1. NASA Smart SkiesTM: The “Plane” Truth About D = R • T
National Aeronautics & Space Administration
NASA Smart SkiesTM:
The “Plane” Truth About D = R • T
Grades 5-9
All Materials Free!
Standards Based!
Rebecca Green
AIAA “Passport to the Future” ~ Denver, CO
August 3, 2009

2. Agenda 60 minutes Name History w/ SS
Ask audience: grade level & subject matter
60 minutes

3. Two Classroom Activity Sets
Overview of SS (FBM, LUWM, MIPV)
Smart Skies consists of two sets of FREE classroom activities, FlyBy Math and LineUp With Math.
Real-world applications
Hands-on experiments
Multiple representations
Free!
Free!

4. Intro to Air Traffic Control
During the busiest travel times, about how many commercial planes are flying in the US?
About 5,000 planes!
About 5,000 planes

5. World’s Largest D-R-T Problem
-- Show the movie “Animation of 24 hours of flight in the US.”
-- The movie is very engaging and provides a terrific motivation for the study of distance-rate-time problems.
-- As night turns to day, notice how the air traffic begins to grow heavy on the East Coast and work its way west.

6. LineUp with MathTM Act as an Air Traffic Controller.
Math-Based Decisions in Air Traffic Control (ATC)
Distance = Rate • Time
Proportional Reasoning
Web-based ATC simulator
Act as an Air Traffic Controller.
Use a simulator and math
to change plane routes and speeds
to keep planes safely separated and on time.

7. LineUp with MathTM Full set of free classroom materials
Simulator with dozens of problems
Student workbooks, videos, teacher support materials
Standards-based
Proportional reasoning
Problem solving
Decision making
Classroom-tested
Over 5,000 students nation-wide

8. Intro to ATC and the Simulator
“Welcome to Sector 33” Video
This is an example of one of the videos available on the website.

9. ATC Simulator Problem 3-8
00:00
Target 3:48
UAL74
600 kts
AAL12
DAL88
Three planes all flying to SFO through Modesto (MOD).

10. The Goal at MOD The planes must be spaced 3 Nmi apart at MOD.
3:48
Target 3:48
AAL12
600 kts
UAL74
600 kts
DAL88
600 kts
The planes must be spaced 3 Nmi apart at MOD.
The last plane must arrive in 3 mins and 48 secs.

11. A Closer Look at the Goal
3:48
Target 3:48 10 5
UAL74
600 kts
AAL12
DAL88
MOD
3 Nmi
The planes must be spaced 3 Nmi apart at MOD.
The last plane must arrive in 3 mins and 48 secs.

12. Select and Run Problem 3-8
– Select and run problem 3-8 on the Simulator to demonstrate the conflicts at Coaldale (OAL) and Modesto (MOD).
– If your participants have access to the simulator in your workshop, you may want to have them select and run problem 3-8.
– We suggest the participants work in pairs as air traffic controllers do.
1. Select Problem
2. Run Problem

13. Analyze Speeds & Distances
00:00
Target 3:48
10 Nmi
12 Nmi
AAL12
600 kts
13 Nmi
DAL88
600 kts
UAL74
600 kts
DAL88
UAL74
AAL12
Speed:
600 kts
600 kts
600 kts
Distance to MOD:
35 Nmi
35 Nmi
35 Nmi

14. Who Arrives First at MOD?
00:00
Target 3:48
UAL74
600 kts
AAL12
DAL88
All 3 planes will arrive at MOD at the same time.
All 3 planes:
Are the same distance, 35 Nmi, from MOD.
Are flying at the same speed, 600 kts.
Arrive at MOD at the same time!!!

15. Ways to Achieve the 3 Nmi Spacing
00:00
Target 3:48
UAL74
600 kts
AAL12
DAL88
All 3 planes will arrive at MOD at the same time.
Route Change(s)
Speed Change(s)

16. Try Using a Route Change
00:00
Target 3:48
AAL12
600 kts
DAL88
600 kts
UAL74
600 kts
Can you change the route for:
UAL74? DAL88? AAL12?

17. Analyze the Route Change
00:00
Target 3:48
AAL12
600 kts
DAL88
600 kts
UAL74
600 kts
Let’s change the route for AAL12.
What’s its new flight distance to MOD?

18. Try Using a Speed Change
00:00
Target 3:48
AAL12
600 kts
DAL88
600 kts
UAL74
600 kts
540 kts
Let’s reduce the speed of UAL74. Try 540 knots (smallest reduction).

19. Try to Solve Problem 3-8
Reset

20. The Math Behind the Speed Changes
D = R • T
3 minutes
2 minutes
1 minute
Gaby 10 steps/minute 10 20 30
Tonisha 9 steps/minute 10 20 30
-- This slide is animated. With each mouse click (representing one minute of travel), Gaby advances 10 steps and Tonisha advances 9 steps.
-- Thus, Tonisha falls behind one step per minute (10 steps/minute – 9 steps/minute = 1 step/minute).
-- So after 1 minute, Tonisha is 1 step behind.
-- After 2 minutes, Tonisha is 2 steps behind.
-- After 3 minutes, Tonisha is 3 steps behind.
Start
Distance - steps

21. Minute by Minute A plane’s speed is 600 knots (600 Nmiles per hour).
In 60 minutes, it flies 600 Nmiles.
In one minute, it flies ? Nmiles. 10
1 hr = 60 minutes
A plane’s speed is 540 knots
In 60 minutes, it flies 540 Nmiles.
In one minute, it flies ? Nmiles. 9

