Overview. NASA Distance-Rate-Time Math In Air Traffic Control. World s Largest D-R-T Problem. Challenges of Air Traffic Control

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National Aeronautics and Space Administration NASA

Welcome Overview Introduction to Standards- Based Physical

Tool How to Access the Classroom Materials Rebecca Green &

Challenges of Air Traffic Control World s Largest D-R-T

LineUp With Math Pre-algebra or Algebra" Pre-algebra"

1 National Aeronautics and Space Administration NASA Distance-Rate-Time Math In Air Traffic Control Grades 5-9 Welcome Overview Introduction to Standards- Based Physical Experiment Six Math Methods Online Graphing Visualization Tool How to Access the Classroom Materials Rebecca Green & Gregory Condon NCTM Annual Meeting Denver, CO 19-Apr-213 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, planes Two Classroom Activity Sets FlyBy Math LineUp With Math Pre-algebra or Algebra" Pre-algebra" Real-world applications Multiple representations Aligned to state math standards 1

Analyze Two-Plane Problems Standards-based & Classroom-tested Planes at same altitude"

Measurement" Alignment to Common Core Standards in process.

How far apart are the planes at that time?

with 6 math methods" Distance traveled 2 15 FlyBy Math Video 1 5 X 1 2 3 Time 4 5 6

Understand Problem 2 5 Speed of each plane = 1/2 foot per second Same Speed Same Speed

2 Analyze Two-Plane Problems Standards-based & Classroom-tested Planes at same altitude" All 5 states D=R Rates" Data collection" Graphing" Problem solving" Modeling" Measurement" Alignment to Common Core Standards in process. T Which plane arrives first at the intersection? How far apart are the planes at that time? Multiple Representations Physical experiment" Introduction to Print-based worksheets with 6 math methods" Distance traveled 2 15 FlyBy Math Video 1 5 X Time Pre-algebra & Algebra" Graphing# Simulator" Five Air Traffic Control Problems Understand Problem 2 5 Speed of each plane = 1/2 foot per second Same Speed Same Speed Different Speeds Different Speeds 16 ft 2 ft Will the planes meet at the intersection?" Grade 5 Grade 6 If not, how far apart Grade 7 Grade 8 Grade 9 Different Speeds will they be when the ﬁrst plane arrives?" 2

Physical Experiment Six Math Methods Students act as Pilots, Controllers, and NASA Scientists." Students measure & lay out two jet routes." Pilots step down the routes.

" Traditional Non-traditional 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

3 Physical Experiment Six Math Methods Students act as Pilots, Controllers, and NASA Scientists." Students measure & lay out two jet routes." Pilots step down the routes." Students measure and record time and separation distance." Traditional Non-traditional 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" Count Feet and Seconds Draw and Stack Blocks Speed = foot per second So in 1 second, the plane travels:? feet foot Thus the plane will travel 1 foot in? seconds sec. 12 sec. 1 sec. 8 sec. 6 sec. 4 sec. 2 sec. 4-foot sec. head start 3 sec. 28 sec. 26 sec. 24 sec. 22 sec. 2 sec. 18 sec. 16 sec. 2 ft 4 sec sec feet 36 sec. 34 sec. 3 sec. 28 sec. 26 sec. 24 sec. 22 sec. 2 sec. 18 sec. 16 sec. 14 sec. 12 sec. 1 sec. 8 sec. 6 sec. 4 sec. 2 sec. start 1 Distance traveled 2 ft. 1 ft. ft. ft/sec = 5 feet in 1? seconds 2 sec. 1 sec. 1 sec. 1 sec. starts here. (4-foot head start) = 1 foot in? 2 seconds Routes meet here at 2 ft 3 sec. 2 sec. 2 sec. 1 sec. start. 1 sec. 1 sec. 1 sec. starts here. 2 ft. 1 1 ft. ft. Plot Points on Two Vertical Lines Plot Points on a Grid Distance traveled 4-foot head start 2 ft. 1 1 ft. ft. Routes meet here at 2 ft 3 sec. 2 sec. 1 sec. start 2 ft. 1 1 ft. ft. X Distance traveled 2 ft. 1 1 ft. ft. 1 1 sec. 2 sec. 3 sec Time traveled - seconds 5 6 3

