STEM LEARNING:

Advanced Air Mobility: Flight 

Control Math 1 (Graphing)

Educator Guide

www.nasa.gov

National Aeronautics and Space Administration
2 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 1 (GRAPHING) EDUCATOR GUIDE

OVERVIEW

Objectives Student Prerequisite Knowledge

Standards

Materials

In this lesson, students use graphing in a real-world situation to learn about geofencing. By combining coordinate 

systems with maps, students locate positions and specified areas. Using this information, students evaluate different 

routes that air taxis can take.

Students will be able to:

• Plot points in all four quadrants of a Cartesian 

coordinate system

• Use points to construct lines and shapes

• Validate air taxi routes based on data

Before beginning this lesson, students should be familiar 

with:

• Plotting coordinates on a graph

CCS.MATH.CONTENT.6.NS.C.6: Understand a rational number as a point on the number line. Extend number line 

diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with 

negative number coordinates.

Next Generation Science Standards

Cross Cutting Concepts

• Systems and system models

Science and Engineering Practices

• Developing and using models

• Analyzing and interpreting data

• Using mathematical and computational thinking

Plotting coordinates on a graph

• Student Guides
ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 1 (GRAPHING) EDUCATOR GUIDE | 3 

Lesson Modifications

Grouping Students

Steps

This lesson can be easily modified depending on 

student needs. More locations can be added to the 

graph to provide more practice. Modifying the shape of 

the geofenced areas can change the difficulty level of 

graphing them.

One version of this activity has all coordinates in quadrant 

1 and another version has some coordinates in each of 

the four quadrants. The answers for both versions can be 

found in this educator guide.

Locations on Earth can all be specified using latitude 

and longitude. As an enrichment activity, students can 

research longitude and latitude using the internet or other 

resources. Comparing and contrasting longitude and 

latitude to the coordinate system in this exercise helps 

students further understood the real-world application of 

graphing while mapping. Have them determine where on 

Earth would be the origin in the latitude/longitude system.

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

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

1. Show the students the NASA video about Safeguard 

(technology used to implement geofencing). The 

video is available at: https://www.youtube.com/

watch?v=0Kc01cV7vCU.

2. Review graphing on the Cartesian coordinate system.

3. Show the map of Cheyenne, Wyoming without the 

grid. Discuss the function of air taxis and the dangers 

associated with flying in some areas, such as over 

the airport.

4. Show the map of Cheyenne, Wyoming with the grid. 

Discuss how using the grid makes it possible to 

specify locations because it provides a reference point.

5. Distribute the student guides and allow students to 

begin working.

6. Allow students to verify answers for the “Getting the 

Coordinates” section. (This allows students to find 

errors that would be compounded in the “Using the 

Distance Formula” section.)
4 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 1 (GRAPHING) EDUCATOR GUIDE

A satellite photo of Cheyenne, Wyoming. Credit: USGS.

A map of Cheyenne, Wyoming with numerous colors. Credit: USGS.
ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 1 (GRAPHING) EDUCATOR GUIDE | 5 

A map of Cheyenne, Wyoming that is blue and white. Credit: USGS.

A map of Cheyenne, Wyoming with a grid overlaid on it that includes the origin near the center. Credit: USGS.
6 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 1 (GRAPHING) EDUCATOR GUIDE

ANSWERS (USING ALL FOUR QUADRANTS)

PART 1 

This student guide includes a coordinate system with the origin set to correspond with the maps shown. You can also 

use regular graph paper to complete this activity.

1. The geofenced area around the state capitol is a 2 x 2 box. The coordinate for the corners of this box are: (1, 1),

(1, -1), (-1, -1), and (-1, 1). Plot these points on the graph and connect the four points to create a box. Shade in 

this area.

2. Because of its runways, the geofenced area around Cheyenne Regional Airport is a bit more complicated. The 

coordinates for the corners of the geofenced areas are: (-4, 12), (0, 12), (0, 9), (13, 9), (13, 4), and (-4, 4). Plot these 

points on the graph and connect the points to show the geofenced area. Shade in this area.

****The graph showing the answers is included later in this guide. 

PART 2

You get a job in Cheyenne, Wyoming managing an air taxi service. Small, unmanned vehicles make up your fleet of 

air taxis. Your job is to determine the routes they need to fly to transport passengers around the city. In an urban 

setting like Cheyenne, air taxis cannot land or take off from anywhere they want. Instead vertiports are established 

throughout the city for this purpose. Vertiports are buildings from which air taxis can land and take off.

** **The graph showing some of the answers is included later in this guide. 

1. Plot the following points and mark each with its corresponding letter. These points represent the vertiports in 

Cheyenne, Wyoming.