22. Speed Changes & Proportional Reasoning
D = R • T
3 minutes
2 minutes
1 minute
Gaby 10 steps/minute 10 20 30
Tonisha 9 steps/minute 10 20 30
-- This slide builds upon the previous one.
-- Remind the participants that Tonisha’s rate is 1 step/minute slower than Gaby’s. So Tonisha falls behind at a rate of 1 step/minute.
-- Notice the plane speeds. As with Gaby and Tonisha, the difference in speeds is one unit per minute–in this case, 1 Nmile/minute.
-- With each mouse click (representing one minute of travel), DAL88 advances 10 Nmiles and UAL74 advances 9 Nmiles.
-- Thus, similarly to Gaby and Tonisha, UAL74 falls behind 1 Nmile per minute.
-- So after 1 minute, UAL74 is 1 Nmile behind.
-- After 2 minutes, UAL74 is 2 Nmiles behind.
-- After 3 minutes, UAL74 is 3 Nmiles behind.
-- Note: To understand why the difference in plane speeds is 1 Nmile per minute, consider the following.
-- Notice that the DAL88 speed is 600 knots and the UAL74 speed is 540 knots, a difference of 60 knots.
-- 60 knots is 60 Nmiles per hour. Since there are 60 minutes in one hour, we can also express 60 knots as 60 Nmiles per 60 minutes. That’s equivalent to 1 Nmile per 1 minute.
-- So the difference in plane speeds, 60 knots, can also be expressed as a difference of 1 Nmile per minute.
Start
Distance - steps
DAL88 at 600 kts 10 Nmiles /minute 10 20 30
UAL74 at 540 kts 9 Nmiles/minute 10 20 30
Start
Distance - Nmiles

23. Reducing Speed in 60-Knot Increments
600 kts 10 Nmi/min
540 kts 9 Nmi/min 10 20 30
1 min
2 min
3 min
-- This slide builds upon the previous two.
-- Remind the participants that Tonisha’s rate is 1 step/minute slower than Gaby’s. So Tonisha falls behind at a rate of 1 step/minute.
-- Notice the plane speeds. As with Gaby and Tonisha, the difference in speeds is one unit per minute–in this case, 1 Nmile/minute.
-- With each mouse click (representing one minute of travel), DAL88 advances 10 Nmiles and UAL74 advances 9 Nmiles.
-- Thus, similarly to Gaby and Tonisha, UAL74 falls behind 1 Nmile per minute.
-- So after 1 minute, UAL74 is 1 Nmile behind.
-- After 2 minutes, UAL74 is 2 Nmiles behind.
-- After 3 minutes, UAL74 is 3 Nmiles behind.
480 kts 8 Nmi/min 10 20 30
420 kts 7 Nmi/min 10 20 30
Distance - Nmiles

24. Create Your Own Air Traffic Problems
Demonstrate Create a Problem

25. 6 Problem Sets Introduction to ATC Speed Changes Route Changes
ATC INTRO D
SPEED INTRO
Route Changes E F B C
CHANGE SPEED
CHANGE SPEED
CHANGE ROUTE
CHANGE ROUTE
Do some or all or Problem Sets in each grade level.

26. A Workbook for Each Problem Set
-- This slide gives an overview of a Student Workbook.
-- Each participant can briefly examine his/her copy of the workbook that you have distributed.
-- Note that Simulator Problems 2-1 and 2-2 (just demoed and explored) are closely examined in this workbook.

27. Classroom Implementation
Explore with the Simulator.
Do the math in the Workbook.
Meet the time challenge.

28. Student Materials Free Online! Ready to Download! Movies
Workbook for each Problem Set
Simulator
Animated Simulator tutorial
Simulator Quick Start Guide

29. Educator Materials Free Online! Ready to Download!
2-page Quick Start Guide
Educator Guide
Teacher Guide for each Problem Set with Answers & Solutions
Answers & Solutions to All Simulator Problems

30. Teacher access to ALL materials
Free!
Teacher access to ALL materials
Smart Skies Homepage
ALL of the Smart Skies materials can be accessed from this homepage.
The Smart Skies website is a teacher website. It is not for students.

31. Free! www.smartskies.nasa.gov/lineup LineUp With Math Homepage
Teacher access to all materials
-- This slide represents the LineUp With MathTM website.

32. Two Ways to Access Materials
The navigation bar at the top of the web page
Alignments
-- The Standards button provides access to alignments to the middle school math standards for all 50 states.
The problem & Simulator buttons at the bottom

33. www.atcsim.nasa.gov Free! Accessible to Students, as well as Teachers
Click Here to Open the Simulator
Accessible to Students, as well as Teachers
– This the Simulator home page. Students and teachers access the simulator here.
– Students have access to this page only. (And not to the LIneUp With Math home page that contains the teacher materials.)
– To run the full version of the simulator, click the indicated link; an Internet connection is required./
– To download a limited demo version of the simulator, click the button on the navigation bar.
Simulator & Student Page

34. Smart Skies Dissemination
Professional development workshops at math and science conferences– e.g., NCTM, NSTA, …
– FlyBy Math (the other Smart Skies activity set) was featured on the cover of the NCTM middle school journal.
NCTM Mathematics Teaching in the Middle School, August 2006

35. Smart Skies Dissemination
Museums
Smithsonian Udvar-Hazy Center
Hiller Aviation Museum
National partnership with FAA
Classroom visits from air traffic controllers
Student visits to air traffic control facilities
– The listed museums feature LineUp With Math student workshops.

36. Materials for Teacher Workshops
Download a PowerPoint presentation
Choose either product
– Teachers can use this website to plan and conduct a professional development workshop.

37. Contact Us By
On the web:
Greg Condon, Project Lead -
Miriam Landesman, Education Lead -