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## PowerPoint Slideshow about ' Smart Skies FlyBy Math TM' - favian

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### Multiple Representations

### Let’s Slow One Plane

### Graphing Visualization Tool

### Crash or No Crash?

### No Crash!

### Crash!

### Challenge!

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

### Speaker Evaluation

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

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

About 5,000 planes!

- Real-world applications
- Hands-on experiments
- Multiple representations

Free!

Free!

Standards-based & Classroom-tested

- 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

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

Five Air Traffic Control Problems

1

2

Same Speed

Same Speed

3

4

Different Speeds

Different Speeds

5

Different Speeds

FlyBy MathTM

Grade Level Focus

4

5

3

1

2

Same Speed

Same Speed

Different Speeds

Different Speeds

Different Speeds

Grade 5

Grade 6

Grade 7

Grade 8

Grade 9

FlyBy MathTM

A Look at Problem 2

2

Same Speed

Students use the Student Workbook to:

- Read the problem

- Do the experiment

- Do the math

FlyBy MathTM

Understand the Problem

- 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

The Physical Experiment

- 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

Six Math Methods

- 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

Count Feet and Seconds

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-foot headstart

4

6sec.

3

4 sec.

2

2 sec.

1

start

0

feet

WAL27

NAL63

FlyBy MathTM

Draw and Stack Blocks

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

Plot Points on Two Vertical Lines

- 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

Plot Points on a Grid

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

Derive and Use the Distance-Rate-Time Formula

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

Graph Two Linear Equations

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.

4-ft headstart

0 ft.

t

FlyBy MathTM

Time traveled - seconds

d

20 ft.

15 ft.

Distance

traveled

10 ft.

5 ft.

4-foot head start

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

- 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.

- When the lines cross on the graph, do the planes collide?
- We can use the simulator to answer the question.

- 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.

- 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.

- 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.

FlyBy Math Homepagefor teachers

New! FlyBy Math Graphing Tool

Click here to access the graphing simulator and materials

- The navigation bar at the top of the web page

Alignments

- The problem buttons at the bottom

FlyBy MathTM

Classroom Materials

- Educator Materials:

Free online!

- 2-page Quick Start Guide

- Educator Guide

- Teacher Guide for each Problem with Answers and Solutions

- Download
- Reproduce
- Distribute

- Student Materials:

- Movies

- Student Workbook for each Problem

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

FlyBy MathTM

Materials for Teacher Workshops

www.smartskies.nasa.gov/trainer

Download a PowerPoint presentation

Choose either product

Dissemination and Outreach

- Professional development workshops at NCTM math conferences

- NCTM Mathematics Teaching in the Middle School, August 2006

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