The purpose of this activity is for students to consider a strategy to find an unknown side length of a figure composed of rectangles. They find the unknown side length by decomposing the figure into non-overlapping rectangles.

• Invite students to share their ideas about Tyler’s reasoning.
• Consider asking:
  • “¿Qué estrategias usaron ustedes o su compañero para encontrar la longitud de lado desconocida?” // “What strategies did you or your partner use to find the unknown side length?” (Encourage students to share on the displayed figure.)

The purpose of this activity is for students to find the area of a figure composed of rectangles with unknown sides by decomposing it into two non-overlapping rectangles. There are several ways to approach these problems, and students are given freedom to choose their own strategy to find the area. They share their reasoning with a partner, who has used a different method, and then prepare to share their partner’s method during the class discussion (MP3). The Activity Synthesis should focus on ways to find unknown side lengths and emphasize different ways to find the area of the figure.

At this point, students should be comfortable multiplying side lengths of rectangles to find the areas. Discussion should focus on how students decompose the figures and how they find the unknown side lengths.

• Select students to share a variety of strategies for finding the area of the second figure.
• Consider asking:
  • “¿Cuál longitud de lado desconocida se tenía que encontrar para usar esta estrategia? ¿Cómo encontraron la longitud de lado desconocida?” // “What unknown side had to be found to use this strategy? How did you find the unknown side length?”
  • “Después de encontrar las longitudes de lado desconocidas, ¿cómo encontraron el área?” // “After you found the unknown side lengths, how did you find the area?”
  • “¿Qué expresión podríamos escribir que corresponda a la forma en que descompusieron la figura?” // “What expression could we write to match how you decomposed the figure?”
  • “¿Hay alguna otra manera en la que podríamos partir esta figura en rectángulos que no se sobreponen?” // “Is there another way that we could break this figure into non-overlapping rectangles?” (Students may see the figure also as 3 rectangles: .)