The purpose of this Number Talk is to elicit the strategies and understandings students have for multiplying three factors, one of which is 10. These understandings help students develop fluency and will be helpful when they apply the standard algorithm to find the product of a three-digit and a two-digit number.
Students have an opportunity to look for and make use of structure (MP7) because they can use previous calculations and the distributive property to find a product.
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.
Encuentra mentalmente el valor de cada producto.
Student Response
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Advancing Student Thinking
Activity Synthesis
“¿Cómo influyó en el resultado haber multiplicado todos los productos por 10?” // “How did multiplying all the products by 10 influence the result?” (It made the result ten times as big, so the digits all shift one place to the left and it has a zero at the end.)
“¿Cómo se relacionan los productos y ?” // “How are the products and related?” (The second one is ten times as big, so the digits shift one place to the left and it has a 0 at the end.)
“Pueden usar esta idea hoy cuando usemos el algoritmo estándar para encontrar productos de números de tres dígitos por números de dos dígitos” // “You can use this idea today when we apply the standard algorithm to find the products of a three-digit number and a two-digit number.”
Activity 1
Standards Alignment
Building On
Addressing
5.NBT.B.5
Fluently multiply multi-digit whole numbers using the standard algorithm.
The goal of this activity is to use the standard algorithm to find the products in which composition of a new unit happens once. Students first calculate a three-digit-number-by-two-digit-number example, using a strategy of their choice, and then analyze the same example, with the composition recorded above the product. Students may use different strategies when they try on their own including:
Partial products.
Mentally accounting for the hundred that is composed when finding the product .
After students discuss how composing new units is recorded in the algorithm, they find the value of two multiplication expressions, using the standard algorithm.
When students interpret a new way of multiplying a three-digit number by a two-digit number, they use their understanding of place value to make sense of the method (MP7).
MLR8 Discussion Supports.Synthesis: At the appropriate time, give groups 2–3 minutes to plan what they will say when they present to the class. “Practiquen lo que van a decir cuando compartan con la clase lo que representa cada número en el problema de Lin. Hablen sobre qué es importante decir y decidan quién va a compartir cada parte” // “Practice what you will say when you share with the class what each number represents in Lin’s problem. Talk about what is important to say, and decide who will share each part.” Advances: Speaking, Conversing, Representing
Launch
Groups of 2
“Ahora van a aprender cómo componer y registrar nuevas unidades en base diez cuando están encontrando el producto de un número de tres dígitos por un número de dos dígitos” // “Now you are going to learn how to compose and record new units for a three-digit-number-by-two-digit-number product.”
Activity
“Trabajen con su compañero en los primeros 2 problemas” // “Work with your partner on the first 2 problems.”
2-3 minutes: independent work time
5-7 minutes: partner work time
Encuentra el valor de .
Lin usa el algoritmo estándar para encontrar el valor de .
multiply. two hundred forty one times 23. 5 rows. First row: two hundred forty one. Second row: multiplication symbol, 23. Horizontal line. Third row: seven hundred twenty three. Fourth row: plus four thousand eight hundred twenty. Horizontal line. Fifth row: five thousand five hundred forty three
¿Dónde ves en el trabajo de Lin?
¿Dónde ves en el trabajo de Lin?
¿Qué representa el 1 encima de 241 en el cálculo de Lin?
Usa el algoritmo estándar para encontrar el valor de .
Usa el algoritmo estándar para encontrar el valor de .
Activity Synthesis
Invite students to share how they interpret Lin’s work of finding .
Display the image of Lin’s calculation.
Circle the 2 in the number 723 in Lin’s calculation.
“¿Qué representa el 2 que está en la posición de las decenas?” // “What does the 2 in the tens place represent?” (It’s 2 of the tens from .)
“¿Qué hizo Lin con las otras 10 decenas?” // “What does Lin do with the other 10 tens?” (She makes 1 hundred out of them and puts them together with the other hundreds when she multiplies 200 by 3.)
Circle the 1 above 241 in Lin's work.
