Lesson 13

The purpose of this warm-up is to elicit the idea that different shapes are used in the design of park areas, which will be useful when students design a park in a later activity. While students may notice and wonder many things about these images, how different shapes are used in the design of the park is the important discussion point.

• Groups of 2
• Display the image.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time

• “Discutan con su pareja lo que pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

• “¿Cómo cambiaría la apariencia del parque si solo pudieramos usar cuadriláteros para diseñarlo?” // “How would it change the look of the park if you could only use quadrilaterals to design it?” (It would be more boxy. There might be some rectangles and rhombuses. You could make it look kind of like it does now, but you wouldn't have any curved lines.)

The purpose of this activity is to provide students an opportunity to apply what they’ve learned about perimeter and area to design a small park. Since diagonal lines that connect the dots are not one length unit, students should use vertical and horizontal lines to design the park. When students make and describe their own choices for how they represent real-world objects, they model real-world problems with mathematics (MP4).

• Groups of 2
• “Van a diseñar un pequeño parque. ¿Qué se puede encontrar comúnmente en un parque?” // “You’re going to design a small park. What are some features that can be in a park?” (a playground, picnic benches, walking trails)
• Give each student a sheet of dot paper.
• “Tómense un momento para leer las instrucciones y escoger algunas de las cosas que van a incluir en su diseño” // “Take some time to read over the directions and choose some of the features you will include in your design.”
• 1 minute: quiet think time

• “Diseñen su pequeño parque individualmente” // “Work independently to design your small park.”
• 5–7 minutes: independent work time
• “Pueden trabajar con un compañero o con un grupo pequeño durante los últimos minutos, o continuar trabajando individualmente. Aun si siguen trabajando solos, estén disponibles por si su compañero quiere pensar en algo con ustedes” // “You can work with a partner or small group for the last few minutes or continue working on your own. Even if you choose to work alone, be available if your partner wants to think through something together.”
• 3–5 minutes: partner, small group, or independent work time

• Pair students up with a new partner.
• “Compartan su diseño con su compañero. Asegúrense de hacer preguntas sobre el diseño de su compañero y de responder preguntas sobre el diseño de ustedes” // “Share your design with your partner. Be sure to ask questions about your partner’s design and answer questions about your design.”
• 2–3 minutes: partner discussion
• Repeat cycles of pairing students up with new partners to share their park design as time allows.

The purpose of this activity is for students to solve problems that involve perimeter and area (MP2). The problems that students solve involve features that could be present in a park.

• Groups of 2

• “Resuelvan los problemas individualmente” // “Work independently to solve the problems.”
• 5–7 minutes: independent work time
• Monitor for drawings of different dimensions that students create for the last problem to share during the synthesis.
• “Discutan con su compañero sus soluciones a los problemas. Hablen sobre cómo los resolvieron” // “Discuss your solutions to the problems and how you solved them with your partner.”
• 2–3 minutes: partner discussion

• For the last problem, display 3–4 different sets of dimensions that students used to find the possible perimeters, one at a time.
• For each set of dimensions, ask:
  • “¿Cómo sabemos que este rectángulo tiene un área de 48 yardas cuadradas?” // “How do we know this rectangle has an area of 48 square yards?” (If you multiply \(6\times8\), it’s 48. I multiplied \(2\times24\) by multiplying \(2\times20\), then \(2\times4\) and adding the products together to get 48.)
  • “¿Cuál es el perímetro de este rectángulo? Expliquen su razonamiento” // “What’s the perimeter of this rectangle? Explain your reasoning.” (I doubled the short sides, then doubled the long sides and added them together. I added the short side and the long side, then doubled the amount.)