# Lesson 13

## Warm-up: Conversación numérica: Paréntesis (10 minutes)

### Narrative

This Number Talk encourages students to think about equivalent expressions and to rely on the properties of operations to mentally solve problems. The strategies elicited here will be helpful later in the lesson when students match diagrams to expressions.

### 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

• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Encuentra mentalmente el valor de cada expresión.

• $$5 \times (7 + 4)$$
• $$(5 \times 7) + (5 \times 4)$$
• $$(5 \times 7) + (5 \times \frac{1}{4})$$
• $$(5 \times 7) - (5 \times \frac{1}{4})$$

### Activity Synthesis

“¿En qué se parecen las dos últimas expresiones? ¿En qué son diferentes?” // “What is the same about the last two expressions? What is different?” (They both have the same two products but one of them is the sum and the other is the difference.)

## Activity 1: Clasificación de tarjetas: Diagramas y expresiones (20 minutes)

### Narrative

The purpose of this activity is for students to analyze area diagrams and use the properties of operations to interpret expressions. The diagrams are decomposed in different ways and the expressions all have a fractional part but sometimes it is written as a mixed number and sometimes the whole number and fraction are separated using the distributive property. The numbers in the diagrams, both the whole number part and the fractional part, are deliberately chosen to resemble one another so students need to analyze the expressions carefully to make matches.

MLR8 Discussion Supports. Students should take turns finding a match and explaining their reasoning to their partner. Display the following sentence frame for all to see: “Observé ___, entonces emparejé . . .” // “I noticed ___ , so I matched . . . .” Encourage students to challenge each other when they disagree.

### Required Materials

Materials to Copy

• Card Sort: Diagrams and Expressions

### 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 from the blackline master.

### Activity

• 1–2 minutes: independent work time
• 8–10 minutes: partner work

### Student Facing

Tu profesor va a entregarles unas tarjetas a ti y a tu compañero.

1. Clasifica las tarjetas de una forma que tenga sentido para ti.
2. Asocia cada expresión a un diagrama que le corresponda. Algunos diagramas corresponden a más de una expresión.
3. Trabaja con tu compañero para encontrar el área de cada región sombreada. Explica o muestra tu razonamiento.

### Activity Synthesis

• Display Diagram C and Expressions J and O.

$$3 \times 5 \frac{2}{5}$$

$$(3 \times 5) + (3 \times \frac {2}{5})$$

• “¿De qué manera cada expresión representa el área de la región sombreada?” // “How does each expression represent the area of the shaded region?” (There are 3 rows and each row has an area of $$5\frac{2}{5}$$ square units.)
• Display Diagram B and Expression L.

$$(5 \times 3) -\left(5 \times \frac{2}{5}\right)$$

• “¿De qué manera la expresión representa el área de la región sombreada?” // “How does the expression represent the area of the shaded region?” ($$5 \times 3$$ is the area of the full rectangle and then I take away the unshaded part, $$5 \times \frac{2}{5}$$.)

## Activity 2: Escribamos expresiones (15 minutes)

### Narrative

The purpose of this activity is for students to write expressions that represent the area of shaded regions. Monitor for students who are writing a variety of expressions that represent the distributive property.

Action and Expression: Internalize Executive Functions. Invite students to verbalize their strategy for writing an expression to match the shaded area in each diagram before they begin. Students can speak quietly to themselves, or share with a partner.
Supports accessibility for: Organization, Conceptual Processing, Language

• Groups of 2

### Activity

• 1–2 minutes: quiet think time
• 5–7 minutes: partner work time

### Student Facing

En cada caso, escribe tantas expresiones como puedas que correspondan al área de la región sombreada.

1.

2.

### Student Response

If students only write one expression for a diagram, partner them with a student who found a different expression and ask:

• “¿De qué manera esta expresión representa la región sombreada?” // “How does this expression represent the shaded region?”
• “¿Cómo pueden dos expresiones diferentes representar la misma región sombreada?” // “How can two different expressions represent the same shaded region?”
• “¿Qué otras expresiones podemos escribir para representar la región sombreada?” // “What other expressions can we write to represent the shaded region?”

### Activity Synthesis

• Select 2–3 students to share their expressions for the first problem.
• If not mentioned by students, display:

$$4 \times 5\frac{1}{3}$$

$$4 \times \frac{16}{3}$$

• “¿De qué manera cada expresión representa el primer problema?” // “How does each expression represent the first problem?” (There are 4 rows and each row has $$5 \frac{1}{3}$$ square units or $$\frac{16}{3}$$ square units.)
• “¿Su estrategia cambió cuando escribieron expresiones para el último diagrama? Si sí, ¿cómo cambió?” // “Did your approach change when writing expressions for the last diagram? If yes, how?” (It was easier to see the square units and apply the distributive property.)
• If not mentioned by students, display these expressions for the area of the last diagram in square units:

$$(7 \times 3) +\left(7 \times \frac{3}{4}\right)$$

$$(7 \times 4) - \left(7 \times \frac{1}{4}\right)$$

## Lesson Synthesis

### Lesson Synthesis

“¿Cuál es su estrategia favorita para encontrar el área de una región sombreada? ¿Hay alguna estrategia nueva que les emocione intentar o conocer mejor?” // “What’s your favorite way to find the area of a shaded region? What is a new way that you are excited to try or learn more about?”

Consider having students write their responses in their journals.