“¿Qué representa este 1?” // "What does this 1 represent?" (It’s the hundred from .)
Circle the partial product 4,820.
“¿Qué representa 4,280 en el cálculo?” // “What does 4,820 represent in the calculation?” (. The 2 from the factor 23 is in the tens place and so it represents 20.)
“Ahora tómense unos minutos para resolver los últimos dos problemas” // “Now take a few minutes to solve the last two problems.”
4-5 minutes independent work time
Invite students to share the products, and ask them what questions they have about the standard algorithm with composition.
Activity 2
Standards Alignment
Building On
Addressing
5.NBT.B.5
Fluently multiply multi-digit whole numbers using the standard algorithm.
The goal of this activity is to multiply numbers with no restrictions on the number of new units composed. Students first multiply a three-digit number by a one-digit number and a three-digit number by a two-digit number, with no ones. They then can put these two results together to find the product of a three-digit number and two-digit number, with many compositions. They then solve another three-digit-number-by-two-digit-number example, with no scaffolding. Because these calculations have new units composed in almost every place value, students will need to locate and use the composed units carefully. It gives students a reason to attend to the features of their calculation and to use language precisely (MP6).
Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. Check in with students to provide feedback and encouragement after each chunk. Supports accessibility for: Organization, Conceptual Processing
Launch
Groups of 2
“Van a encontrar productos en los que se componen muchas unidades en base diez nuevas. Mientras trabajan, piensen con cuidado en dónde poner estos valores” // “You are going to find products with many new composed units. As you work, think carefully about where you place these values.”
Activity
8–10 minutes: independent work time
3–5 minutes: partner discussion
Monitor for students who:
Use the results of the first two calculations to find the third calculation.
Correctly compose all the new place values.
Usa el algoritmo estándar para encontrar el valor de cada producto.
Student Response
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Advancing Student Thinking
Activity Synthesis
Display the expression: .
“¿Cómo les ayudaron los primeros dos cálculos a resolver el tercer problema?” // “How did you use the first two calculations to help with the third problem?” (They gave me the two partial products for the product , so I just had to add them up.)
Invite students to share their responses for the last product, focusing on the newly composed units.
Lesson Synthesis
“Hoy practicamos cómo usar el algoritmo estándar para multiplicar números de varios dígitos componiendo nuevas unidades en base diez” // “Today, we practiced using the standard algorithm to multiply multi-digit numbers with new units composed.”
“¿En qué deben pensar cuando están multiplicando y se componen muchas nuevas unidades?” // “What do you have to think about when you are multiplying and a lot of new units are composed?” (I have to keep track of how I record the units. I can make an estimate to see if my answer is reasonable.)
Display students’ work for , from Activity 2, or use the example from the Student Responses:
multiply. two hundred sixty four times 38. 5 rows. First row: two hundred sixty four. Second row: multiplication symbol, 38. Horizontal line. Third row: two thousand one hundred twelve. Fourth row: plus seven thousand nine hundred twenty. Horizontal line. Fifth row: ten thousand thirty two
“¿En dónde tuvimos que componer nuevas unidades cuando resolvimos este problema?” // "Where did we compose new units when we solved this problem?" (When we multiplied to find the two partial products, we had to compose new units above the 2 and the 6 in 264. When we added the partial products, we composed a new 1 thousand above the 2.)
“¿En qué se parece componer nuevas unidades cuando multiplicamos a componer nuevas unidades cuando sumamos?” // "How is composing new units when we multiply the same as composing new units when we add?" (When we multiply or add numbers, sometimes we get a value that's too much for the place we’re in. The composed units are recorded separately, and then we add them.)
“¿En qué se diferencia componer nuevas unidades cuando multiplicamos a componer nuevas unidades cuando sumamos?” // "How is composing new units when we multiply different from composing new units when we add?" (When we multiply, we are multiplying and then adding the new units. When we add, we are adding the whole time, there is no multiplication.)
Standards Alignment
Building On
Addressing
5.NBT.B.5
Fluently multiply multi-digit whole numbers using the standard algorithm.
