1. How are the diagrams alike? How are they different?

2. How is finding the area of the shaded region in each diagram alike? How is it different?

1. What is the area of this rectangle? Explain or show your reasoning.

   

2. What is the area of the shaded region? Explain or show your reasoning.

   
3. How are these two area calculations alike? How are they different?

The shaded part of this diagram represents the top of a stove. What is the area of the stovetop? Explain or show your reasoning.

Select all of the expressions that represent the area of the shaded region in square feet.

1. \(3 + 5 \frac{3}{4}\)
2. \(3 \times 5 \frac{3}{4}\)
3. \(3 \times \left(5 + \frac{3}{4}\right)\)
4. \((3 \times 5) + \frac{3}{4}\)
5. \(3 \times 6 - \left(3 \times \frac{1}{4}\right)\)

Write one more expression that represents the area of the shaded region in square feet.

Tyler says that \(9 \frac{11}{12} \times 5\) is a little less than 50. 

1. Do you agree with Tyler? Explain or show your reasoning.
2. What is the value of \(9 \frac{11}{12} \times 5\)?

A banner at a sporting event is 8 feet long and \(2 \frac{1}{3}\) feet wide.

1. Sketch and label a diagram of the banner.
2. Find the area of the banner.

Find the value of each expression. Explain or show your reasoning.

1. \(3\frac{2}{5} \times 10\)
2. \(8 \times \frac{14}{3}\)
3. \(3 \frac{41}{100} \times 5\)

1. A standard rectangular sheet of paper is \(8\frac{1}{2}\) inches wide and 11 inches long. How many times would you need to fold the sheet of paper in half before the area is less than 1 square inch? Explain or show your reasoning.

2. A rectangular piece of chart paper is 23 inches wide by 33 inches long. How many times would you need to fold it in half before its area is less than 1 square inch?

Part of the rectangle is shaded.

1. Write a multiplication expression that represents the shaded area.
2. Write a division expression that represents the shaded area.
3. Write some other expressions that represent the shaded area.

Here is an image of the Empire State Building in New York City.

The base of the Empire State Building is shaped like a rectangle. What do you think the area of the rectangle is in square meters?

(Hint: A typical bathtub covers about 1 square meter. A typical car parking space is about 10 square meters.)

1. Make an estimate that is too low.
2. Make an estimate that is too high.
3. The length of the rectangle is about 129\(\frac{1}{5}\) meters. The width is about 57 meters. What is the area of the base of the Empire State Building?