Guided Lessons

# Perfect Perimeter

Go to any length to test your students' understanding of perimeter calculations. Students will use their understanding of the perimeter of rectangular shapes to create rectangles that have different side measurements but equal perimeters.

No standards associated with this content.

No standards associated with this content.

No standards associated with this content.

No standards associated with this content.

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Students will be able to create different rectangular shapes with equal perimeters.

(5 minutes)
• Draw two rectangles of different sizes with equal perimeters on the board.
• Write the perimeter equation on the board (e.g., 2 L x 2 W = Perimeter). Ask students to find the perimeter.
• Have students turn and talk to their neighbour regarding the similarities and differences of the rectangles.
• Choose students to share their observations. Correct any misconceptions and highlight that the rectangles, while they look different, have the same perimeter.
• Ask a volunteer to read the student objective. Have another student define the key terms and write their responses on the board.
(8 minutes)
• Reiterate that we find the PerimeterOf an object when we add up all the sides, or use the equation 2L x 2WWhen finding the perimeter of rectangles. Explain that when we’re looking for rectangles with an equal perimeter, we are looking for rectangles that have the same perimeter, but not necessarily the same length and width. EqualMeans that something has the same value (e.g., 1 dollar equals 100 cents).
• Review the definitions the students gave for "perimeter" and "equal" and adjust them as necessary so that they’re accurate.
• Display the first problem in the Find the Rectangle’s Perimeter worksheet and demonstrate how the two rectangles have equal perimeters.
• Model how to create an additional rectangle with an equal perimeter. Think aloud about your process. For example, "I notice the example answer for the first problem subtracted 2 feet from the width and then added 2 feet to the length. I’m going to try to see if I can follow that example and subtract 4 feet from the length and add 4 feet to the width to get an equal perimeter for a new rectangle. So, I have 7 feet for the width and 14 feet for the length. That gives me a perimeter of 42 feet. They have equal perimeters!"
• Write the perimeter equation for each of the rectangles when calculating the perimeter.
(10 minutes)
• Ask a student to tell you the dimensions of the next rectangle. Then, ask for another volunteer to choose how many feet to subtract from one side and add to the other.
• Distribute whiteboards and markers to each student and ask them to draw an equal perimeter for the second problem with you. Explain the process step-by-step as you find the dimensions of a new rectangle.
• Ask students to turn and talk to their partners about whether they could just add to both sides and get the same perimeter. Allow students to share their answers aloud with the class.
• Permit students to draw their thinking on the board for the class and prove their answer. They should understand that they will need to subtract feet from one side and add the feet to the other side in order to get an equal perimeter to the original rectangle.
• Ask students to do the last problem in partners. Choose two partners to share their answers and explain the process they used to create their rectangle.
(10 minutes)
• Distribute the Match the Perimeter worksheet and explain the directions.
• Choose another student to explain the example problem at the top of the page to the class.
• Remind students they will need to check their answers by calculating the perimeter of the first rectangles and compare them to their drawn rectangles.

Support:

• Allow students to use grid paper when creating their rectangles.
• Ask students to complete only one new rectangle per problem.
• Monitor their progress and ask comprehension questions during their partner and independent work. For instance: "Why would you add on this side and subtract on the other? What do you need to do to find the perimeter?"
• Provide the following sentence stems:
• First, I ____.
• Then I ____.
• I think my answer is correct because ____.

Enrichment:

• Challenge students to find the area and perimeter of the shapes and then explain how the area and perimeters of the shapes were the same or different.
• Assign the exercise Perimeter of a Rectangle for additional practise finding the perimeter of rectangles.
(7 minutes)
• Distribute the lined paper.
• Draw a rectangle that is 20 units by 18 units on the board. Have the students find the perimeter of the shape and draw another shape that has an equal perimeter. Ask students to explain their process in writing of finding the perimeter. Have them tell why they think their answer is correct.
(5 minutes)
• Ask students to turn and talk to their partners and tell you whether they think they can create a square with the same perimeter as a rectangle.
• Allow the students to share their answers and provide an example to support their answer.
• Explain that even though they focused on rectangles with different side dimensions today, many different shapes, and even irregular shapes, can have the same perimeter. Just because shapes look the same or different does not mean they will have the same perimeter.