Understanding Area and Perimeter Module 12

Revisiting Perimeter and Area A rectangular playground is 15 feet long and 20 feet wide. What is the perimeter of the playground? What is perimeter? Turn to a partner, and talk about how to find the perimeter of the playground. How did you find it?

Revisiting Perimeter and Area cont. How does the model help to solve the problem? Can you solve the problem with only two sides labeled? Explain. What is the rule for finding perimeter? What is the perimeter of the playground? How is the answer labeled? Why? 15 feet 20 feet

Revisiting Perimeter and Area cont. What if we wanted to find the area of the playground? What are we finding when we find the area? Could you use the same diagram? Turn to your partner and talk about how to find the area of the playground. How would you use the problem data? 15 feet 20 feet

Revisiting Perimeter and Area cont. When we find the area, what operation are we using? How is finding the area of a rectangle like some of the arrays we built when multiplying? How can we use multiplication to find the area of the playground? What measurement units do we use when we find the area? Why?

Revisiting Perimeter and Area cont. *It’s your turn* Find the area and perimeter for the following problems. 1. A square has a side of 7 feet. 2. A rectangle is 14 feet long and 8 feet wide. 3. A rectangle has a length of 9 yards and a width of 7 yards.

Area or Perimeter? Amy is building a fence for her rectangular garden. The garden is 6 feet wide and 8 feet long. How much fencing will she need? Turn and tell your partner what is happening in this problem. What do we need to know? Are we looking for area or perimeter? Explain. How much fencing does she need? Justify your answer.

Area or Perimeter? cont. Jamie is putting mulch on her yard. She wants to know how much ground she will have to cover with mulch. Her yard is 10 feet wide and 10 feet long. How much ground will she cover with mulch? Turn and tell your partner what is happening in this problem. Are we looking for area or perimeter? Explain. How many square feet of mulch does she need to cover the garden? Justify your answer. Turn and talk to your partner. How did you know whether to find perimeter or area for each of these problems?

Perimeter Known, Sides Missing The perimeter of a rectangular painting is 90 inches. The length is 25 inches. What is the width? Turn to your partner and describe what you know and what you are trying to find out. How can we solve the problem? If you add 25 and 25 inches, is that the perimeter? Why or why not? Will it help to draw a picture? How can we create a diagram to show what we know about the painting?

Perimeter Known, Sides Missing cont. *Have the students draw a diagram to help explain their thinking* Does looking at the diagram help? How? What did you label as 25 inches? How can you use the perimeter and the two side lengths to find the width?

Perimeter Known, Sides Missing cont. The perimeter of the rectangle is 52 feet. The width is 6 feet. What is the length? Draw a diagram and solve the problem. Be sure to show the equations you use.

Area Known, Sided Missing The area of a rectangular chicken pen is 54 square feet. If the length is 9 feet, what is the width? Turn to your partner, and talk about how you might solve this problem. What do you know, and what are you trying to find out? Would drawing a diagram help you visualize the problem? Draw a diagram to show what you know. How do you find the area of a rectangle? Why did some of you use division? Explain.

Area Known, Sided Missing cont. *Work with a partner to build equations for and solve the following problems* The area of a rectangle is 60 square inches. If the width is 10 inches, what is the length? The area of a rectangle is 42 square feet. If the length is 7 feet, what is the width? The area of a rectangle is 24 square centimeters. If the width is 8 centimeters, what is the length?

Finding the Area and Perimeter of Irregular Figures What do you notice about this figure? Turn to a partner, and describe the figure. How could you find the perimeter of this figure? Do you have all the information you need? Talk to your partner. What is the perimeter? Now let’s find the area. With your group, find the area. Be ready to share your strategy. 4 ft. 4 ft. 4 ft. 4 ft. 10 ft. 4 ft. 10 ft. 12 ft.

Exploring Perimeters *Put students in pairs. Give each student four tiles* QUESTIONS: If you placed the tiles next to each other in a row, what is the area? What is the perimeter? Can you create a figure with your four tiles that has a larger perimeter than when the tiles were four in a row? What is the area of your figure? Turn and tell your partner the perimeter of your figure. Are they the same? Did you make any mistakes? Should they all be the same? Explain.

Same Perimeter, Different Areas Intro. Questions What have we discovered about figures that have the same area? Can they have different perimeters? Do you think if you have the same perimeter, you can have different areas? The Jacksons want to make a pen for their new puppy. They have 24 yards of fencing. What is the largest area for the pen with 24 yards? What does the 24 yards represent? - Is this a problem in which models could help? Turn to your partner and solve this problem. - What pen would have the largest area?