Point X Y

A 9 -1

B -11 8

C -9 -4

D -3 -2

E 3 14

F 16 3

G 23 15
ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 1 (GRAPHING) EDUCATOR GUIDE | 7 

2. Your company’s headquarters are located by the vertiport represented by point A. This is where all your air taxis are 

housed when not in use. 

This morning, you want to send air taxis from point A to each of the other vertiports. On your graph, draw a line for 

each of the six paths. For each path, determine whether it can fly straight from point A to its destination without 

going into a geofenced area and write your answer below. Your graph should prove evidence for each.

From A to B: It cannot fly straight 

From A to C: It can fly straight 

From A to D: It can fly straight 

3. The city is planning on building a new vertiport at the coordinates (11, 13). Because of the geofenced area around 

the airport, you cannot send an air taxi straight from your headquarters to this new vertiport.

So, you decide to create a waypoint where your air taxi can turn. The air taxi should be able to fly straight from 

headquarters to this point and then straight from this point to the new vertiport, all without entering a geofenced 

area. You need to find one point east (to the right) of the geofenced area that could act as the waypoint. Enter 

the coordinates of your point below, graph it, and show both legs on the air taxi’s flightpath as evidence that the 

waypoint you chose met the criteria.

Coordinates of the waypoint: There are many possible answers; the graph shows the point (19, 4) as one possible 

solution.

From A to E: It cannot fly straight 

From A to F: It can fly straight 

From A to G: It can fly straight 

Blank graph.
8 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 1 (GRAPHING) EDUCATOR GUIDE

Answer Key Graph.
ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 1 (GRAPHING) EDUCATOR GUIDE | 9 

ANSWERS (USING ONLY QUADRANT 1)

The following can be used to complete this activity with all points in quadrant 1 of the coordinate system.

PART 1 

This student guide includes a coordinate system with the origin set to correspond with the maps shown. You can also 

use regular graph paper to complete this activity.

1. The geofenced area around the state capitol is a 2 x 2 box. The coordinate for the corners of this box are: (12, 4),

(12, 6), (14, 6), and (14, 4). Plot these points on the graph and connect the four points to create a box. Shade in 

this area.

2. Because of its runways, the geofenced area around Cheyenne Regional Airport is a bit more complicated. The 

coordinates for the corners of the geofenced areas are: (9, 17), (13, 17), (13, 14), (26, 14), (26, 9), and (9, 9). Plot these 

points on the graph and connect the points to show the geofenced area. Shade in this area.

** **The graph showing the answers is included later in this guide. 

PART 2

You get a job in Cheyenne, Wyoming managing an air taxi service. Small, unmanned vehicles make up your fleet of 

air taxis. Your job is to determine the routes they need to fly to transport passengers around the city. In an urban 

setting like Cheyenne, air taxis cannot land or take off from anywhere they want. Instead vertiports are established 

throughout the city for this purpose. Vertiports are buildings from which air taxis can land and take off.

** **The graph showing some of the answers is included later in this guide.****

1. Plot the following points and mark each with its corresponding letter. These points represent the vertiports in 

Cheyenne, Wyoming.

Point X Y

A 22 4

B 2 4

C 4 1

D 11 3

E 16 19

F 29 8

G 36 20
10 | ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 1 (GRAPHING) EDUCATOR GUIDE

2. Your company’s headquarters are located by the vertiport represented by point A. This is where all your air taxis are 

housed when not in use. 

This morning, you want to send air taxis from point A to each of the other vertiports. On your graph, draw a line for 

each of the six paths. For each path, determine whether it can fly straight from point A to its destination without 

going into a geofenced area and write your answer below. Your graph should prove evidence for each.

From A to B: It cannot fly straight 

From A to C: It can fly straight 

From A to D: It can fly straight 

3. The city is planning on building a new vertiport at the coordinates (24, 18). Because of the geofenced area around 

the airport, you cannot send an air taxi straight from your headquarters to this new vertiport.

So, you decide to create a waypoint where your air taxi can turn. The air taxi should be able to fly straight from 

headquarters to this point and then straight from this point to the new vertiport, all without entering a geofenced 

area. You need to find one point east (to the right) of the geofenced area that could act as the waypoint. Enter 

the coordinates of your point below, graph it, and show both legs on the air taxi’s flightpath as evidence that the 

waypoint you chose met the criteria.

Coordinates of the waypoint: There are many possible answers; the graph shows the point (19, 4) as one possible 

solution.

From A to E: It cannot fly straight 

From A to F: It can fly straight 

From A to G: It can fly straight 
ADVANCED AIR MOBILITY: FLIGHT CONTROL MATH 1 (GRAPHING) EDUCATOR GUIDE | 11 
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