# Lesson 13

Descompongamos decenas o centenas

## Warm-up: Cuál es diferente: Bloques y bloques (10 minutes)

### Narrative

This warm-up prompts students to compare four images of base-ten blocks. This gives the teacher an opportunity to hear how students describe the blocks and how they use “compose” or “decompose” to describe their understanding of equivalent forms of a hundred and a ten. This will be helpful as students decompose hundreds and tens to subtract and interpret base-ten representations in the lesson activities.

### 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 your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

### Student Facing

¿Cuál es diferente?

### Activity Synthesis

• “¿Cuáles imágenes podrían mostrar una forma de descomponer una centena? Expliquen” // “Which images could show a way to decompose a hundred? Explain.” (B because 10 tens is the same as a hundred. A is close, but I think it shows composing a hundred.)
• “¿Cuáles imágenes no muestran una forma de descomponer una centena?” // “Which images do not show a way to decompose a hundred?” (C because 10 ones are not the same as a hundred. D because it could show a ten as 10 ones.)

## Activity 1: Restemos con diagramas en base diez (15 minutes)

### Narrative

The purpose of this activity is for students to interpret base-ten diagrams that represent decomposing a unit when subtracting by place (MP2). Students analyze a base-ten diagrams that show decomposing a hundred into 10 tens. They make connections between representing with base-ten blocks and base-ten diagrams and between decomposing a hundred and decomposing a ten.

MLR5 Co-Craft Questions. Keep books or devices closed. Display only the images, without revealing the question, and ask students to write down possible mathematical questions that could be asked about the situation. Invite students to compare their questions before revealing the task. Ask, “¿Qué tienen en común estas preguntas? ¿En qué son diferentes?” // “What do these questions have in common? How are they different?” Reveal the intended questions for this task and invite additional connections.

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• “Mai usó bloques en base diez para encontrar el valor de $$336-52$$. Ella empezó a hacer un diagrama en base diez para mostrar lo que pensaba” //  “Mai found the value of $$336-52$$ using base-ten blocks. She started recording her thinking with a base-ten diagram.”
• “Tómense un minuto para examinar el diagrama de Mai. ¿Qué hizo en el paso 2?” // “Take a minute to look at Mai’s diagram. What did she do in Step 2?”
• 1 minute: quiet think time
• “Hablen con su compañero sobre la representación que hizo Mai. Expliquen qué hace en cada paso” // “Talk to your partner about Mai’s representation. Explain what she is doing in each step.”
• 1–2 minutes: partner work time
• “¿Qué hace Mai en su primer paso?” // “What does Mai do in her first step?” (First, she draws 336 with 3 hundreds, 3 tens, and 6 ones.)
• “¿Qué hace Mai después?” // “What does Mai do next?” (Next, she breaks apart a hundred into 10 tens.)
• “¿Qué debería hacer Mai después para encontrar la diferencia? Muestren su trabajo en el diagrama de Mai” // “What should Mai do next to find the difference? Show your work on Mai’s diagram.”
• 1–2 minutes: independent work time
• “Compartan con su compañero cómo pensaron” // “Share your thinking with your partner.”
• Display sentence frames:
• “Primero, yo . . .” // “First, I . . .”
• “Después, yo . . .” // “Then, I . . .”
• “La diferencia es . . .” // “The difference is . . .”
• Invite a student who describes crossing out tens first then ones and a student who describes crossing out ones first then tens to share their steps and the difference.

### Activity

• “Con su compañero, emparejen cada expresión con uno de los diagramas. Después, encuentren el valor de cada diferencia” // “Work with your partner to match each expression to one of the diagrams. Then find the value of each difference.”
• 3–5 minutes: partner work time

### Student Facing

Mai usó bloques en base diez para encontrar el valor de $$336-52$$. Después, empezó a hacer un diagrama para mostrar su trabajo.

Explica qué hizo Mai en el paso 2. Muestra qué debe hacer Mai después para encontrar la diferencia.

