es __________ veces 1 cuarto de galón.
Un galón es __________ veces 1 taza.
Un cuarto de galón es __________ veces 1 taza.
Para una fiesta en la que se comparte comida, Priya y otros 3 familiares traen lassi de mango.
¿Quién preparó la mayor cantidad de lassi de mango? Explica o muestra cómo razonaste.
guest
amount of lassi
Priya
10 tazas
tío
3 cuartos de galón
primo
8 tazas
abuela
2 galones
¿Cuántas tazas de lassi en total trajeron los invitados?
Completa esta oración: La abuela de Priya preparó __________ veces la cantidad de lassi que preparó el primo de Priya. Muestra cómo lo sabes.
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 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?”
Activity 2
15 mins
Plastilina para la clase de arte
Standards Alignment
Building On
Addressing
4.MD.1
Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), …
Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
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.
Launch
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.
MLR6 Three Reads
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. Una 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.)
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 pounds).
Student Task Statement
En un almacén de manualidades, la plastilina se vende en paquetes de diferentes tamaños: 1 libra, 24 onzas, 3 libras y 5 libras.
Una profesora de arte necesita 120 onzas de plastilina para su clase.
Si ella compra una de cada una de las siguientes combinaciones, ¿tendría suficiente plastilina? Explica o muestra cómo razonaste.
paquete de 1 libra
paquete de 24 onzas
paquete de 3 libras
paquete de 5 libras
A
1
1
B
1
1
1
1
C
1
2
En cada caso, decide si la afirmación es verdadera o falsa. Explica o muestra cómo razonaste.
Un paquete de 3 libras pesa 2 veces lo que pesa un paquete de 24 onzas.
Si combinamos un paquete de 1 libra, un paquete de 3 libras y un paquete de 5 libras, tendríamos 6 veces lo que tiene un paquete de 24 onzas.
Student Response
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Advancing Student Thinking
Activity Synthesis
Select students to briefly share their responses and their reasoning.
“¿Alguien llegó a la misma conclusión, pero razonó de otra forma?” // “Did anyone reach the same conclusion but reasoned in a different way?”
Lesson Synthesis
“Hoy, para resolver problemas, convertimos una unidad en otra unidad (primero de galones a cuartos de galón o tazas, o al contrario; después, de libras a onzas, o al contrario). Convertir medidas nos ayuda a hacer comparaciones, a encontrar cantidades totales y a muchas cosas más” // “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
“Si alguien dijera que 3 cuartos de galón es más que 2 galones porque 3 es mayor que 2, ¿cómo le explicarían que esto no es cierto? ¿Qué le corregirían?” // “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.)
“Si alguien dijera que 24 onzas es 8 veces 3 libras, ¿estarían de acuerdo? ¿Por qué sí o por qué no?” // “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.)
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