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# Smart Skies FlyBy Math TM - PowerPoint PPT Presentation

Smart Skies FlyBy Math TM. National Aeronautics and Space Administration. Six Approaches to Distance-Rate-Time Problems in Air Traffic Control. Grades 5-9. Free!. Beth A. White . Greater San Diego Math Council Conference. Overview. Intro to Air Traffic Control.

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Presentation Transcript

Six Approaches to Distance-Rate-Time Problems in Air Traffic Control

Free!

Beth A. White

Greater San Diego Math Council Conference

### Overview

During the busiest travel times, about how many commercial planes are flying in the US?

World’s Largest D-R-T Problem

vide

• Real-world applications

• Hands-on experiments

• Multiple representations

Free!

Free!

• Rates

• Data collection

• Modeling

• Measurement

• Graphing

• Problem solving

FlyBy MathTM

Planes at same altitude

D = R • T

• Which plane arrives first at the intersection?

• How far apart are the planes at that time?

FlyBy MathTM

### Multiple Representations

20

15

10

Distance traveled

5

XWAL27

0

0

10

20

30

40

50

60

Time

Physical experiment

Print-based worksheets with 6 math methods

Pre-algebra & Algebra

Graphing SimulatorTool

1

2

Same Speed

Same Speed

3

4

Different Speeds

Different Speeds

5

Different Speeds

FlyBy MathTM

4

5

3

1

2

Same Speed

Same Speed

Different Speeds

Different Speeds

Different Speeds

FlyBy MathTM

2

Same Speed

Students use the Student Workbook to:

• Do the experiment

• Do the math

FlyBy MathTM

• Speed of each plane = 1/2 foot per second

16 ft

20 ft

• Will the planes meet at the intersection?

• If not, how far apart will they be when the first plane arrives?

WAL27

NAL63

FlyBy MathTM

• Students act as Pilots, Controllers, and NASA Scientists.

• Students lay out two jet routes.

• Pilots step down the routes.

• Students measure and record time and separation distance.

FlyBy MathTM

• 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 MathTM

32sec.

40sec.

20 ft

30sec.

38sec.

19

28sec.

36sec.

18

26sec.

34sec.

17

24sec.

32sec.

16

30sec.

22sec.

15

28sec.

20sec.

14

18sec.

26sec.

13

16sec.

24sec.

12

14sec.

22sec.

11

12sec.

20sec.

10

10sec.

18sec.

8sec.

9

16sec.

8

6sec.

14sec.

7

12sec.

4 sec.

6

10sec.

2 sec.

5

8sec.

start

4

6sec.

3

4 sec.

2

2 sec.

1

start

0

feet

WAL27

NAL63

FlyBy MathTM

Routes meet here

2 sec.

32 sec.

10 sec.

30 sec.

2 sec.

Distance traveled

10 sec.

10 sec.

20 sec.

10 sec.

10 sec.

10 sec.

10 sec.

start.

WAL27 starts here.

NAL63 starts here.

20 ft.

20 ft.

15 ft.

15 ft.

10 ft.

10 ft.

5 ft.

5 ft.

0 ft.

0 ft.

FlyBy MathTM

• Routes meet here

32 sec.

30 sec.

Distance traveled

20 sec.

10 sec.

start

0 ft.

NAL63

WAL27

20 ft.

20 ft.

15 ft.

15 ft.

10 ft.

10 ft.

5 ft.

5 ft.

0 ft.

FlyBy MathTM

20 ft.

32 sec.

15 ft.

30 sec.

Distance

traveled

10 ft.

20 sec.

5 ft.

10 sec.

X WAL27

NAL63

0 ft.

0

10

20

30

40

50

60

Time traveled - seconds

FlyBy MathTM

d =

r

t

d

t =

r

16 feet

tWAL27 =

= 32 seconds

0.5 feet/sec.

20 feet

tNAL63 =

= 40 seconds

0.5 feet/sec.

FlyBy MathTM

0

10

20

30

40

50

60

NAL63

WAL27

d = 0.5 t

d = 0.5 t + 4

t

d

t

d

seconds

feet

seconds

feet

0

4

0

0

10

9

10

5

32

sec

d

20

14

30

sec

20

10

20 ft.

30

19

30

15

20

sec

40

24

40

20

15 ft.

10

sec

Distance

traveled

10 ft.

5 ft.

0 ft.

t

FlyBy MathTM

Time traveled - seconds

### Let’s Slow One Plane

d

20 ft.

15 ft.

Distance

traveled

10 ft.

5 ft.

0 ft.

t

Time traveled - seconds

0

10

20

30

40

50

60

What happens to the planes where the lines intersect?

Distance from route start

### Graphing Visualization Tool

• 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.

### Crash or No Crash?

• When the lines cross on the graph, do the planes collide?

• We can use the simulator to answer the question.

### 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.

### Crash!

• 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.

### Challenge!

• For 2 planes on 2 routes, configure the graphto represent a collision.

• Hint: Where is the only place on the routes a collision can occur?

At the intersection at 20 feet.

### www.smartskies.nasa.gov

Smart Skies Homepage

### www.smartskies.nasa.gov/flyby

FlyBy Math Homepagefor teachers

New! FlyBy Math Graphing Tool

• The navigation bar at the top of the web page

Alignments

• The problem buttons at the bottom

FlyBy MathTM

• Educator Materials:

Free online!

• 2-page Quick Start Guide

• Educator Guide

• Teacher Guide for each Problem with Answers and Solutions

• Reproduce

• Distribute

• Student Materials:

• Movies

• Student Workbook for each Problem

• (Optional) Problem pre-test and post-test

FlyBy MathTM

### www.atcviztool.nasa.gov

Free!

For Students & Teachers

www.smartskies.nasa.gov/trainer

Choose either product

• Professional development workshops at NCTM math conferences

• NCTM Mathematics Teaching in the Middle School, August 2006

http://smartskies.nasa.gov

www.nasa.gov

beth.a.white@nasa.gov

http://aesp.psu.edu/request

Smart SkiesTM

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