# Lesson 5

Compongamos y descompongamos números hasta 1,000

## Warm-up: ¿Qué sabes sobre el 308? (10 minutes)

### Narrative

The purpose of this What Do You Know About _____ is to invite students to share what they know about and how they can represent the number 308. Students use place value understanding as they describe the meaning of the digits in 308 and the different ways they can represent the number (MP7).

### Launch

• Display the number.

### Activity

• “¿Qué saben sobre el 308?” // “What do you know about 308?”
• 1 minute: quiet think time
• Record responses.

### Student Facing

¿Qué sabes sobre el 308?

### Activity Synthesis

• “¿De qué formas distintas podríamos representar 308?” // “What are different ways we could represent 308?”
• If it doesn’t come up in student responses, consider asking:
• “Si alguien dice que 308 no tiene decenas, ¿qué creen que quiere decir? ¿Estarían de acuerdo?” // “What do you think someone means if they said 308 has no tens? Would you agree?”
• “¿Hay alguna forma en la que podamos representar 308 con decenas?” // “Is there a way we could represent 308 with tens?”

## Activity 1: ¿Cuántos obtuvieron? (15 minutes)

### Narrative

The purpose of this activity is for students to represent numbers in different ways. The structure of the task encourages students to practice composing units and decomposing units. Students also have opportunities to use and connect concrete and abstract representations of three-digit numbers (MP2).

Action and Expression: Internalize Executive Functions. Check for understanding by inviting students to explain in their own words. Ask questions regarding the base-ten blocks to check for deeper understanding. For example, “¿Qué representa la centena? ¿Cómo lo saben?” // “What does the hundred represent? How do you know that?” Look for students to explain in terms of tens and ones. Examples of this include: “There are ten rows of ten and that makes 100.” “There are 100 ones that make up the 100.” Tie these responses to the place value of the digit to reinforce the meaning behind the numbers.
Supports accessibility for: Memory, Organization

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Give base-ten blocks to each group.

### Activity

• “Vamos a representar números de varias maneras. Empiecen con bloques en base diez, pero también pueden usar diagramas, símbolos u otras representaciones para mostrar su número” // “We are going to represent numbers in different ways. Start with base-ten blocks, but you may use diagrams, symbols, or other representations to show your number.”
• 8 minutes: partner work time
• Consider taking a picture of groups’ blocks before and after they compose or decompose units for use in the synthesis.

### Student Facing

1. Empieza con 2 centenas. Agarra un puñado de decenas y unidades.

1. ¿Qué número representan tus bloques en base diez? _______
2. Representa el mismo número de otra manera. Muestra cómo pensaste. Usa diagramas, símbolos u otras representaciones.

2. Junta tus bloques con los bloques de tu compañero.

1. ¿Qué número representan los bloques en base diez? _______
2. Representa el mismo número de otra manera. Muestra cómo pensaste. Usa diagramas, símbolos u otras representaciones.

3. Representa el número de tu grupo de las siguientes maneras:

1. sin usar centenas

2. sin usar decenas

3. sin usar centenas ni decenas

### Activity Synthesis

• Display a picture or drawing of a group’s blocks before they composed or decomposed units, such as:
• “¿Cómo podría este grupo representar su número de otra forma?” // “How could this group represent their number in another way?” (exchange 1 of the tens for 10 ones, exchange 10 tens for 1 hundred)
• Display a picture or drawing of a group’s blocks that uses the fewest number of blocks, such as:
• “¿Cómo podría este grupo representar su número de otra forma?” // “How could this group represent their number in another way?” (exchange 1 of the hundreds for 10 tens, exchange 1 ten for 10 ones, exchange all the tens for 40 ones)

## Activity 2: Déjenme contar las maneras (20 minutes)

### Narrative

The purpose of this activity is for students to represent the same number in multiple ways. During the gallery walk, students are encouraged to connect different representations of a number that make use of structure in similar ways (for example, connecting a diagram and an equation that show the number using the same number of hundreds, tens, and ones). The lesson synthesis focuses on the different ways students represent 356 with expressions or equations. Students demonstrate their understanding of the structure of the base-ten system when they describe, compare, and connect different representations of the same three-digit number (MP7).

This activity uses MLR7 Compare and Connect. Advances: representing, conversing

### Launch

• Groups of 3–4
• Give each group a piece of chart paper and markers.

### Activity

• “Representen 356 de al menos 3 maneras distintas. Usen diagramas, símbolos u otras representaciones. Si les queda tiempo, pueden representar 356 de más de 3 maneras” // “Represent 356 in at least 3 different ways. You may use diagrams, symbols, or other representations. If you have time, you can represent 356 in more than 3 ways.”
• 5 minutes: independent work time
• “Compartan con su grupo las representaciones que hicieron. Juntos, pongan en el póster de su grupo todas las maneras que tengan. Si les queda tiempo, pueden agregar otras maneras de representar el número” // “Share your representations with your group. Work together to put each different way on your group’s poster. If you have time, you may add other ways to represent the number.”
• 5 minutes: group work time
• “Van a ir a ver los pósteres de otros grupos. Una persona de su grupo debe escribir una marca junto a las representaciones que su grupo también haya usado para mostrar 356” // “You are going to rotate to see other group’s posters. One person from your group should place a checkmark next to any representation your team also used to show 356.”
• Prompt groups to rotate to the next chart every 1 minute.

### Student Facing

1. Representa 356 por lo menos de 3 maneras distintas. Muestra cómo pensaste. Usa diagramas, símbolos u otras representaciones.
2. Haz un póster con tu grupo para mostrar 356 de distintas maneras.

### Student Response

If student groups use a limited variety of representations (for example, most groups only use different base-ten drawings), consider asking:
• “¿Cómo podrías representar este número usando ecuaciones?” // “How could you represent this number with equations?”
• “¿Cómo podrías representar este número en palabras?” // “How could you represent this number with words?”
• “¿Cómo podrías representar este número usando dígitos?” // “How could you represent this number with digits?”

### Activity Synthesis

• Display:
• 3 hundreds + 4 tens + 16 ones
• “¿En esta expresión se muestra 356? Expliquen sus ideas” // “Does this expression show 356? Explain.” (Yes. 16 ones is the same as one ten and 6 ones so it’s the same as 3 hundreds 5 tens and 6 ones.)
• “Así podemos mostrar 356 como una expresión. ¿Qué otros grupos vieron que representaban a 356 como una expresión?” // “This is one way we could show 356 as an expression. What other ways did you see groups represent 356 as an expression?”
• Record responses.
MLR7 Compare and Connect
• “¿En qué se parecen las expresiones? ¿En qué son diferentes?” // “How are the expressions the same? How are they different?” (They all show 356. Some expressions have different amounts of hundreds and tens. Some expressions use words.)
• 30 seconds: quiet think time
• 2 minute: partner discussion
• Share responses.

## Lesson Synthesis

### Lesson Synthesis

“Hoy representamos números con bloques en base diez, dibujos, palabras y ecuaciones. Compusimos unidades en base diez grandes a partir de otras más pequeñas y descompusimos unidades en base diez grandes en otras más pequeñas” // “Today we represented numbers with base-ten blocks, drawings, words, and equations. We composed larger units from smaller units and we decomposed larger units into smaller units.”

“¿Por qué creen que es importante poder representar números de varias maneras?” // “Why do you think it is important to be able to represent numbers in different ways?” (It can help you understand place value and numbers better. You may need to do it if you add or subtract numbers.)