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Smart Skies: LineUp with Math

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Smart Skies: FlyBy Math graphic of a sector map with the title Math-Based Decisions in Air Traffic Control (ATC).



Grade Levels

Grades 5-8, Grades 9-12, Informal Education


Mathematics, Physical Science, Measurement and Data Analysis, Problem Solving, Flight and Aeronautics


Educator Guides, Hands-on Activities, Lesson Plans / Activities, Other Multimedia, Videos, Websites

Smart Skies: LineUp with Math

Smart Skies: LineUp with Math is intended for teachers or facilitators that wish to use LineUp With Math to help their students use math in real-world air traffic control scenarios.

LineUp With Math consists of six Problem Sets. Each enables students to explore and apply decision-making and proportional reasoning skills to resolve distance-rate-time conflicts in realistic air traffic control problems.

To solve the problems, students use a web-based interactive Air Traffic Control (ATC) Simulator that represents an air traffic controller’s screen. The accompanying workbooks provide the underlying mathematics and strategies to enable students to optimize their solutions. The simulator is also available from the Apple App Store and runs on an iPhone or iPad.

LineUp with Math has two overarching goals:

  • To enable students to use mathematical reasoning and problem-solving skills to investigate and solve realistic distance-rate-time problems in air traffic control.
  • To offer students a variety of problem solving approaches, tools, skills, and experiences in the context of challenging, yet accessible, real-world problems.

Real-life Applications

LineUp With Math was developed under Smart Skies, part of the NASA Airspace Systems Program’s educational efforts. Smart Skies supports the Program’s goal to develop advanced computer-based systems to help pilots and air traffic controllers operate the nation’s air transportation system with reduced flight delays and improved efficiency and access.

In LineUp With Math, students apply proportional reasoning to make decisions and resolve conflicts in realistic air traffic control problems involving two or more planes. The challenge in each problem is to “line up” the planes safely, with proper spacing, at a given intersection of jet routes.

Getting Started

You should begin by downloading and reading through the Educator Guide. It provides an in-depth explanation of LineUp With Math and should answer any questions you have.

Download the Educator Guide (PDF)

Problem Sets

For each Problem Set, a print-based Student Workbook provides a structured learning environment. Each Workbook contains paper-and-pencil worksheets that introduce students to pertinent air traffic control concepts as well as problem analysis and solution methods.

  • Problem Set A: Workbook A introduces students to the environment of real air traffic control.
  • Problem Sets B and C: Students use Workbooks B and C to analyze conflicts between two or three planes and to resolve the conflicts by rerouting.
  • Problem Set D: Workbook addresses the basic effects of differences in speed.
  • Problem Sets E and F: Students use Workbooks E and F to analyze conflicts between two or three planes and to resolve the conflicts by changing plane speed.

Workbooks B, C, E, and F include worksheets that support selected Simulator problems. For these worksheets, the title matches the number of the associated Simulator problem. Four- and five-plane problems are found on the Simulator only and are not supported by the Student Workbooks. These higher-level Simulator problems enable students to explore more challenging scenarios.

​Each of the six Problem Sets is accompanied by a Teacher Guide that includes:

  • an overview​
  • a list of objectives, prerequisites, and materials
  • a discussion and specification of the relevant ATC Simulator Problems (or other interactive/multimedia components)
  • a discussion of key points for each Simulator problem and for each Workbook worksheet
  • the soutions for each Simulator problem
  • the answers for each Workbook worksheet

Problem Set A

  • Educator Guide
  • Student Workbook

Problem Set B

  • Educator Guide
  • Student Workbook

Problem Set C

  • Educator Guide
  • Student Workbook

Problem Set D

  • Educator Guide
  • Student Workbook

Problem Set E

  • Educator Guide
  • Student Workbook

Problem Set F

  • Educator Guide
  • Student Workbook

Preparing to Teach LineUp With Math:

  1. View the movie “Animation of 24 hours of flight in the U.S.” which is available in the “Videos” section to see the world’s largest distance-rate-time problem.
  2. View the movie “What is LineUp With Math?”.
  3. View the movie “Welcome to Sector 33” to see an overview of the vocabulary, units, and graphical reprsentations of air traffic control problems. This material is the backbone of both the simulator and the print-based-workbooks.
  4. Using the link in the toolbar, access and try the on-line Simulator. Online instructions are provided to assure that your computer is configured to support the Simulator. Once you have the simulator running, click on the help button, represented by a “?” and look through the introduction to the simulator.
  5. Select the Problem Set you will use to introduce your students to LineUp With Math. We strongly recommend starting with Problem Set A.
  6. Select and download the materials for the Problem Set you have selected.
  7. Duplicate the Student Workbook to provide each student with one copy. You can also provide them a digital copy of the PDF.


Animation of 24 hours of flight in the US

Welcome to Sector 33

I’m a Controller


This activity is part of the Smart Skies Program