# Lesson 6

Representemos números usando expresiones

## Warm-up: Verdadero o falso: Valor posicional (10 minutes)

### Narrative

The purpose of this True or False is to elicit the strategies and understandings students have for explaining why an equation is true based on place value. These understandings will be helpful later when students need to find ways to make equations true by attending to place value.

### Launch

• Display one statement.
• “Hagan una señal cuando sepan si la afirmación es verdadera o no, y puedan explicar cómo lo saben” // “Give me a signal when you know whether the statement is true and can explain how you know.”
• 1 minute: quiet think time

### Activity

• Share and record answers and strategies.
• Repeat with each statement.

### Student Facing

En cada caso, decide si la afirmación es verdadera o falsa. Prepárate para explicar cómo razonaste.

• 5 centenas + 2 decenas + 7 unidades = 527
• 4 centenas + 12 decenas + 7 unidades = 527
• 5 centenas + 7 unidades + 2 decenas = 527

### Activity Synthesis

• “¿De qué otras maneras podemos escribir una expresión que tenga un valor de 527?” // “What other ways could we write an expression that has a value of 527?”

## Activity 1: Hagamos que las ecuaciones sean verdaderas (20 minutes)

### Narrative

The purpose of this activity is for students to use their understanding of place value to find the number that makes each equation true. Students must consider how units may be composed or decomposed to find the unknown number (MP7). The number choices intentionally emphasize the types of compositions and decompositions students may use to add and subtract within 1,000. The synthesis focuses on the equations that involve composing or decomposing two units.

### Required Materials

Materials to Gather

• Groups of 2

### Activity

• 5 minutes: independent work time
• “Por turnos, compartan con su compañero cómo pensaron. Muestren o expliquen cómo saben que su ecuación es verdadera” // “Take turns sharing your thinking with your partner. Show or explain how you know your equation is true.”
• 3 minutes: partner discussion
• For finding the number that makes 2 hundreds + 9 tens + 17 ones true, monitor for students who:
• explain by using base-ten blocks or place value diagrams
• explain how they noticed when they would need to compose or decompose more than one unit

### Student Facing

En cada caso, encuentra el número que hace que la ecuación sea verdadera.

1. 5 centenas + _____ decenas + 6 unidades = 5 centenas + 5 decenas + 16 unidades

2. 1 centena + 1 decena + 17 unidades = 1 centena + _____ decenas + 7 unidades

3. 4 centenas + 15 decenas + 3 unidades = _____ centenas + 5 decenas + 3 unidades

4. 4 centenas + 3 decenas + 7 unidades = 3 centenas + _____ decenas + 7 unidades

5. 7 centenas + 8 decenas + 4 unidades = 7 centenas + 7 decenas + _____ unidades

6. 6 centenas + 9 unidades = 5 centenas + _____ decenas + 9 unidades
7. 2 centenas + 9 decenas + 17 unidades = _____ centenas + 7 unidades
8. 3 centenas + 1 decena + 5 unidades = 2 centenas + 10 decenas + _____ unidades

Si te queda tiempo: Escribe tu propia ecuación que tenga un valor desconocido y dásela a tu compañero para que la complete.

### Student Response

If students create equations that are not true, prompt students to make the known side of the equation with base-ten blocks, consider asking:

• “¿Cómo puedes componer o descomponer unidades en base diez para mostrar que la ecuación es verdadera?” // “How can you compose or decompose units to show the equation is true?”

### Activity Synthesis

• Invite previously identified students to share their method for finding the unknown number for 2 hundreds + 9 tens + 17 ones = _____ hundreds + 7 ones.
• For students who use base-ten blocks, draw place value diagrams to record their explanation.
• “¿Cómo saben que ambos lados de la ecuación son iguales?” // “How do you know both sides of the equation are equal?”
• “¿Compusieron o descompusieron unidades en base diez? ¿Compusieron o descompusieron más de una vez?” // “Did you compose or decompose units? Did you compose or decompose more than one time?”

## Activity 2: Clasificación de tarjetas: Expresiones con valores de tres dígitos (15 minutes)

### Narrative

The purpose of this activity is for students to use their understanding of place value to find and create matching expressions. The activity encourages students to write expressions that show the same value by composing or decomposing hundreds, tens, and ones. Although students may find the value of each expression to find matches, monitor for the ways they reason why two expression match or do not match by using what they know about hundreds, tens, and ones (MP7).

MLR8 Discussion Supports. Students should take turns finding a match and explaining their reasoning to their partner. Display the following sentence frames for all to see: “Observé _____, entonces agrupé . . .” // “I noticed _____, so I matched . . . .” Encourage students to challenge each other when they disagree.
Engagement: Develop Effort and Persistence. Chunk this task into smaller, more manageable parts. Instead of giving all 12 expressions, start with 4 (be sure that there are matches) and check in with students to provide feedback and encouragement on their thinking and effort. Ask students about their strategy, or about how they were able to determine the expressions that were the same. Look for thoughts on place value and combining some of the parts, not always just basic addition.
Supports accessibility for: Conceptual Processing, Attention, Organization

### Required Materials

Materials to Copy

• Match Expressions Cards 2.9, Spanish

### Required Preparation

• Create a set of cards from the blackline master for each group of 2.

### Launch

• Groups of 2
• Give each group a set of cards.

### Activity

• “Con su compañero, encuentren tres expresiones que tengan el mismo valor” // “Work with your partner to find three expressions that have the same value.”
• “Anoten las letras de las tarjetas que queden en el mismo grupo y escriban su propia expresión que tenga el mismo valor” // “Record the letters of the matching cards and write your own expression that has the same value.”
• 10 minutes: partner work time

### Student Facing

Agrupa las tarjetas que muestran expresiones que tienen el mismo valor. Anota las letras de las tarjetas que queden en el mismo grupo. En cada caso, escribe una nueva expresión que represente el mismo valor.
1. letras de las expresiones del mismo grupo: __________________

nueva expresión:

2. letras de las expresiones del mismo grupo: __________________

nueva expresión:

3. letras de las expresiones del mismo grupo: __________________

nueva expresión:

4. letras de las expresiones del mismo grupo: __________________

nueva expresión:

### Student Response

If students find matches that are not equivalent or do not explain their matches, consider asking:

• “¿Cómo podrías usar bloques en base diez o diagramas para mostrar cómo pensaste?” // “How could you use base-ten blocks or diagrams to show your thinking?”

### Activity Synthesis

• Display cards C, H, and J.
• “¿Estas expresiones quedaron en el mismo grupo? Expliquen sus ideas” // “Do these expressions match? Explain.”
• “¿Qué otras expresiones escribieron que tuvieran el mismo valor que estas expresiones?” // “What other expressions did you write that match these expressions?”