Overview
National Aeronautics and
Space Administration
NASA Distance-Rate-Time Math
In Air Traffic Control
Welcome
Grades 5-9
Introduction to FlyBy Math™
Physical Experiment
sdard
Stan sed
a
B
ree!
Six Math Methods
F
Online Graphing Visualization Tool
How to Access the Classroom Materials
Rebecca Green & Gregory Condon
NCTM Annual Meeting – Denver, CO
19-Apr-2013
Smart Skies™
Challenges of Air Traffic Control
World’s Largest D-R-T Problem
During the busiest travel times, about how
many commercial planes are flying in the US?
About 5,000 planes!
Smart Skies™
Smart Skies™
Two Classroom Activity Sets
FlyBy Math!
LineUp With Math!
Pre-algebra or Algebra"
Pre-algebra"
!
Free
!!Real-world applications
!!Multiple representations
Free!
!!Aligned to state math standards
Smart Skies™
www.smartskies.nasa.gov/flyby
1
Analyze Two-Plane Problems
Standards-based & Classroom-tested
Planes at same altitude"
All 50 states
D=R
!! Rates"
!! Data collection"
!! Graphing"
!! Problem solving"
!! Modeling"
!! Measurement"
Alignment to Common Core Standards in process.
FlyBy Math™
• T!
!! Which plane arrives first at the intersection?
!! How far apart are the planes at that time?
FlyBy Math™
Multiple Representations
Physical experiment"
Introduction to FlyBy Math™
Print-based worksheets
with 6 math methods"
Distance traveled!
20!
15 !
FlyBy Math Video
10 !
5!
0!
X WAL27
0
!
10
!
20
30
! Time !
40
!
50
!
60
!
Pre-algebra & Algebra"
Graphing#
Simulator"
FlyBy Math™
Five Air Traffic Control Problems
1
2
4
3
Understand Problem 2
5
!! Speed of each plane =
1/2 foot per second!
Same Speed!
Same Speed!
Different Speeds!
Different Speeds!
16 ft
20 ft
WAL27
NAL63
!! Will the planes meet
at the intersection?"
Grade 5!
Grade 6!
!! If not, how far apart
Grade 7!
Grade 8!
Grade 9!
FlyBy Math™
Different Speeds!
will they be when the
first plane arrives?"
FlyBy Math™
2
Six Math Methods
Non-traditional
Physical Experiment
•! Students act as Pilots, Controllers, and
NASA Scientists."
Traditional
•! Students measure & lay out two jet routes."
•! Pilots step down the routes."
•! Students measure and record time
and separation distance."
FlyBy Math™
!! Count feet and seconds"
!! Draw and stack blocks "
!! Plot points on two vertical lines"
!! Plot points on a grid"
!! Derive & use the distance-rate-time formula"
!! Graph two linear equations"
FlyBy Math™
Count Feet and Seconds
32 sec.
30 sec.
28 sec.
26 sec.
24 sec.
22 sec.
20 sec.
18 sec.
16 sec.
14 sec.
12 sec.
10 sec.
8 sec.
6 sec.
4 sec.
2 sec.
0 sec.
•! Speed = ! foot per second
•! So in 1 second,
the plane travels:
? feet
!
foot
•! Thus the plane will
travel 1 foot in
?
2 seconds.
4-foot
head start
WAL27!
FlyBy Math™
Draw and Stack Blocks
! ft/sec = 5 feet in 10
? seconds
20 ft! 40 sec.
19! 38 sec.
18! 36 sec.
17! 34 sec.
16! 32 sec.
30 sec.
15!
28 sec.
14!
26 sec.
13!
24 sec.
12!
22 sec.
11!
20 sec.
10!
18 sec.
9!
16 sec.
8!
14 sec.
7!
12 sec.
6!
5!
4!
3!
2!
1!
0!
feet!
= 1 foot in ?2 seconds
Routes meet here at 20 ft
20 ft.
!
10 sec.
!
!
!
4-foot
head start
!
start.
0 ft.!
FlyBy Math™
WAL27 starts here.
(4-foot head start)
0 ft.!
NAL63 starts here.!
Plot Points on a Grid
32 sec.
30 sec.
Distance
traveled
!
10 ft.!
20 sec.
10 ft.!
!
10 sec.
!
5 ft.
X
WAL27
5 ft.!
10 sec.
NAL63
0 ft.!
start
0 ft.!
WAL27 !
FlyBy Math™
5 ft.
10 sec.
15 ft.!
15 ft.!
!
20 sec.
5 ft.
10 ft.!
!
20 ft.!
32 sec.
10 ft.!
!
15 ft.!
!
10 sec.
10 sec.
20 ft.
!
30 sec.
15 ft.!
!
20 sec.
10 sec.
5 ft.
Routes meet here at 20 ft
Distance
traveled
2 sec.
10 sec.
