# Lesson 4

Sumemos y restemos de formas diferentes números de tres dígitos

## Warm-up: Conversación numérica: Contemos hacia atrás usando el valor posicional (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for counting back by place as a strategy for subtraction. These understandings help students develop fluency with subtracting multiples of 10 and 100 from three-digit numbers. As students share, represent their thinking on an open number line.

### Launch

• Display one expression.
• “Hagan una señal cuando tengan una respuesta y puedan explicar cómo la obtuvieron” // “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

### Activity

• Record answers and strategy on an open number line.
• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Encuentra mentalmente el valor de cada expresión.

• $$586 - 100$$
• $$486 - 20$$
• $$457 - 200$$
• $$257 - 30$$

### Activity Synthesis

• Display $$457 - 230$$.
• “¿Cómo nos ayudan las últimas 2 expresiones a pensar sobre este problema?” // “How can the last 2 expressions help us think about this problem?” (Even though it is 230 being taken away, we can still subtract the hundreds and then the tens.)
• “Hoy veremos cómo podemos usar métodos para contar que nos ayuden a restar números más grandes” // “Today we will see how we can use counting methods to help us subtract bigger numbers.”

## Activity 1: Cero decenas y cero unidades (20 minutes)

### Narrative

The purpose of this activity is for students to use the relationship between addition and subtraction to make sense of different counting methods for subtracting three-digit numbers. Students analyze 2 different methods for a given problem where a number is being subtracted from a multiple of 100. They consider how thinking about a subtraction expression as an unknown addend equation can be helpful and discuss how counting on can be a useful method for subtraction. The number line can support this method, so they have the opportunity to make connections between counting on a number line and adding on or subtracting by place using equations.

Action and Expression: Develop Expression and Communication. Identify connections between the strategies that Mai and Lin use alongside a number line representation. The strategies result in the same outcomes but use differing approaches. The number line is less abstract. Add the context of an animal jumping (frog, rabbit, grasshopper, etc.) to enhance the conceptual model as well.
Supports accessibility for: Conceptual Processing, Organization

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• “A Mai y a Lin les pidieron que encontraran el valor de $$500 - 387$$. Este es su trabajo” // “Mai and Lin were asked to find the value of $$500 - 387$$. Here is their work.”
• Display the images of Mai and Lin’s work.
• “¿En qué se parecen y en qué son diferentes los métodos que usaron para encontrar la diferencia?” // “What is the same and different about the methods they used to find the difference?” (They both represented it with equations, but Mai also used a number line. Mai showed it as addition with a missing addend. They both broke apart the second number. They both got 113 as the answer.)
• 30 seconds: quiet think time
• “Discutan con un compañero” // “Discuss with a partner.”
• 2 minutes: partner discussion
• If it doesn’t come up, ask, “¿En qué parte de la representación de Mai ven la respuesta?” // “Where do you see the answer in Mai’s representation?” (How far she jumped shows the difference.)
• “¿Por qué creen que Lin empezó con $$387 = 300 + 80 + 7$$?” // “Why do you think Lin started with $$387 = 300 + 80 + 7$$?” (That way she could see each part that she needed to take away.)

### Activity

• “Intenten encontrar estas diferencias de las formas en las que Mai y Lin restaron” // “Now try Mai’s way and Lin’s way.”
• 10 minutes: independent work time

### Student Facing

A Mai y a Lin les pidieron que encontraran el valor de  $$500 - 387$$.

Este es su trabajo.

El trabajo de Mai

$$387 + {?} = 500$$

$$387 + 100 = 487$$

$$487 + 10 = 497$$

$$497 + 3 = 500$$

$$100 + 10 + 3 = 113$$

El trabajo de Lin

$$387 = 300 + 80 + 7$$

$$500 - 300 = 200$$

$$200 - 80 = 120$$

$$120 - 7 = 113$$

Encuentra el valor de cada expresión.

Muestra cómo pensaste.

1. Intenta encontrar el valor de $$600 - 476$$ de la forma en la que Mai restó.

2. Intenta encontrar el valor de $$400 - 134$$ de la forma en la que Lin restó.

### Activity Synthesis

• “¿Cuál método prefieren? Expliquen” // “Which method do you prefer? Explain.” (I prefer counting on because you count until you get to the number. When you count on, you can do it in parts so you can make each part something that is easy for you and get to a ten. The number line helped me. I prefer the equations because it helps me see the parts as they are taken away.)

