The purpose of this Warm-up is to elicit the idea that 3 groups of 40 can also be seen as 12 groups of 10, which will be useful when students multiply one-digit whole numbers by multiples of 10 in a later activity. While students may notice and wonder many things, seeing that the total can be decomposed into rows of 30 and further decomposed into units of 10 are the important discussion points.
Launch
Groups of 2
Display the image.
“¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
“Discutan con su pareja cómo pensaron” // “Discuss your thinking with your partner.”
1 minute: partner discussion
Share and record responses.
¿Qué observas? ¿Qué te preguntas?
Student Response
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Advancing Student Thinking
Activity Synthesis
“¿Qué valor está representado por el diagrama?” // “What is the value the diagram represents?” (120)
“¿Cómo nos puede ayudar ver los grupos de diez a encontrar el número total de cuadrados?” // “How could noticing groups of tens help us find the total number of squares?” (There are 3 groups of 4 tens, which is 12 tens. There are 4 groups of 30, which is 12 tens. We could count by tens to find the total. We know 12 tens would be 120.)
Record equations that reflect student thinking, such as and .
Activity 1
Standards Alignment
Building On
Addressing
3.NBT.A.3
Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., , ) using strategies based on place value and properties of operations.
The purpose of this activity is for students to work with products of whole numbers and multiples of 10 in a concrete and familiar context before reasoning more abstractly about them. Given some numbers of dollar bills (for instance, four \$20 bills), students write expressions to represent the amount () and then find its value using strategies that make sense to them. For example, students may count by 20 four times or think of \$20 in terms of two \$10 bills and find (or ). Consider giving students access to play money, if available, to help them visualize the quantities and support their reasoning.
The reasoning here prompts students to use strategies based on place value and properties of operations (especially the associative property). It prepares students to work more flexibly with products involving factors and multiples of 10 in which the product is greater than 100.
MLR8 Discussion Supports. Prior to solving the problems, invite students to make sense of the situations and take turns sharing their understanding with their partner. Listen for and clarify any questions about the context. Advances: Reading, Representing
Engagement: Develop Effort and Persistence. Check in and provide each group with feedback that encourages collaboration and community. For example, ensure that each member of the group has a chance to share their solution and thinking. Supports accessibility for: Social-Emotional Functioning
Launch
Groups of 2
“Vamos a resolver un problema sobre un juego en el que se usa dinero de juguete. ¿Qué saben sobre los juegos en los que se usa dinero de juguete?” // “We’re going to solve a problem about a game that involves play money. What do you know about games that involve play money?”
1 minute: quiet think time
Share responses.
Give students access to base-ten blocks, grid paper, and play money, if available.
Activity
“Completen los problemas con su compañero” // “Work with your partner to complete the problems.”
7–10 minutes: partner work time
In the last problem monitor for students who use the following strategies to highlight in the Activity Synthesis:
Count by multiples of 10 to find a total, such as 50, 100, 150, 200, 250, 300.
Use place value to find a total, such as knowing that 14 tens is 10 tens or 100, and 4 more tens or 40, which makes 140.
6 amigos juegan un juego de mesa en el que se usa dinero de juguete. Hay billetes de papel con valores de \$5, \$10, \$20, \$50 y \$100.
Cada jugador empieza con \$100. ¿Cuáles de los siguientes podrían ser los billetes que recibe cada jugador al comienzo?
Escribe una expresión que represente los billetes de juguete y escribe la cantidad de dólares.
billetes
expresión
cantidad de dólares
un billete de \$100
cuatro billetes de \$20
diez billetes de \$10
diez billetes de \$5
cinco billetes de \$20
veinte billetes de \$10
veinte billetes de \$5
dos billetes de \$50
En el juego, Noah tuvo que pagarle \$150 a Lin. Le dio esa cantidad usando billetes del mismo tipo.
¿Cuáles y cuántos billetes podría haber usado Noah para completar \$150? Escribe todas las posibilidades.
Escribe una expresión para cada forma en la que Noah podría haberle pagado a Lin.
La tabla muestra lo que tenían los jugadores al final del juego. Ganaba la persona con más dinero. ¿Quién ganó?
