STEM LEARNING:

Advanced Air Mobility: Flight 

Control Math 3 (Distance/Speed)

Educator Guide

www.nasa.gov

National Aeronautics and Space Administration
2 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 3 (DISTANCE/SPEED) EDUCATOR GUIDE

OVERVIEW

Objectives Student Prerequisite Knowledge

Standards

Materials

This lesson provides a real-world scenario through which students get practice using the distance and speed formulas. 

Students calculate the distance between coordinates and use the speed formula to determine time, distance, or speed. 

Through this lesson, students are introduced to the concept of Advanced Air Mobility, or AAM, and air metro services.

Students will be able to:

• Use the distance formula to calculate the distance 

between two points

• Use the formula for speed to help develop a 

schedule for an air metro system

Before beginning this lesson, students should be familiar 

with:

• Obtaining coordinates of points plotted on a graph

• Plotting coordinates on a graph

• Determining the distance between two points using 

the distance formula

• Using the speed formula

CCS.MATH.CONTENT.6.NS.C.8: Solve real-world and mathematical problems by graphing points in all four quadrants 

of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same 

first coordinate or the same second coordinate.

CCS.MATH.CONTENT.6.RP.A.3: Use ratio and rate reasoning to solve real-world and mathematical problems (for 

example, by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations).

CCS.MATH.CONTENT.7.RP.A.1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, 

and other quantities measured in like or different units.

CCS.MATH.CONTENT.8.G.B.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate 

system.

Next Generation Science Standards

Science and Engineering Practices

• Developing and using models

• Using mathematical and computational thinking

• Student Guides (one per student)
ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 3 (DISTANCE/SPEED) EDUCATOR GUIDE | 3 

Lesson Modifications

Grouping Students

Steps

This lesson can be modified depending on student needs. 

Coordinates can be changed to adjust the difficulty of 

the calculations. More stops can be added to the air 

metro routes, or additional loops may be added (or both). 

Skipping different parts of the assignment allows for 

further tailoring of the lesson.

The difficulty can be varied by allowing or prohibiting the 

use of calculators. If calculators are not used, answers will 

need to be expressed as square roots unless locations are 

changed so that the math leads to perfect squares.

This activity is designed to be completed independently. Grouping can, however, be used if necessary. Students working 

in pairs can independently solve the problems and then compare answers to validate their solutions or find errors.

1. Use a warm-up or other method to introduce the 

students to the concept of AAM. Students can read 

through the information found in the student guide as 

an introduction to this topic.

2. Review the distance and speed formulas with students 

to ensure they understand how to use it.

3. Distribute the student guide(s) and allow students to 

begin working.

4. As students are working, their work should be 

checked to discover if they are making errors. If they 

are, they can be shown the correct method.
4 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 3 (DISTANCE/SPEED) EDUCATOR GUIDE

ANSWERS

PART 1 : USING THE DISTANCE FORMULA

Begin by determining the distances between the various vertiports. Remember that each square is equal to 1 kilometer 

(km). Use the distance formula to fill in the missing information in the data tables:

Blue Loop

Distance (km)

Distance between vertiports 1 and 6 8.5

Distance between vertiports 6 and 4 10.4

Distance between vertiports 4 and 5 6.0

Distance between vertiports 5 and 1 17.0

Purple Loop

Distance (km)

Distance between vertiports 3 and 8 13.5

Distance between vertiports 8 and 10 10.0

Distance between vertiports 10 and 9 10.6

Distance between vertiports 9 and 3 10.8

Red Loop

Distance (km)

Distance between vertiports 2 and 5 15.0

Distance between vertiports 5 and 7 12.2

Distance between vertiports 7 and 8 11.4

Distance between vertiports 8 and 2 13.6

Green Loop

Distance (km)

Distance between vertiports 1 and 2 4.1

Distance between vertiports 2 and 3 2.8

Distance between vertiports 3 and 1 3.6
ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 3 (DISTANCE/SPEED) EDUCATOR GUIDE | 5 

PART 2: USING THE SPEED FORMULA

1. To determine the speed the aircraft can fly for the suburban routes, a test was performed. In this test, the aircraft flew 

1273⁄4 km in 1 hour and 4 minutes.

Calculate the speed (show your work):

2. Using the speed you calculated, calculate the time it takes to fly each leg of the Blue Loop. Show your work.

a. From vertiport 1 and vertiport 6:

b. From vertiport 6 to vertiport 4:

c. From vertiport 4 to vertiport 5:

d. From vertiport 5 to vertiport 1:
6 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 3 (DISTANCE/SPEED) EDUCATOR GUIDE

3. Houses continue to be built in the eastern suburb, so a new stop is being considered for the Purple Loop. The 

systems engineers are trying to determine a good location for a new stop.

a. The desired flight time to the new stop is between 2.5 minutes and 8 minutes. Using the speed you calculated 

previously, calculate how close and how far the new stop can be.

b. The engineers have narrowed the search down to two possible spots, (14,10) and (17, 12). Determine which one, 

or both, of these would be in the desired distance range from both vertiports 8 and 10.

Vertiport 10 to (14, 10):

Vertiport 10 to (17, 12):

Vertiport 8 to (14, 10):

Vertiport 8 to (17, 12):

Vertiport 10 is in range of both, but vertiport 8 is not.
ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 3 (DISTANCE/SPEED) EDUCATOR GUIDE | 7 

4. The first schedule below was created for the Red Loop. Unfortunately, there is an error in the portion of the chart that 

contains the times. Assume that the aircraft must be on the ground at the vertiport for at least 1 minute, but no more 

than 2 minutes, making the departures time always 2 minutes later than the arrival time.

Find the error, correct it (as well as any other times that would change), and enter the correct times in the blank 

schedule.

 Enter the correct times in the table above.

Vertiport 2 to Vertiport 5:

Vertiport 5 to Vertiport 7:

Vertiport 7 to Vertiport 8:

Vertiport 8 to Vertiport 2:

Good on the schedule

Good on the schedule

Good on the schedule

Error on the schedule 

(only 5 minutes allotted)
8 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 3 (DISTANCE/SPEED) EDUCATOR GUIDE

5. For the Green Loop, aircraft fly in the downtown portion of the city. To lower the noise and ensure safety, they fly 

slower than their capacity. To calculate the average speed, a researcher collects the following data.

Calculate the average speed, in , of the aircraft. Only count the time spent flying, not the time on the ground. 

Show your work. (Hint: To calculate the total time spent flying, subtract the sum of the times on the ground in each 

vertiport from the time between arriving in vertiport 1 the first time and arriving there the second time.)
ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 3 (DISTANCE/SPEED) EDUCATOR GUIDE | 9 

Figure 1. Satellite image of Indianapolis, Indiana. Credit: USGS

Figure 2. Map of Indianapolis, Indiana. Credit: USGS
10 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 3 (DISTANCE/SPEED) EDUCATOR GUIDE

Figure 3. Map of Indianapolis, Indiana and the surrounding area with a grid overlaid on it. Credit: USGS

Figure 4. Graph showing air metro routes.
EP-2020-04-507-HQ

National Aeronautics and Space Administration

Headquarters

300 E Street SW

Washington, DC 20546