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Activity 1

Standards Alignment

Building On

Addressing

Instructional Routines

MLR1 Stronger and Clearer Each Time

Materials

None

Activity Narrative

In this activity, students make sense of the relationships between the values of the same digit in different numbers, and write multiplication and division equations to represent these relationships.

As they complete and analyze the table, students recognize that the value of the digit in one row is ten times as much as the value of the digit in the row below. Students work to articulate these relationships precisely, using words and equations, and receive feedback from their peers on the equations they are writing. During the Activity Synthesis, students discuss why a multiplication or a division equation can be used to represent the same relationship.

When students express place value relationships with multiplication and division they observe structure in the place values (MP7). When they help one another improve their explanations, they critique each other's reasoning (MP3).

This activity uses MLR1 Stronger and Clearer Each Time. Advances: reading, writing.

Launch

Groups of 2

Activity

MLR1 Stronger and Clearer Each Time

5 minutes: independent work
“Compartan con su compañero su respuesta al segundo problema. Por turnos, uno habla y el otro escucha. Si es su turno de hablar, compartan sus ideas y lo que han escrito hasta ese momento. Si es su turno de escuchar, hagan preguntas y comentarios que ayuden a su compañero a mejorar su trabajo” // “Share your response to the second problem with your partner. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”
3–5 minutes: structured partner discussion
Repeat with 2–3 different partners.
If needed, display question starters and prompts for feedback.
- “¿Pueden dar un ejemplo que ayude a mostrar . . . ?” // “Can you give an example to help show . . . ?”
- “¿Pueden usar la palabra _____ en su explicación?” // “Can you use the word _____ in your explanation?”
- “Ajusten su borrador inicial basándose en los comentarios que les hicieron sus compañeros” // “Revise your initial draft based on the feedback you got from your partners.”
2–3 minutes: independent work time
Monitor for students who write a multiplication and division equation to represent the relationship between the values of the 8 in two different numbers.

Completa la tabla escribiendo cuál es el valor que tiene el 8 en cada número.

180,000

número	valor del 8
180,000
108,000
100,800
100,080
100,008

Describe la relación que hay entre los valores del 8 en cada número.
Escribe una ecuación de multiplicación o de división para representar la relación que hay entre los valores del 8 en dos números diferentes de la tabla.

Student Response

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Advancing Student Thinking

Activity Synthesis

Select 1-2 students to share a multiplication and a division equation.

Activity 2

Standards Alignment

Building On

Addressing

Instructional Routines

None

Materials

None

Activity Narrative

In this activity, students use the context of money to deepen their understanding of the relationship between the value of digits in different places—by counting equal groups of tens, hundreds, thousands, and ten-thousands. Writing the value of each stack of bills reinforces the “ten times” relationship between the place values, which supports students in writing multiplication and division equations (MP7).

If play money is available, consider creating a counting collection. Ask students to organize each stack and write equations to represent the stacks of bills. Ultimately, students evaluate the expressions used by different groups and discuss the reasoning behind each equation.

Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts by providing scaffolding questions. For example, you might help students approach question 2 by saying, “Empecemos por explorar la relación que hay entre el montón de billetes de diez y el montón de billetes de cien. ¿Qué relación hay entre y ?” // “Let’s start by looking at the relationship between the stack of tens and the stack of hundreds. What is the relationship between and ?” For question 3, you might say, “¿Cuál es el valor del montón de billetes de mil? ¿Cuál es el valor del montón de billetes de diez mil? ¿Qué tipo de ecuación quieren escribir para mostrar la relación que hay entre estos dos valores?” // “What is the value of the stack of thousands? What is the value of the stack of ten-thousands? What kind of equation do you want to write to show the relationship between these two values?”
Supports accessibility for: Conceptual Processing, Organization, Attention

Launch

Groups of 2
“Tómense un minuto para leer las instrucciones de la actividad y explicárselas a su compañero” // “Take a minute to read over the directions to the activity and explain them to a partner.”

Activity

5 minutes: independent work
10 minutes: partner work
As students work, monitor for the different ways they describe the relationship between the stack of bills.
- Each stack has the same number of bills but have different values.
- The value of some stacks can be multiplied by ten to have the same value as another stack.

En la clase de Matemáticas de Diego cuentan colecciones de dinero de juguete. Hay 4 tipos de billetes: de diez, de cien, de mil y de diez mil.

Diego encuentra 9 billetes de cada tipo. Él organiza los billetes en 4 montones, uno para cada tipo de billete.

¿Cuánto dinero hay en cada montón de billetes?
1. 9 de diez
2. 9 de cien
3. 9 de mil
4. 9 de diez mil
Describe la relación que hay entre los valores de cada montón de billetes.
¿Cómo se relaciona el valor del montón de billetes de mil con el valor del montón de billetes de diez mil? Escribe una ecuación para mostrar esta relación.
Clare tiene 21 billetes de cada tipo. ¿Cuánto dinero tiene Clare en cada montón de billetes?
1. 21 de diez
2. 21 de cien
3. 21 de mil
4. 21 de diez mil
¿Cuál es el valor del 2 en cada montón de billetes?
¿Cómo se relaciona el valor del 2 en el montón de mil con el valor del 2 en el montón de diez mil? Escribe una ecuación para mostrar esta relación.

Activity Synthesis

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Lesson 10

Diez veces el valor

Warm-up

Instructional Routines

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Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Activity 1

Standards Alignment

Building On

Addressing

4.NBT.A.1

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Activity 2

Standards Alignment

Building On

Addressing

4.NBT.A.1

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Activity Synthesis

Lesson Synthesis

Standards Alignment

Building On

Addressing

4.NBT.B.4

Building Toward

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Advancing Student Thinking

Building Toward

4.NBT.A.2

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