In this activity, students solve geometric problems by reasoning about length and area, decomposing and recomposing of rectangles, considering units of measurements, and performing operations.

Each question can be approached in a variety of ways. Consider asking students to create a visual display of their approach and to share it with the class.

The first problem offers students an opportunity to make sense of a problem and persevere in solving it (MP1). They may focus on the area of the banner and poster paper or think about cutting up the poster paper into pieces that can be used for the banner. Students will also need to convert between feet and inches at some point in their solution.

• Select students who use different strategies to share their reasoning. Record and display their strategies.
• If it does not come up as a strategy, consider asking, “¿Cómo podría la profesora de Jada recortar la cartulina y reorganizarla para hacer un cartel?” // “How could Jada's teacher cut the paper up and rearrange it to make a banner?”
• Consider discussing any benefits or potential challenges of the different approaches. “¿Algunas estrategias son más eficientes que otras? ¿Con algunas estrategias es más fácil equivocarse?” // “Are some strategies more efficient or more prone to error than others?” (When cutting the paper into more pieces, there are more measurements to account for, making it more likely to miss something. Cutting the paper into more pieces is also less efficient for Jada's teacher, as it means more taping as well.)

In this activity, students perform operations on multi-digit numbers to solve situations about perimeter and area. They use operations to convert units of measurements along the way. Converting inches to feet could be done by dividing by 12, but this is not an expectation at this point. Students could perform the conversion with multiplicative reasoning. To convert 180 inches into feet, they could reason , or and .

In IM Grade 3, students learned that area is additive, and that the area of rectilinear figures can be found by decomposing them into non-overlapping rectangles. Students apply that understanding in this activity, after converting lengths in different units into the same unit.

• Select students to share how they reasoned about the area of the room. Record and display their reasoning.
• If some students found the area using different units, ask how they would find out if the two answers represent the same amount.