# Lesson 6

¿Cuánto es 10,000?

## Warm-up: ¿Qué sabes acerca del 1,000? (10 minutes)

### Narrative

The purpose of this What Do You Know About _____? is to invite students to share what they know and how they can represent the number 1,000. This routine allows teachers to collect information about students' ideas about the relative magnitude of 1,000.

### Launch

• Display the number.
• “¿Qué saben acerca del 1,000?” // “What do you know about 1,000?”
• 1 minute: quiet think time

### Activity

• Record responses.
• “¿Cómo podríamos representar el número 1,000?” // “How could we represent the number 1,000?”

### Student Facing

¿Qué sabes acerca del 1,000?

### Activity Synthesis

• “¿Pueden recordar alguna vez en la que hayan visto 1,000 de algo?” // “Can you think of a time you have seen 1,000 of something?”

## Activity 1: Construyamos números (15 minutes)

### Narrative

The purpose of this activity is to generate, say, and represent multi-digit numbers. Students arrange digit cards to create multi-digit numbers, and use base-ten blocks to represent each number. Teachers should remove cards showing 1 before distributing the set of digit cards, as they will be used later in the activity.

As students build numbers to the ten-thousands place, they may struggle to name the number. As they make sense of the value of the number, they should realize a need for more base-ten blocks, but should be given space to represent the number in a way that makes sense to them. It is not critical to name the number correctly or accurately describe how to build it. The idea is to create a bit of struggle to motivate another way to make sense of the number (MP1). Students see one way to represent 10,000 in the next activity.

Engagement: Develop Effort and Persistence. Check in with groups and provide feedback that encourages collaboration and community. Look for instances of students supporting each other’s understanding, as well as students ensuring that each group member is participating in the activity. Consider pausing the activity to share these instances (including specific language and actions) with the whole class.
Supports accessibility for: Attention, Social-Emotional Functioning

### Required Materials

Materials to Gather

Materials to Copy

• Build Numbers (1-5 Digit Cards)

### Required Preparation

• Create a set of cards from the blackline master for each group of 4. Remove the cards showing 1. These cards will be redistributed during the activity.
• Each group of 4 needs a small collection of base-ten blocks (for instance: 2 thousands, 5 hundreds, 10 tens, and 20 ones).

### Launch

• Groups of 4
• Give each group a small set of base-ten blocks and a set of number cards. Ask them to find all the cards that show 2, 3, 4, or 5 and put the rest of the cards aside.

### Activity

• “Vamos a crear números usando tarjetas de dígitos” // “We are going to create numbers with digit cards.”
• “Presten mucha atención a las instrucciones porque no siempre van a usar todas las tarjetas” // “Pay close attention to the directions because you will not use all the cards each time.”
• “Tómense un minuto para leer las dos primeras instrucciones y piensen qué preguntas surgen luego de leer” // “Take a minute to read the first two directions and think about any questions you have after reading them.”
• 1 minute: Collect and answer questions.
• 5 minutes: group work time
• Monitor for students who:
• rearrange digits to make a new number and representation each time
• add a digit to each number without rearranging digits
• Provide each group with the digit “1” and say “Asegúrense de que el 1 sea el primer dígito de su número (el de más a la izquierda)” // “make sure the 1 is the first digit in your number.”
• 5 minutes: group work time

### Student Facing

1. Usa dos tarjetas para formar un número de dos dígitos. Nombra el número y constrúyelo con bloques en base diez.
2. Usa una tercera tarjeta para formar un número de tres dígitos. Nombra el número y constrúyelo con bloques en base diez.
3. Usa una cuarta tarjeta para formar un número de cuatro dígitos. Nómbralo y constrúyelo.

Si no tienes suficientes bloques, describe qué necesitarías para construir el número.

4. Tu profesor te va a dar otra tarjeta de dígitos. Usa esta última tarjeta para formar un número de cinco dígitos (haz que la nueva tarjeta sea el primer dígito). Nombra y construye el número que formaste.

Si no tienes suficientes bloques, describe los bloques que necesitarías para construir el número.

### Advancing Student Thinking

Students may recognize that it is challenging to represent numbers greater than 1,000 with a small set of base-ten blocks. Consider asking:

• “¿Tienes bloques suficientes para representar el número?” // “Do you have enough blocks to represent the number?”
• “Si tuvieras bloques suficientes, ¿cuáles usarías?” // “If you had enough blocks, which would you use?”
• “¿Qué podrías dibujar o escribir para explicarle esto a un compañero?” // “What could you draw or write to explain this to a classmate?”

### Activity Synthesis

• “¿Cómo construirían 9,000?” // “How would you build 9,000?” (Use 9 of the large cubes)
• “¿Qué número formaríamos si añadiéramos un 1,000 más?” // “What number would we make if we add one more 1,000?” (10,000)

## Activity 2: ¿Qué es 10,000? (20 minutes)

### Narrative

The purpose of this activity is to develop a sense of the magnitude of 10,000 and to establish ten-thousand as a unit consisting of 10 units of one-thousand.

In the launch, students learn that the 10-by-10 grid that represented 1 whole in a previous section now represents 100 in this activity. (It is important to establish that in these representations, each small square in the grid represents 1.) Students begin by organizing grids of 100 into groups of 1,000. Some students may intuitively decide to group grids by ten, while others may depend on counting each grid by 100. In the synthesis, students are invited to use their grids to create a class chart to show 10,000 as 10 units of one-thousand.

