The purpose of this activity is for students to differentiate methods for finding perimeter from those for finding area. While addition and multiplication are both involved in various ways, students need to understand the problem situation and think about whether the operations performed will provide the desired information. As in earlier problems, students can find perimeter in various ways. The emphasis should be on how understanding the problem situation and the information given should inform the solution method.

When students analyze claims about how to use addition and multiplication to find the perimeter of a rectangle, they construct viable arguments (MP3). 

• Invite students to share who they agreed with and why. Record their reasoning for all to see.
• “¿Cómo supieron que al multiplicar  no se obtendría la cantidad total necesaria de cuerda?” // “How did you know that multiplying would not give you the total amount of rope needed?” (Multiplying would give us the area of the rectangle, not the distance around the rectangle.)
• “¿Cómo supieron que la estrategia de Diego iba a funcionar?” // “How did you know that Diego’s strategy would work?” (Diego is finding the perimeter by adding the side lengths of the garden.)
• “¿En qué casos puede ser apropiado usar la multiplicación para encontrar el perímetro?” // “When might it be appropriate to use multiplication to find the perimeter?” (When there are two or more sides that are the same length. When we know half of the perimeter, we can double that number to find the whole perimeter.)

This Information Gap activity gives students a chance to understand that given the area and one side length of a rectangle, the perimeter can be found, and that given the perimeter and one side length of a rectangle, the area can be found. In both cases, students need to find the missing side length to solve the problem. There are several ways students might find the missing side length and then the perimeter or area once the missing side length is known.

This activity uses MLR4 Information Gap.

The Information Gap structure requires students to make sense of problems by determining what information is necessary, and then to ask for information they need to solve it. This may take several rounds of discussion if their first requests do not yield the information they need (MP1). It also allows them to refine the language they use and ask increasingly more precise questions until they get the information they need (MP6).

• Share and record responses.
• Display the Info Gap cards.
• “¿Qué necesitan saber para encontrar el perímetro o el área de estos rectángulos?” // “What do you need to know in order to find the perimeter or area of these rectangles?” (The missing side length.)
• “¿Cómo usaron el área y un lado conocido para encontrar la longitud de los otros lados?” // “How did you use the area and one side you knew to find the missing side length?”
• “¿Cómo usaron el perímetro y un lado conocido para encontrar la longitud de los otros lados?” // “How did you use the perimeter and one side to find the missing side length?”