4 Derive and Use Distance-Rate-Time Formula d = r " t t = d r t = t = 16 feet.5 feet/sec = 32 seconds 2 feet = 4 seconds.5 feet/sec d =.5 t t d seconds feet Distance from route start 4-foot head start Graph Two Linear Equations 2 ft. 1 1 ft. ft. d 1 sec 32 3 sec sec 2 sec Time traveled - seconds 5 d =.5 t t d seconds feet t Let s Slow One Plane Graphing Simulator What happens to the planes where the lines intersect? 2 ft. d 1 Distance Distance from route traveled start 4-foot head start 1 ft. ft Time traveled - seconds 5 6 t 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? No Crash 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 (3, 15). At 3 sec, each plane is 15 ft from its jet route start. Note: the planes are on 2 routes that intersect at 2 ft. 4

Crash Challenge On the graph, the lines again intersect at (3, 15).

Note: the planes are flying on the same route.

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

foot per second" Will the planes meet at the intersection?

" 1/3 ft/sec 1/2 ft/sec www.smartskies.nasa.

5 Crash Challenge On the graph, the lines again intersect at (3, 15). At 3 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 graph to represent a collision. Where is the only place on the routes a collision can occur? Problem 4 Problem 4 Speed of = # 1/3 foot per second# " Speed of = # 1/2 foot per second" Will the planes meet at the intersection?" 16 ft 2 ft If not, how far apart will they be when the first plane arrives?" 1/3 ft/sec 1/2 ft/sec Smart Skies Homepage For Teachers FlyBy Math Homepage For Teachers New FlyBy Math Graphing Tool Click here to access the graphing simulator & materials LineUp With Math 5

FlyBy Math Educator Materials FlyBy Math Student Materials FlyBy Math: Quick Start Guide Educator Guide Free Online Answer Guide for each workbook and assessment Video and Poster FlyBy Math:

assessment Animated Introduction to the Simulator FlyBy Math Simulator: Simulator Animated Introduction to the Simulator Worksheet for each problem set Assessment for each problem set

Smart Skies Dissemination Professional development workshops: NCTM, NSTA, CMC," MTMS cover article, August 26 Chosen for NCTM s online project, Making Connections: Mathematics across

6 FlyBy Math Educator Materials FlyBy Math Student Materials FlyBy Math: Quick Start Guide Educator Guide Free Online Answer Guide for each workbook and assessment Video and Poster FlyBy Math: Movies Role playing signs Workbook for each problem set Assessment for each problem set Free Online FlyBy Math Simulator: Quick Start Guide Teacher Guide Answer Guide for each worksheet and assessment Animated Introduction to the Simulator FlyBy Math Simulator: Simulator Animated Introduction to the Simulator Worksheet for each problem set Assessment for each problem set (except problem set A) Materials for Teacher Workshops For Students & Teachers Click this image to open the multiple representation simulator. Smart Skies Dissemination Professional development workshops: NCTM, NSTA, CMC," MTMS cover article, August 26 Chosen for NCTM s online project, Making Connections: Mathematics across Disciplines By Contact Us smartskies@mail.nasa.gov On the web: Rebecca Green, Project Lead rebecca.a.green@nasa.gov Greg Condon, Project Lead gregory.condon@nasa.gov 6

Elem Calc w/trig II Spring 08 Class time: TR 9:30 am to 10:45 am Classroom: Whit 257 Helmi Temimi: PhD Teaching Assistant, 463 C

Elem Calc w/trig II Spring 08 Class time: TR 9:30 am to 10:45 am Classroom: Whit 257 Helmi Temimi: PhD Teaching Assistant, 463 C Email: temimi@vt.edu Office Hours 11:00 am 12:00 pm Course contract, Syllabus