# Lesson 12

Rectángulos que tienen la misma área

## Warm-up: Conversación numérica: Dividamos en partes (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for dividing within 100. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to divide fluently within 100.

When students use properties of operations and quotients with a value of 10 to find other quotients, they look for and make use of structure (MP7).

### 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.

• $$40 \div 4$$
• $$60 \div 4$$
• $$80 \div 4$$
• $$96 \div 4$$

### Activity Synthesis

• “¿Cómo les ayuda saberse el primer hecho a encontrar otros hechos?” // “How does knowing the first fact help you find other facts?”
• “¿Alguien puede expresar el razonamiento de _____ de otra forma?” // “Who can restate _____’s reasoning in a different way?”
• “¿Alguien usó la misma estrategia, pero la explicaría de otra forma?” // “Did anyone have the same strategy but would explain it differently?”
• “¿Alguien pensó en el problema de otra forma?” // “Did anyone approach the problem in a different way?”
• “¿Alguien quiere agregar algo a la estrategia de _____?” // “Does anyone want to add on to _____’s strategy?”

## Activity 1: Área de 24 (15 minutes)

### Narrative

The purpose of this activity is for students to understand that rectangles with the same area do not necessarily have the same perimeter. The work here reinforces the idea that area and perimeter are two separate measures of shapes. An area of 24 was chosen because it has many factors and is a familiar number to students.

MLR8 Discussion Supports. Synthesis: Provide students with the opportunity to rehearse what they will say with a partner before they share with the whole class.
Action and Expression: Develop Expression and Communication. Provide access to blank pre-formatted graph paper to create rectangles.
Supports accessibility for: Fine Motor Skills, Social-Emotional Functioning

### Launch

• Groups of 2
• “Tómense un par de minutos para dibujar algunos rectángulos que tengan un área de 24 unidades cuadradas” // “Take a couple of minutes to draw some rectangles that have an area of 24 square units.”
• 2–3 minutes: independent work time

### Activity

• “Compartan sus rectángulos con su compañero y juntos miren si se les ocurren otros rectángulos. Después, encuentren el perímetro de todos los rectángulos” // “Share your rectangles with your partner and see if there are any other rectangles you can think of together. Then, find the perimeter of each rectangle.”
• 6–8 minutes: partner work time
• Monitor for different rectangles students draw to share in the synthesis.

### Student Facing

2. Encuentra el perímetro de todos los rectángulos que dibujaste. Explica o muestra cómo razonaste.

### Activity Synthesis

• Invite students to share the rectangles they drew and to explain how they knew the area was 24.
• “¿Cómo decidieron qué rectángulos dibujar?” // “How did you decide what rectangles to draw?” (I thought about what numbers could be multiplied to give 24, like 6 times 4, and made those the side lengths of the rectangle.)
• “Acabamos de mostrar que los rectángulos que tienen cierta área no siempre tienen el mismo perímetro” // “We just showed that rectangles with a certain area do not always have the same perimeter.”
• “¿Qué le dirían a alguien para explicarle cómo dibujar rectángulos que tengan un área de 30 unidades cuadradas, pero perímetros diferentes?” // “How would you explain to someone how to draw rectangles with an area of 30 square units but different perimeters?” (Think about pairs of numbers that multiply to 30, use those numbers for the side lengths, and find the perimeter of each.)

## Activity 2: Misma área, diferente perímetro (20 minutes)

### Narrative

The purpose of this activity is for students to draw rectangles with the same area and different perimeters. Students draw a pair of rectangles for each given area, then display their rectangles and make observations about them in a gallery walk.

### Required Materials

Materials to Gather

Materials to Copy

• Square Dot Paper Standard

### Required Preparation

• Create 4 visual displays. Each visual display should be labeled with one of the following areas: 12 square units, 20 square units, 42 square units, 48 square units.
• Students will cut out and tape their rectangles on to one of the visual displays.

### Launch

• Groups of 2
• Display the visual display labeled with each of the four areas in the first problem.
• Give each group 2 sheets of dot paper, scissors, and access to tape.

### Activity

• “Completen el primer problema con su compañero” // “Work with your partner to complete the first problem.”
• 6–8 minutes: partner work time
• “Escojan cuáles rectángulos quieren compartir y pónganlos en el póster apropiado. Traten de buscar rectángulos que sean diferentes de los que ya han puesto otros grupos” // “Choose which rectangles you want to share and put them on the appropriate poster. Try to look for rectangles that are different from what other groups have already placed.”
• 3–5 minutes: partner work time
• Monitor to make sure each visual display has a variety of rectangles.
• When all students have put their rectangles on the posters, ask students to visit the posters with their partner and discuss one thing they notice and one thing they wonder about the rectangles.
• 5 minutes: gallery walk

### Student Facing

Tu profesor te va a dar papel de puntos para dibujar rectángulos.

1. Para cada una de las siguientes áreas, dibuja 2 rectángulos que tengan esa área, pero perímetros diferentes.

5. Escoge tu propia área.
2. Recorta los rectángulos que quieras para compartirlos y pegarlos en el póster apropiado. Trata de buscar rectángulos que sean diferentes de los que ya han puesto otros grupos.
3. Recorrido por el salón: cuando vayan a ver los pósteres, discutan algo que observen y algo que se pregunten.

### Activity Synthesis

• “Cuando fueron a ver los pósteres, ¿qué observaron? ¿Qué se preguntaron?” // “As you visited the posters, what did you notice? What did you wonder?”
• Discuss observations or questions that can reinforce the connections between side lengths, perimeter, and area of rectangles.
• Consider asking: “¿Qué área escogieron con su compañero cuando podían escoger su propia área? ¿Por qué escogieron esa área?” // “What area did you and your partner choose to work with when you could choose your own area? Why did you choose that area?”

## Lesson Synthesis

### Lesson Synthesis

“En las últimas lecciones, hemos estado aprendiendo sobre el área y el perímetro” // “Over the last few lessons, we’ve been learning about area and perimeter.”

“¿Qué han aprendido sobre el área y el perímetro que quieran asegurarse de recordar?” // “What have you learned about area and perimeter that you want to be sure to remember?” (Rectangles can have the same area and different perimeters. Rectangles can have the same perimeter, but different areas. Area is measured in square units. Perimeter is measured in length units. Perimeter and area are both measures of a shape.)