!
Plot Points on Two Vertical Lines
20 ft.
!
30 sec.
10 sec.
10 ft.!
!
start
NAL63!
32 sec.
15 ft.!
Distance !
traveled
10 sec.
8 sec.
6 sec.
4 sec.
2 sec.
20 ft.
!
2 sec.
0 ft.!
0
!
NAL63 !
10
!
20
30
40
!
!
!
Time traveled - seconds
50
!
60
!
FlyBy Math™
3
Derive and Use
Distance-Rate-Time Formula
NAL63
d = 0.5 t!
d = !r !•" t!
t!
seconds!
d!
t =!
r!
tWAL27
16 feet!
=!
= 32 seconds!
0.5 feet/sec!
tNAL63 = !
Graph Two Linear Equations
d = 0.5 t + 4!
t!
seconds!
d!
feet!
0!
0!
10!
5!
20!
10!
30!
15!
40!
20!
d!
4-foot head start!
32
30 sec!
sec!!
20 ft.!
20
sec!
15 ft.!
10
sec!
Distance from 10 ft.!
route start!
20 feet!
= 40 seconds!
0.5 feet/sec!
!
!
Let’s Slow One Plane
4!
10!
9!
20!
14!
30!
19!
40!
24
5 ft.!
!
0
!
FlyBy Math™
d!
feet!
0!
!
0 ft.!
FlyBy Math™
WAL27
10
20
30
40
50
!
!
!
!
!
Time traveled - seconds
60
!
t!
Graphing Simulator
What happens to the planes where the lines intersect?
d!
20 ft.!
15 ft.!
Distance
Distance
from
10 ft.!
traveled
route
start!
!
4-foot head start!
5 ft.!
t!
0 ft.!
0
!
10
!
20
30
40
!
!
!
Time traveled - seconds
50
!
60
!
FlyBy Math™
!! In each panel, we can change speed & starting position.
!! A change in one panel changes the other two panels.
!! Helps students link the math to the real world.
FlyBy Math™
Crash or No Crash?
!! When the lines cross on the graph, do the planes collide?
!! We can use the simulator to answer the question.
FlyBy Math™
No Crash!
!! On the graph, the lines intersect at (30, 15).
!! At 30 sec, each plane is 15 ft from its jet route start.
!! Note: the planes are on 2 routes that intersect at 20 ft.
FlyBy Math™
4
Crash!
Challenge!
!! On the graph, the lines again intersect at (30, 15).
!! At 30 sec, each plane is again 15 ft from the jet route start.
!! Note: the planes are flying on the same route.
FlyBy Math™
FlyBy Math™
!! For 2 planes on 2 routes, configure the graph
to represent a collision.
!! Where is the only place on the routes
a collision can occur?
Problem 4
Problem 4
!! Speed of WAL27 = #
1/3 foot per second#
"
!! Speed of NAL63 = #
1/2 foot per second"
16 ft
20 ft
WAL27
NAL63
1/3 ft/sec
1/2 ft/sec
!! Will the planes meet
at the intersection?"
!! If not, how far apart
will they be when the
first plane arrives?"
FlyBy Math™
FlyBy Math™
www.smartskies.nasa.gov
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www.smartskies.nasa.gov/flyby
!
Free
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FlyBmepag
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New! FlyBy Math Graphing Tool
Click here to
access the
graphing
simulator &
materials
LineUp With Math™
FlyBy Math™
5
FlyBy Math Educator Materials
FlyBy Math:
•! Quick Start Guide
Free O
nline!
FlyBy Math Student Materials
FlyBy Math:
Free O
nline!
•! Movies
•! Educator Guide
•! Role playing signs
•! Answer Guide for each workbook and assessment
•! Workbook for each problem set
•! Video and Poster
•! Assessment for each problem set
FlyBy Math Simulator:
FlyBy Math Simulator:
•! Quick Start Guide
•! Simulator
•! Teacher Guide
•! Animated Introduction to the Simulator
•! Answer Guide for each worksheet and assessment
•! Worksheet for each problem set
•! Animated Introduction to the Simulator
•! Assessment for each problem set (except problem set A)
www.atcviztool.nasa.gov
Materials for Teacher Workshops
www.smartskies.nasa.gov/trainer
!
Free
For nts
de
Stu &
rs
che
Tea
Click this
image to open
the multiple
representation
simulator.
FlyBy Math™
Smart Skies Dissemination
•! Professional development
workshops: NCTM, NSTA,
CMC,"
Contact Us
•! By email:
•! On the web: www.smartskies.nasa.gov
•! Rebecca Green, Project Lead
[email protected]
•! MTMS cover article,
August 2006
•! Greg Condon, Project Lead
[email protected]
•! Chosen for NCTM’s online
project, Making Connections:
Mathematics across Disciplines
Smart Skies™
[email protected]
Smart Skies™
6