1. Writing Problems for Solution with Technology Dr. Steve Armstrong LeTourneau University Longview, TX SteveArmstrong@letu.edu

2. Welcome to Texas

3. Words of Wisdom from Texas  Always drink upstream from the herd.

4. Words of Wisdom from Texas  The quickest way to double your money is to fold it over and put it back in your pocket.

5. Words of Wisdom from Texas  Never order chicken fried steak in a restaurant without a juke box.

6. Words of Wisdom from Texas  Never kick a cow chip on a hot day.

7. Words of Wisdom from Texas  Don't squat with your spurs on.

8. New Attraction

9. Writing Problems for Solution with Technology Dr. Steve Armstrong LeTourneau University Longview, TX SteveArmstrong@letu.edu

10. Necessity of Technology Messy numbers Functions that are difficult to graph Varieties of regression seek to find an appropriate modeling function Multiple views of a problem graphical numerical symbolic textual

11. Motivation Develop students' abilities to think mathematically Need for good judgment about mathematical claims advertisers government media Problems should … require thought and analysis development ability to communicate results

12. Sources for Problems World Almanac population figures finance figures sports results Amusement parks physics motion business strategies

13. Sources for Problems World Wide Web science news graphs "off the wall" facts NCTM Mathematics Teacher Media Clips NCTM Mathematics Teacher Media Clips Interesting quotes Warning: take care lifting questions from existing text books Jail Releases Upset Judges

14. Writing the Questions Begin with statements that grab the students' interest "Recent evidence of skin cancer caused by excessive sun exposure has made us aware of the intensity of the sun. When might be the best/worst time of day to soak up sun?" "A TV satellite dish service has hired you as a consultant to determine the best price for the initial fees for their dish and receiver." "Consider a recent e-mail hoax about Bill Gates. People who participated in a pyramid e-mail experiment would be eligible for the prize of a trip to Disney World."

15. Writing the Questions Two possible approaches: Present total task in detail, students come up with all of solution Lead students through derivation of intermediate formulas, functions, relationships Occasionally state questions a bit loosely Real life problems are rarely accurately and succinctly stated Ask for preliminary guesses, reassessment

16. Use a Variety of Viewpoints Numeric tables of values dimensions distances profit, loss View results of graphs max, min, roots, intersections combining functions (arithmetically, composition) Can give clues as to the window required to graph a function

17. Use a Variety of Viewpoints Symbolic representation manipulated with technology enables proofs necessary for communication Pictures, diagrams for description of original problem may be to scale or purposefully generic may be required as part of solution

18. Presenting Solutions Written format State the problem Describe the solution Give all formulas used Use full sentences, well formed paragraphs Diagrams with labels Screen shots from calculator What expectations would you want for written reports?

19. Presenting Solutions Verbal presentations Use of visuals Encourage presentation technology All members of group participate Speak plainly, avoid "verbal commas" Give points for "dressing up" What elements should be included in verbal presentations?

20. Presenting Solutions Post web pages Consistent backgrounds, fonts Logical sequence of ideas Easily used links Links to other relevant pages Diagrams, screen shots from calculator Describe recommendations you would give for a sequence of web pages.

21. Problem Categories Find real datareal data plot the data points use regression for a modeling function Given two functions graphed together, what questions can be asked? http://lib.stat.cmu.edu/DASL/DataArchive.html

22. Problem Categories Use Parametric Equations Model objects moving on the graph as a function of time straight line, spirals, circular time 0

23. Problem Categories Model two objects that must (not) meet Measure distance between the moving objects Use parametric equations

24. Levels of Problems Usually we do not write our own homework questions More likely to write test questions write them to require technology Also write project questions for a one day exercise for a long term for groups or for individuals

25. Group Project Management Best to assign the groups randomize and manually alter as needed Assign locations for group gathering Assign one person to be the "scribe" who will record the official results Provide a handout that precisely describes the task to be performed, problem to be solved

26. Project Grading Instructor should carefully read the handout note specific answers asked for assign values to be awarded create a grading checklist Inform students how grade is weighted in relation to total term grade Award bonus points for … extra elegance portions of the problem early or first submission

27. A Project for this Workshop A problem for solution with technology concerning a roller coaster.

28. Roller Coaster Questions Which is the best seat? see better in front seat pull higher g's in back (100 feet from front) Millennium Force facts 310 foot high hill (300 foot drop) first hill 80° angle 92 mph max track length 6595 feet ride takes 2:45 Facts about the Millennium Force

29. Roller Coaster Questions What comparisons/contrasts can you make?

30. Roller Coaster Questions The newest coaster is 420 feet high Goes from 0 to 120 mph in 4 sec More Facts

31. Your Task … Write a problem that requires technology for its solution Use whatever portion of the facts about the ride that you choose Try to use/require all of symbolic, numeric, graphic, textual expressions Lead students through solution steps Final objective must be clearly stated Suggest enrichment/elegance pursuits Specify level: algebra, precalc, calculus

32. Teams Gather in groups of 4 – 5 people Person in group with first letter of family name closest to end of alphabet is the scribe Write up your problem Another group will use checklist to evaluate your submissionchecklist

33. F.Y.I. Technology used: Ink Link pen, by Seico This presentation available (PowerPoint and Web versions) at www.letu.edu/people/SteveArmstrong/NCTM/Web2