## Activity 2: Sumar o restar con la forma desarrollada (15 minutes)

### Narrative

The purpose of this activity is for students to use their understanding of expanded form, place value, and properties of operations to reason about adding and subtracting by place (MP7). Students analyze different methods and representations that show adding hundreds and hundreds, tens and tens, and ones and ones. Students notice that hundreds, tens, and ones can be added in any order. In the next section, the focus will be on strategies based on place value and will include composing and decomposing tens and hundreds. In the synthesis, there are discussions that honor all methods while connecting each strategy to place value in preparation for the work of the upcoming lessons.

MLR7 Compare and Connect. Synthesis: After all strategies have been presented, lead a discussion comparing, contrasting, and connecting the different approaches. Ask, “¿Alguien resolvió el problema de la misma manera, pero lo explicaría de otra forma?” // “Did anyone solve the problem the same way, but would explain it differently?”

### Required Materials

Materials to Gather

• Groups of 2

### Activity

• “Hemos usado bloques en base diez, diagramas y ecuaciones para sumar y restar números usando lo que sabemos sobre el valor posicional” // “We have used base-ten blocks, diagrams, and equations to add and subtract numbers using what we know about place value.”
• “Andre y Diego mostraron cómo pensaron de diferentes formas. ¿En qué se parece y en qué es diferente su trabajo?” // “Andre and Diego showed their thinking in different ways. What is the same and what is different about their work?” (They both grouped the same places together. Andre used a different equation to show adding each place. Diego put each number in expanded form and put the places on top of one another.)
• 1 minute: quiet think time
• 3 minutes: partner discussion
• Record responses.
• “¿En qué parte de su trabajo ven cada número?” // “Where do you see each number in their work?” (Diego shows the place value in expanded form, but Andre adds 1 place at a time. In Andre’s I see the numbers up and down, but in Diego’s I see the numbers across.)
• 30 seconds: quiet think time
• Share responses
• “Intenten encontrar el valor de las expresiones de la forma en la que Andre y Diego lo hicieron” // “Try Andre’s way and Diego’s way.”
• 8 minutes: independent work time
• “Comparen con un compañero” // “Compare with a partner”
• 2 minutes: partner discussion
• Monitor for students who use Andre’s way, but add by place value in different orders.

### Student Facing

1. Andre y Diego mostraron con ecuaciones cómo pensaron para encontrar el valor de $$427 + 351$$.

El trabajo de Andre

El trabajo de Diego

¿En qué se parece y en qué es diferente su trabajo?

Discute con tu pareja.

2. Intenta encontrar el valor de $$725 + 243$$ de la forma en la que Andre lo hizo.

3. Intenta encontrar el valor de $$863 - 432$$ de la forma en la que Diego lo hizo.

4. Escoge tu propia forma de encontrar el valor de $$163 + 326$$. Muestra cómo pensaste.

5. Escoge tu propia forma de encontrar el valor de $$692 - 571$$. Muestra cómo pensaste.

### Activity Synthesis

• Invite 12 students to share how they used each way.
• “¿Cuál forma prefirieron? ¿Por qué?” // “Which way did you prefer? Why?” (I prefer Diego’s way because I can see how things are grouped and I write fewer equations OR I prefer Andre’s way because it helps me remember to add ones and ones, tens and tens, and hundreds and hundreds.)
• “¿En qué se parecen encontrar la suma y encontrar la diferencia? ¿En qué son diferentes?” // “How was it the same or different when finding the sum versus finding the difference?” (It worked either way. I liked Diego’s way of finding the difference because it was lined up by place, so the answer is across the bottom when you are done.)

## Lesson Synthesis

### Lesson Synthesis

“Hoy compartieron diferentes formas de representar la suma y la resta de números. También hablaron sobre cómo pensar en el valor posicional y en la forma desarrollada puede ayudarles a encontrar el valor de expresiones” // “Today you shared different ways to represent adding and subtracting numbers. You also talked about how thinking about place value and expanded form can help you find the value of expressions.”

“¿Qué fue lo que más les ayudó a encontrar la diferencia?” // “What was most helpful to you when finding the difference?”

“¿Qué aprendieron cuando compararon con un compañero cómo sumar o restar números de tres dígitos usando el valor posicional?” // “What is something that you learned from comparing with a partner when adding or subtracting three-digit numbers by place value?”