# Lesson 12

Descompongamos para restar

## Warm-up: ¿Qué sabes sobre 354? (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 354. It gives the teacher an opportunity to hear how students think about representing a three-digit number by decomposing or renaming units. This will be helpful as students decompose units to subtract within 1,000 in future activities.

### Launch

• Display the number.
• “¿Qué saben sobre 354?” // “What do you know about 354?”
• 1 minute: quiet think time

### Activity

• Record responses.
• “¿Cómo podemos representar el número 354?” // “How could we represent the number 354?”

### Student Facing

¿Qué sabes sobre 354?

¿Cómo podemos representar el número 354?

### Activity Synthesis

• “¿Por qué podrían tener que representar 354 de diferentes maneras?” // “Why might you need to represent 354 in different ways?” (You might want to show the value of each digit to compare numbers. You might want to decompose to subtract.)

## Activity 1: Restémosle a 354 (15 minutes)

### Narrative

The purpose of this activity is for students to subtract one-digit and two-digit numbers from a three-digit number using the methods that make sense to them. Each difference would require students to decompose a ten to subtract by place. They may count back or count on by place to find the difference. They may also use their understanding of place value and their experiences decomposing a ten when they subtracted within 100. In the synthesis, focus on connecting and comparing these different methods and making sense of representations that show decomposing a unit when subtracting by place.

When students use base-ten blocks, number lines, or equations to find the value of each difference they use appropriate tools strategically (MP5).

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

Engagement: Provide Access by Recruiting Interest. Optimize meaning and value. Invite students to share ideas of items to sell (cupcakes, sports cards, video games, etc.) and use that as the context around the problems to solve. Discuss the action of selling to represent subtraction.
Supports accessibility for: Attention, Conceptual Processing

### Required Materials

Materials to Gather

• Groups of 2

### Activity

• “Encuentren el valor de cada expresión de una manera que tenga sentido para ustedes. Expliquen o muestren cómo razonaron” // “Find the value of each expression in any way that makes sense to you. Explain or show your reasoning.”
• 3–4 minutes: independent work time
• 3–4 minutes: partner discussion
• Monitor for an expression that generates a variety of student methods or representations to share in the synthesis, such as:
• using base-ten blocks
• drawing a number line
• writing their reasoning in words
• writing equations

### Student Facing

Encuentra el valor de cada expresión de una manera que tenga sentido para ti. Explica o muestra cómo razonaste.

1. $$354 - 7$$
2. $$354 - 36$$
3. $$354 - 48$$

### Activity Synthesis

MLR7 Compare and Connect
• Invite one previously identified student who used a method that did not explicitly show decomposing a ten to share.
• Invite one previously identified student to show how they decomposed a ten to subtract with base-ten blocks or a base-ten diagram.
• “¿En qué se parece la manera en la que _____ representó el problema a la manera en la que _____ lo hizo? ¿En qué son diferentes?” // “What is the same and what is different about the ways _____ and _____ represented the problem?” (____ used base-ten blocks and showed decomposing a ten. _____ showed a number line and counting back 36. They used the same numbers. They found the same difference.)

## Activity 2: Descompongamos usando bloques en base diez (20 minutes)

### Narrative

The purpose of this activity is for students to practice decomposing a unit to subtract by place. In this activity, all students use base-ten blocks to find the value of each difference. Some students may be able to find the difference without blocks, but since this is the first time they decompose a unit when subtracting beyond 100, the blocks allow all students to see the work of decomposing a unit. This concrete experience will help students interpret other representations and anticipate when they may need to decompose units in future lessons. The blocks also provide a support for students as they create arguments for why they think they will decompose a unit and explain how they find the difference (MP3).

As needed, ask students to decompose a tower of ten connecting cubes into ones. Ask students how they would show the same decomposition with base-ten blocks.

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Give students base-ten blocks.

### Activity

• “Ahora todos vamos a usar bloques en base diez para restar” // “Now we are all going to use base-ten blocks to subtract.”
• “Con su compañero, encuentren el valor de cada expresión. Para empezar, un compañero lee la expresión y usa bloques para representar el número más grande” // “Work with your partner to find the value of each expression. One partner will start by reading the expression and representing the larger number using blocks.”
• “El otro compañero decide si van a descomponer alguna de las unidades en base diez para restar. Después, quita bloques para mostrar la diferencia” //  “The next partner will decide if they think they will decompose any units to subtract. Then they will take away blocks to show the difference.”
• “Discutan la diferencia y anótenla” // “Discuss the difference and record it.”
• As needed, demonstrate with $$142 - 25$$.
• 10 minutes: partner work time

### Student Facing

Con su compañero, encuentren el valor de cada expresión.

• Compañero A: lee la expresión y usa bloques para representar el número más grande.
• Compañero B: decide si van a descomponer una decena y explica. Después, resta.
• Discutan la diferencia y escríbanla.
• Intercambien roles y repitan lo anterior.
1. $$264 - 38$$
2. $$274 - 41$$

3. $$336 - 115$$
4. $$343 - 127$$
5. $$485 - 266$$
6. $$451 - 315$$

### Student Response

If students add ones to their representation without taking away a ten when they show a decomposition, ask the group to explain their steps. Consider asking:
• “¿Descompusiste una decena para restar?” // “Did you decompose a ten to subtract?”
• “¿Cómo puedes usar los bloques para mostrar que descompusiste una decena?” // “How could you use the blocks to show that you decomposed a ten?”

### Activity Synthesis

• Invite a group to share how to use blocks to find the value of $$336 - 115$$.
• “¿Qué hizo _____ para encontrar el valor de la diferencia?” // “What did _____ do to find the value of the difference?”
• Invite a group to share how to use blocks to find the value of $$343-127$$.
• “¿Qué hizo _____ para encontrar el valor de la diferencia?” // “What did _____ do to find the value of the difference?”

## Lesson Synthesis

### Lesson Synthesis

“Hoy vimos que podemos restar usando el valor posicional con números más grandes y que, algunas veces, se descompone una decena” // “Today we saw that we can subtract by place with larger numbers, and sometimes a ten is decomposed.”

“¿Cómo supieron cuándo se descompondría una decena cuando restaron números de tres dígitos?” //  “How did you know when a ten would be decomposed when you subtracted three-digit numbers?” (I could tell when I looked at the ones place and saw I didn't have enough ones to subtract ones from ones.)

“¿En qué se pareció esto a cuando restaron números de dos dígitos? ¿En qué fue diferente?” // “How was this the same as when you subtracted two-digit numbers? How was it different?” (It was just like when we subtracted two-digit numbers. It's different because one of the numbers has hundreds.)