Paso 1

Paso 2

1. Escribe cada expresión al lado del diagrama que le corresponde. Luego, encuentra el valor de cada diferencia.

$$244 - 28$$

$$256 - 64$$

$$244 - 64$$

### Student Response

If students match an expression to a diagram that doesn't show the same value, consider asking:

• “¿Cómo muestra el diagrama cada número de la expresión?” // “How does the diagram show each number in the expression?”

### Activity Synthesis

• Invite students to share the expression that matches each diagram.
• “¿A qué tenían que prestarle atención cuando emparejaron cada diagrama con una expresión?” // “What did you have to pay attention to as you matched each diagram to an expression?” (I had to look at the numbers that were being subtracted. I looked for where there were more tens or more ones drawn when there weren’t enough tens or ones.)

## Activity 2: Descompongamos una decena o una centena (20 minutes)

### Narrative

The purpose of this activity is for students to subtract by place and record their thinking. Students decompose either a ten or a hundred as they subtract. They should have access to base-ten blocks, but can represent their thinking in any way that makes sense to them. Throughout the activity, as students share their thinking with their peers, listen for the way they use place value vocabulary and provide them with opportunities to revise their language for precision and clarity.

Action and Expression: Develop Expression and Communication. Provide students with alternatives to writing on paper. Students can share their learning by creating a video using the base-ten blocks, or writing out their steps and explaining on video.
Supports accessibility for: Language, Attention, Social-Emotional Functioning

### Required Materials

Materials to Gather

• Groups of 2

### Activity

• “Vamos a practicar la resta usando el valor posicional. Muestren cómo pensaron de una manera que tenga sentido para los demás” // “We are going to practice subtracting by place. Show your thinking in a way that will make sense to others.”
• 5 minutes: independent work time
• 4 minutes: partner work time
• Monitor for students who use base-ten diagrams and explain their steps clearly.

### Student Facing

Encuentra el valor de cada diferencia. Muestra cómo pensaste. Prueba el método de Mai en una expresión.

1. $$245 - 28$$
2. $$352 - 71$$
3. $$364 - 182$$
4. $$293 - 147$$
5. Comparte con tu compañero cómo encontraste el valor de una de las expresiones. Usa estos esquemas de oraciones como ayuda para explicar:

• “Primero, yo . . .”
• “Después, yo . . .”
• “Luego, yo . . .”
• “Por último, yo . . .”

### Student Response

If students only use base-ten blocks to solve and do not show their thinking with a diagram, equations, or words, consider asking:

• “¿Cómo puedes mostrar con un diagrama o con ecuaciones de qué manera usaste los bloques?” // “How could you record how you used the blocks with a diagram or with equations?”

### Activity Synthesis

• Invite previously identified students to share how they found the value of each difference.
• After each student shares, consider asking:
• “¿_____ descompuso para restar? ¿Por qué? ¿Cómo pueden usar el diagrama que hizo para saberlo?” // “Did _____ decompose to subtract? Why? How can you use their diagram to tell?”
• “¿En qué se parece el método de _____ a la forma en la que ustedes encontraron esta diferencia? ¿En qué es diferente?” // “How is _____’s method the same as how you found this difference? How is it different?”
• “¿Qué preguntas quieren hacerle a _____ sobre sus pasos o su representación?” // “What questions do you have for _____ about their steps or their representation?”

## Lesson Synthesis

### Lesson Synthesis

“Hoy descompusimos decenas y centenas para restar usando el valor posicional” // “Today we decomposed tens or hundreds to subtract by place.”

Display $$534 - 41$$ and draw a base-ten diagram to represent 534.

“Kiran quería restar quitando y usando el valor posicional. Usó un diagrama en base diez para llevar un registro de lo que pensaba. Primero, Kiran dibujó 534 como 5 centenas, 3 decenas y 4 unidades. ¿Qué puede hacer Kiran ahora? Expliquen” // “Kiran wanted to take away by place and use a base-ten diagram to keep track of his thinking. First, Kiran drew 534 as 5 hundreds, 3 tens, and 4 ones. What could Kiran do next? Explain.” (He could take away 1 one because he has enough to subtract. He could cross out 1 hundred and draw 10 tens, because he needs more tens to subtract.)
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