# Lesson 6

Representemos números de distintas formas

## Warm-up: Cuál es diferente: Números de distintas formas (10 minutes)

### Narrative

This warm-up prompts students to carefully analyze and compare four different representations of three-digit numbers. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear the terminologies students know and how they talk about place value and different representations of numbers.

### Launch

• Groups of 2
• Display the image.
• “Escojan una que sea diferente. Prepárense para compartir por qué es diferente” // “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

### Activity

• “Discutan con su compañero lo que pensaron” // “Discuss your thinking with a partner.”
• 23 minutes: partner discussion
• Share and record responses.

### Student Facing

¿Cuál es diferente?

### Activity Synthesis

• “¿Cuáles representaciones fueron las más útiles para entender el valor del número? Expliquen” // “Which representations best help you understand the value of the number? Explain.” (A has a lot of words to read, so I prefer C. D tells you how many of each. With B you just have to count the blocks.)
• “A nos muestra 325 representado solamente en palabras. Ustedes tendrán la oportunidad de hacer esto en la siguiente actividad” // “A shows us 325 represented using only words. You will have a chance to do this in the next activity.”

## Activity 1: Los números en palabras (15 minutes)

### Narrative

The purpose of this activity is for students to use words to represent three-digit numbers. Students are given numbers represented in different ways and asked to represent the same number in another way, including using words. Spelling numbers might present a challenge for some students. As students learn to spell and write numbers, encourage them to say the name aloud and then write it down. Also encourage them to use what they know about place value to say and write the name. Consider using an anchor chart or poster with words, including the words for numbers 0 to 20 and the multiples of ten, to provide support in this activity and later lessons.

### Required Materials

Materials to Gather

### Required Preparation

• Prepare an anchor chart for the launch showing:
• 253 represented with a base-ten diagram.
• This number has _____ hundreds, _____ tens, and _____ ones.
• The expanded form of this number is _____________________.
• The three-digit number is _____________________.

### Launch

• Groups of 2
• Display the anchor chart that shows the different forms of 253.
• Complete the chart together.
• “Este número tiene _____ centenas, _____ decenas y _____ unidades” // “This number has _____ hundreds, _____ tens, and _____ ones.” (2, 5, 3)
• “La forma desarrolla de este número es ______________________” // “The expanded form of this number is ______________________.”
• “El número de tres dígitos es ________________” // “The three-digit number is ________________.”
• “Estas otras formas nos pueden ayudar a pensar sobre la escritura de un número usando números en palabras” // “These other forms can help us think about writing a number using number names.”
• “¿Cuál es este número?” // “What is this number?” (two hundred fifty-three)
• Write the number name as the students say two hundred fifty-three.
• “En inglés, cincuenta y tres se escribe ‘fifty-three’ porque todos los números del 21 al 99 que tienen decenas y unidades se escriben con un guión para mostrar las 2 partes que tienen” // “In English, fifty-three has a hyphen because numbers with tens and ones representing 21 through 99 use a hyphen to show the 2 parts of a two-digit number.”
• “En español, cincuenta y tres tiene una ‘y’. Los números del 31 al 99 se escriben usando una ‘y’ para mostrar las 2 partes que tienen. Para los números de 16 a 29, ambas palabras se juntan en una, como veintitrés en vez de 'veinte y tres'” // “In Spanish, fifty-three is written as cincuenta y tres. Numbers between 31 and 99 use the word y to show the 2 parts of a two-digit number. Numbers between 16 and 29 change the y to i and join the 2 parts together, such as veintitrés instead of veinte y tres.

### Activity

• “En cada pregunta, encuentren con su compañero las palabras para describir cada número. Piensen en cuándo necesitarían usar una ‘y’” // “For each question, work with your partner to figure out the names of each number. Think about when you will need to use a hyphen.”
• 8 minutes: partner work time
• Monitor for the different ways students represent 318. Look for examples of:
• base-ten diagrams
• unit form
• expanded form
• three-digit number
• number name

### Student Facing

1. Llena los espacios en blanco para representar 248 en palabras.

dos ___________________ cuarenta y ________________

2. Llena los espacios en blanco para representar 562 con palabras.

______________  _____________ y _______

3. Representa este número con palabras.

4. Representa 627 con palabras.

5. Representa $$900 + 50 + 1$$ con palabras.

6. Representa trescientos dieciocho de dos formas distintas.

### Activity Synthesis

• Invite previously selected students to share their representations of 318.
• As needed, ask students how 318 could be represented in forms that you did not see them use during the activity.
• “¿Cuál representación tiene más sentido para ustedes?” // “Which representation makes the most sense to you?”
• “¿Cómo pueden usar esa representación como ayuda para entender las otras?” // “How can you use that representation to help you understand the others?”

