Perimeter vs. Length Lab

Est. Class Sessions: 4

Developing the Lesson

Part 1: Introduce Lab Scenario

Define the Variables. Read the introductory section on the Perimeter vs. Length Lab pages in the Student Guide. Discuss Myrna's problem and what it means to plan or design runways.

Use the following discussion questions:

What is Myrna's job? (Myrna's job is to design runways for an airport.)
Why does Myrna need to know the perimeter of the runways? (Myrna needs to string lights around the runways, so she needs to know how much wire will be needed to connect the lights.)
What does Myrna need to know to find the perimeter of each runway? (Myrna needs to know the width and the length of each runway.)
Are the variables Length (L) and Perimeter (P) numerical or categorical? (Both variables are numerical.)
How do you know? (The values are numbers.)
For each type of runway, which variable stays the same—width, length, or perimeter? (The width of each type of runway is held constant.)
What is the width of all the light plane runways? (The width of the light plane runway is 1 inch.)
What is the width of all the short haul jet runways? (3 inches)

Once students understand that the width of each runway remains constant in their investigation, you can define this as a fixed variable, that is, a variable whose value does not change throughout the investigation.

Model the Process with Light Plane Runways. Make several light plane runways on a class display using square-inch tiles. Point out to the students that all the light plane runways will have the same width, one inch. The width will be the same when finding the perimeter for runways with different lengths, so long as you are working with only light plane runways.

Ask each group of students to find the perimeter of one of the runways that you displayed. Have them write number sentences that show how they think about the problem and how the numbers relate to the sides of the runway.

Have each group record the widths, lengths, and perimeters of each of the runways on a display of a Four-Column Data Table as shown in Figure 1. Even though the width remains the same for each type of runway, it should be included in the table so students are reminded that it is necessary for calculating perimeter. Note that students will use the fourth column of the data table to write ordered pairs for graphing in Part 3.

As students write their number sentences, ask them to:

Show the class how the numbers in your number sentence match the sides of the runway. Point to the sides of your rectangle that correspond to each number in your number sentence.

Examine the patterns in the data table the class creates for Light Plane Runways.

Ask:

What patterns do you notice in the data table for Light Plane Runways?
Describe the pattern in the column for width. (It is always one inch.)
What patterns do you see in the Length of Runway column? (The class chose to increase the length of the runway by one inch.)
What patterns do you see in the Perimeter of Runway column? (The perimeters go up by 2 when the length goes up by 1.)
What is the relationship between the length and the perimeter? (Possible responses: The perimeter is two lengths plus 2 inches when the width is one; or the length plus the width is equal to half the perimeter; or the perimeter is equal to two lengths plus two widths.)
Which of these patterns will be the same for the runway you will be building? (The width of runway remains the same for each type of runway.)
Which of these patterns will be different for the runway you will be building? (Each group will choose the lengths of the runways. The perimeters will be different.)

To reinforce the idea of perimeter and side length as linear measures, use both methods of finding perimeter: counting the edges of square tiles and measuring with a ruler.

Draw the Picture for the Assigned Runway. Organize students into groups of 3–4 and assign each group one type of runway: commuter plane, short-haul jet, long-haul jet, or heavy transport. As you assign each group a type of plane, discuss the width of their runways and remind them that all their runways will be that width.

To help students become comfortable working cooperatively as a group, assign roles for each group member. Possible roles: a student to record and keep track of data, a student to gather materials and keep track of manipulatives, a student to set up the models of the runways, and a student who asks the teacher questions. (All group members must first try to answer the question, before the designated student can go to the teacher for assistance.)

Use the Draw section of the Perimeter vs. Length Lab pages in the Student Guide to help students decide what they will include in their picture. Ask students to read and discuss Questions 1–3 in their groups. If a group is having difficulty getting started, the following discussion prompts can be used to help clarify what should be included in their picture.

Ask:

What should go in your picture?
Which type of plane are you using?
How wide will your runways be?
What variables do you need to show and label?

Emphasize that a good picture shows the equipment, identifies the variables, and communicates the procedures as shown in the student drawing in Figure 2. Note that the square-inch tiles, the type of plane, the width, and the variables (P for the perimeter of the runway and L for its length) are clear in the picture.

The groups that are assigned heavy-transport planes will need 60 square-inch tiles. If you have a limited supply of tiles, give the other groups fewer tiles than the group with heavy-transport planes.

When students are ready to begin their drawings, they will use the Draw section of the Exploring Perimeter vs. Length pages in the Student Activity Book to record their work.

Some students may ask, “Do the larger planes need longer runways than the smaller planes?” This is an excellent question. The Antopolis airport planning commission has not decided how long the runways will be, but it is possible that the runways for the bigger airplanes will have to be longer as well as wider. Another interesting question is whether smaller planes can land on runways meant for larger planes. The answer is that indeed they can, but it would clog the runways for the larger planes.

Student Guide: 54 55 56

Answers