Escribe una expresión que represente los billetes que tenía cada persona y escribe la cantidad de dólares.
jugador
billetes
expresión
cantidad de dólares
Andre
nueve billetes de \$10 y diez billetes de \$5
Clare
catorce billetes de \$10
Jada
diez billetes de \$10 y tres billetes de \$50
Lin
ocho billetes de \$20
Noah
seis billetes de \$50
Tyler
veintiún billetes de \$10
Activity Synthesis
Invite students to share different combinations of the same bill that could be used to make \$150. Record and display expressions for each combination.
Select previously identified students to share their strategies for how they found one of the totals in the last problem.
Activity 2
Standards Alignment
Building On
Addressing
3.NBT.A.3
Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., , ) using strategies based on place value and properties of operations.
The purpose of this activity is for students to continue to reason about products of a whole number and a multiple of 10, this time using base-ten blocks or base-ten diagrams to support their thinking. Students analyze two strategies for multiplying. Both strategies are based on place value, but the second strategy also uses the associative property to think about as or .
Launch
Groups of 2
“Durante un momento, examinen las estrategias de Jada y de Kiran para multiplicar ” // “Take some time to look at Jada and Kiran’s strategies for multiplying .”
30 seconds: quiet think time
“Hablen con su compañero sobre cómo podemos ver las estrategias de Jada y de Kiran en el diagrama” // “Talk to your partner about how we can see Jada and Kiran’s strategies in the diagram.” (We can see Jada’s skip-counting by 30 in the rows. The 8 in Kiran’s strategy is the 8 rows and the 3 is the 3 tens in each row, so there are 24 tens.)
2–3 minutes: partner discussion
Share responses.
Give students access to grid paper and base-ten blocks.
Activity Synthesis
Select 2–3 students who used a strategy based on the associative property (for example, thinking of as 28 tens) to share their responses.
Consider asking:
“¿En qué parte del trabajo de _____ vemos la expresión original?” // “Where do we see the original expression in _____’s work?”
“¿Cómo cambió _____ la expresión original para que fuera más fácil encontrar el total?” // “How did _____ change the original expression to make it easier to find the total?”
“¿Cómo funciona la estrategia para multiplicar que usó _____?” // “How does _____’s strategy for multiplying work?”
Lesson Synthesis
“Hoy multiplicamos números enteros de un dígito por múltiplos de 10” // “Today we multiplied one-digit whole numbers by multiples of 10.”
“¿Cómo nos ayudó pensar en decenas a encontrar el valor de los productos que eran mayores que los que habíamos encontrado antes?” // “How did thinking about tens help us find the value of products that were greater than we had found before?” (Using tens helped us count or multiply a lot faster. If we know , we can think of that many tens to find . We can use what we already know to find other products.)
“¿Qué estrategias fueron útiles cuando multiplicaron números enteros de un dígito por múltiplos de 10?” // “What were some strategies that were helpful as you multiplied one-digit whole numbers by multiples of 10?” (Decomposing one of the factors and finding smaller products. Using place value to multiply by 10 since we know 10 tens is 100.)
Standards Alignment
Building On
Addressing
3.NBT.A.3
Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., , ) using strategies based on place value and properties of operations.
If students don’t find the product of one-digit whole numbers and multiples of 10 in the last problem, consider asking:
“¿Qué has intentado hasta ahora para encontrar el producto?” // “What have you tried so far to find the product?”
“¿Cómo podrías representar el producto con bloques en base diez?” // “How could you represent the product with base-ten blocks?”
Activity
“Trabajen en el primer problema con su compañero” // “Work with your partner on the first problem.”
2–3 minutes: partner discussion
Invite students to share how the strategies are alike and how they’re different
“¿Cómo pudo Kiran convertir en ?” // “How was Kiran able to turn into ?” ( is 8 groups of 3 tens, so that’s 24 tens. You can see and in the same diagram, so they are the same amount.)
“Ahora encuentren el valor de los demás productos con su compañero” // “Now, work with your partner to find the value of other products.”
5–7 minutes: partner work time
Monitor for students who use the associative property as a strategy to highlight during the Activity Synthesis.
Dos estudiantes usaron bloques en base diez para encontrar el valor de .
Ellos dibujaron este diagrama para mostrar los bloques.
Jada contó: 30, 60, 90, 120, 150, 180, 210, 240. Dijo que el producto es 240.
Kiran dijo que él sabía que es 24. Después encontró el valor de y obtuvo 240.
¿En qué se parecen las estrategias de Jada y de Kiran? ¿En qué son diferentes?
Encuentra el valor de cada expresión. Explica o muestra tu razonamiento.