## Activity 2: Representemos los números (20 minutes)

### Narrative

The purpose of this activity is for students to represent numbers in all the ways they have seen so far in this unit. Students are given a number in one form and they represent the same number in different ways. In the synthesis, students share which representations are most helpful. When students relate the different ways to represent a three-digit number (words, expanded form, diagrams, numerals) they deepen their understanding of the structure of the base-ten system (MP7).

MLR7 Compare and Connect. Synthesis: After the Gallery Walk, lead a discussion comparing, contrasting, and connecting the different representations of numbers. To amplify student language and illustrate connections, follow along and point to the relevant parts of the displays as students speak.
Engagement: Develop Effort and Persistence. Check in and provide each group with feedback that encourages collaboration and community. For example, comment on the group’s communication and how all members are actively engaged in creating the poster.
Supports accessibility for: Attention, Social-Emotional Functioning

### Required Preparation

• Create an anchor chart for the launch showing:
• 253 represented with a base-ten diagram
• This number has _____ hundreds, _____ tens, and _____ ones.
• The expanded form of this number is ______________________.
• The three-digit number is ________________.

### Launch

• Groups of 34
• Give each group tools for making a display.

### Activity

• “Cada grupo recibirá un número. En grupo, representen ese número de distintas formas” // “Each group will be given a number. Work with your group to represent that number in different ways.”
• Display the chart from the first activity.
• “Piensen en cómo podrían organizar sus representaciones y asegurarse de que cada miembro del grupo contribuya por igual” // “Think about how you might organize your representations and make sure that each group member does their fair share.”
• “Su grupo debe representar el número como un número de tres dígitos, con un diagrama en base diez, en forma desarrollada y en palabras” // “Your group should represent the number as a three-digit number, with a base-ten diagram, using expanded form, and using words.”
• Give each group a three-digit number to represent.
• If time permits, groups can represent the number in the additional ways suggested.
• 12 minutes: small-group work time

### Student Facing

Representa el número que está en tu póster. Asegúrate de representar el número usando:

• un número de tres dígitos
• un diagrama en base diez
• palabras

Si te queda tiempo: Usa solo decenas y unidades para representar el número. Representa el número componiéndolo de otra manera.

### Student Response

If students have representations that do not match the value of other representations on their poster, consider asking:

• “¿De qué manera tus representaciones muestran _____ (número dado al grupo)?” // “How do your representations show _____ (number given to group)?”
• “¿En qué se parecen y en qué son diferentes las distintas representaciones?” // “What is the same and different about all the different representations?”

### Activity Synthesis

• Display the chart paper from each group.
• “Ahora van a caminar por el salón para observar los otros números y las distintas formas en las que los representaron” // “Now you will walk around and see other numbers and how they were represented in different ways.”
• “Piensen en cuáles representaciones muestran con más claridad el valor de cada número” // “Think about which representations most clearly show you the value of the number.”
• “Luego, revisen que todas las representaciones muestren el mismo número” // “Then, check that all of the representations show the same number.”
• 5 minutes: gallery walk

## Lesson Synthesis

### Lesson Synthesis

“Hoy tuvieron la oportunidad de representar números de distintas formas e hicieron conexiones entre las representaciones” // “Today you had the chance to represent numbers in different ways and make connections across representations.”

“Mientras caminaban, ¿qué representación buscaron primero para que les ayudara a identificar el número? ¿Por qué?” // “While you walked around, what representation did you look for first to help you identify the number? Why?” (I looked at the base-ten numeral first and compared it to the expanded form. Then I checked the others.)

“¿Qué preguntas tienen sobre números de tres dígitos o sobre cualquiera de las representaciones que vieron hoy?” // “What questions do you have about three-digit numbers or any of the representations you saw today?”

## Student Section Summary

### Student Facing

En esta sección de la unidad, aprendimos distintas formas de representar números mayores que 99. Representamos centenas usando bloques en base diez y diagramas. Representamos números describiendo el número de centenas, decenas y unidades que conforman el número. Aprendimos a leer y escribir números como números de tres dígitos, como una suma del valor de cada dígito y usando palabras.

3 centenas 5 decenas 7 unidades

357

$$300 + 50 + 7$$

trescientos cincuenta y siete