MLR8 Discussion Supports. Students should take turns using the 10-by-10 grids to represent a given number and explaining their reasoning to their group. Encourage students to challenge each other when they disagree. Display the following sentence frames for all to see: “Observé _____, entonces usé . . .” // “I noticed _____ , so I used . . .” and “Estoy en desacuerdo porque . . . ” // “I disagree because . . . .”
Advances: Representing, Speaking, Conversing

### Required Materials

Materials to Copy

• 10-by-10 Square Grids

### Launch

• Groups of 4
• Give each student a copy of the black line master.
• Display the 10-by-10 grid
• “¿Qué cantidad está representada por esta cuadrícula?” // “What amount is represented by this grid?” (1, 100, $$\frac{100}{100}$$)
• “En la sección anterior, usamos una cuadrícula como esta para representar decimales y fracciones. En esta sección, esta cuadrícula va a representar centenas, como las que hay en los bloques de valor posicional” // “In the previous section a grid like this was used to represent decimals and fractions. In this section this grid will represent hundreds like those found in place value blocks.”
• “En la siguiente actividad, vamos a practicar cómo construir números usando estas cuadrículas” // “We are going to practice building numbers using these grids during the next activity.”
• “En grupo, construyan números usando las cuadrículas de 10 por 10” // “Work together to build numbers using 10-by-10 grids.”

### Activity

• 10 minutes: group work time
• Monitor for students who organize the grids in groups of 1,000.
• As students work, consider asking,
• “¿Cómo están agrupando sus cuadrículas?” // “How are you grouping your grids?”
• “¿Por qué decidieron agrupar sus cuadrículas de esa manera?” // “Why did you decide to group your grids that way?”

### Student Facing

Tu profesor te va a dar varias cuadrículas de 10 por 10.

1. Usa las cuadrículas para representar cada uno de los siguientes números. Luego, describe tu representación o dibújala.

1. 800

2. 1,000

3. 1,500

4. 2,000

2. ¿Cuántas cuadrículas de 10 por 10 necesitarías para representar cada uno de los siguientes números? Explica o haz un dibujo para mostrar tu razonamiento.

1. 3,000

2. 6,400

3. 9,000

4. 9,900

3. Haz un dibujo para representar 10,000 usando cuadrículas de 10 por 10. Asegúrate de marcar claramente cada grupo de 1,000 en tu dibujo.

### Advancing Student Thinking

Students may be unsure how to represent larger numbers in the thousands with the grids. Encourage them to represent numbers in the hundreds and work their way up, by adding more hundreds (one at a time, if helpful).

### Activity Synthesis

• “Organicemos nuestras cuadrículas en grupos de 1,000 para hacer un póster de 10,000. ¿Qué tan grande creen que será el póster?” // “Let’s organize our grids into groups of 1,000 to make a chart of 10,000. How large do you think the chart is going to be?” (Sample responses: As big as the wall, the length of the whiteboard.)
• Combine groups of 10-by-10 grids to form 10 rows of 1,000 to create a class chart of 10,000.
• Choral count by 1,000 and highlight how the chart reflects the count.
• “Anotemos los grupos de 1,000 en el póster a medida que contamos” // “Let’s record the groups of 1,000 on the chart as we count.”

## Lesson Synthesis

### Lesson Synthesis

“Hoy trabajamos con números grandes y usamos bloques en base diez, cuadrículas y dibujos para representar cada número de varios dígitos. También usamos grupos de centenas para construir 10,000” // “Today we worked with large numbers, we used base-ten blocks, grids, and drawings to represent each multi-digit number, and we used groups of hundreds to build 10,000.”

“En primer grado, aprendimos que hay 10 unidades en cada decena. La decena es una unidad de diez. En segundo grado, aprendimos que hay 10 decenas en cada centena. La centena es una unidad de cien. Si agrupamos 10 centenas (es decir, 10 unidades de cien), obtenemos una nueva unidad en base diez: la unidad de mil” // “In first grade, we learned that 10 ones are in each unit of ten. In second grade, we learned that 10 tens are in each unit of one hundred. If we count 10 units of a hundred, we have a thousand, which is a new unit.”

“¿En qué parte de este póster observan que se forma una nueva unidad en base diez con diez de algo?” // “Where in this class chart do you see ten of something making a new unit?” (Ten of the hundred grids make a row or a unit of one thousand. Ten of the thousand rows make a unit of ten-thousand.)

“Si fuéramos a representar un número como 13,000, ¿cómo lo haríamos?” // “If we were going to represent a number like 13,000, how might we do this?” (Add three more rows of 1,000 to the chart.)

“¿Cuál creen que será la unidad en base diez que sigue después de la unidad de diez mil?” // “What do you think the next unit will be after ten-thousands?” (Students may guess hundred-thousands or millions.)

“Diez grupos de diez mil forman una nueva unidad en base diez: la unidad de cien mil. Vamos a aprender acerca de esta unidad en base diez en lecciones posteriores” // “Ten groups of ten-thousand makes a new unit, hundred-thousand. We will learn about this unit in future lessons.”