The purpose of this activity is for students to practice finding the perimeter of shapes that have labeled side lengths. The Activity Synthesis focuses on approaches students have for looking for and making use of the structure of shapes as a way to find their perimeter (MP7). As students discuss and justify their decisions, they share a mathematical claim and the thinking behind it (MP3).

Monitor for and select students with the following approaches for finding the perimeter of the hexagon to share in the Activity Synthesis:

• Add the individual side lengths around the shape.
• Add the two 8–inch side lengths together, add the four 4–inch side lengths together, and then add those sums together.
• Multiply like side lengths, then add, such as for the long sides and for the short sides, and then add those products together.
• Use symmetry to split the shape in half horizontally, add for the top half of the shape, and then double that for the sides on the bottom half of the shape.

The approaches are sequenced from more concrete to more abstract to encourage students to make sense of approaches that connect the properties of the shapes (for example, same side lengths) to operations that help them find the perimeter in fewer steps (for example, multiplication). Aim to elicit both key mathematical ideas and a variety of student voices, especially students who haven't shared recently.

• Invite previously selected students to share in the given order. Record or display their work for all to see.
• Give students a chance to ask questions about each approach as it is shared.
• Connect students’ approaches by asking:
  • ”¿En qué se parecen estas estrategias para encontrar el perímetro? ¿En qué son diferentes?” // “How are these ways of finding the perimeter the same? How are they different?”
  • “¿Por qué funciona la estrategia de _____ para encontrar el perímetro de esta figura? ¿Funcionará para todas las figuras?” // “Why does ______'s way work for finding the perimeter of this shape? Would it work for all shapes?”
• Connect students’ approaches to the learning goal by asking:
  • “¿Fue más fácil encontrar el perímetro de unas figuras que de otras en esta actividad? ¿Por qué?” // “Was it easier to find the perimeter of some shapes in this activity than others? Why?” (Yes, some of the shapes had several sides that are the same length, so we could multiply. In a rectangle, we can add two sides and then double the result to find the whole perimeter.)
  • “¿Cómo nos ayuda tener lados de la misma longitud a encontrar el perímetro?” // “How does having sides of the same length help us find the perimeter?” (You can look for ways to use multiplication instead of having to add many different lengths.)

The purpose of this activity is for students to find the perimeter of shapes when some of the side lengths are not given. Students use their knowledge of shapes to reason about the length of the missing sides before they find the perimeter of the shape (MP7). 

This activity uses MLR7 Compare and Connect. Advances: representing, conversing

• “Tuvimos que encontrar muchas longitudes desconocidas de los lados de esta figura antes de poder encontrar el perímetro” // “We had to find a lot of missing side lengths in this shape before we could find the perimeter.”
• “Cuando fueron a ver las presentaciones de los demás, ¿qué observaron acerca de cómo encontraron ellos las longitudes desconocidas de los lados?” // “As you visited the displays, what did you notice about how others found the missing side lengths?” (I noticed some groups counted the number of short sides and multiplied by 40. I noticed some put the short side lengths into smaller groups before finding their combined lengths.)
• Consider asking:
  • “¿Alguien encontró las longitudes de lado desconocidas de una manera diferente a como ustedes y su compañero lo hicieron?” // “Did anyone find the missing side lengths in a different way than you and your partner?”
  • “¿Alguien encontró el perímetro de una manera diferente a como ustedes y su compañero lo hicieron?” // “Did anyone find the perimeter in a different way than you and your partner?”