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

1. Smart Skies FlyByMathTM National Aeronautics and Space Administration Six Approaches to Distance-Rate-Time Problems in Air Traffic Control Grades 5-9 Free! << Your Name>> <<Your Venue>> <<Date>>

2. Overview

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

4. World’s Largest D-R-T Problem <<Show the video: “24-Hours of Flight”>>

5. Two Classroom Activity Sets • Real-world applications • Hands-on experiments • Multiple representations Free! Free!

6. www.smartskies.nasa.gov/flyby

7. Standards-based & Classroom-tested • Rates • Data collection • Modeling • Measurement • Graphing • Problem solving FlyBy MathTM

8. Analyze 2-Plane Problems 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

9. 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

10. Five Air Traffic Control Problems 1 2 Same Speed Same Speed 3 4 Different Speeds Different Speeds 5 Different Speeds FlyBy MathTM

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

22. Let’s Slow One Plane 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

23. 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.

24. Crash or No Crash? • When the lines cross on the graph, do the planes collide? • We can use the simulator to answer the question.

25. 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.

26. 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.

27. 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.

28. www.smartskies.nasa.gov Teacher access to ALL materials Smart Skies Homepage

29. www.smartskies.nasa.gov/flyby FlyBy Math Homepagefor teachers New! FlyBy Math Graphing Tool Click here to access the graphing simulator and materials

30. Two Ways to Access Materials • The navigation bar at the top of the web page Alignments • The problem buttons at the bottom FlyBy MathTM

31. 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

32. www.atcviztool.nasa.gov Free! For Students & Teachers Click here to open the graphing simulator

33. Materials for Teacher Workshops www.smartskies.nasa.gov/trainer Download a PowerPoint presentation Choose either product

34. Dissemination and Outreach • Professional development workshops at NCTM math conferences • NCTM Mathematics Teaching in the Middle School, August 2006

35. Contact Us << Your contact information>>

36. Thank you from Smart SkiesTM What’s on your radar screen?