1. Creating Problems for Solution with Technology

2. Necessity of Technology
_____________ numbers
Functions that are difficult to graph
Varieties of _________________
seek to find an appropriate modeling function
Multiple views of a problem

3. Motivation Develop students' abilities to ______________
Need for good judgment about mathematical claims
Problems should …
require thought and analysis
development ability to communicate results

4. Sources for Problems World Almanac Amusement parks
__________________ figures
sports results
Amusement parks
physics
motion
_______________ strategies

5. Sources for Problems World Wide Web Interesting quotes
____________________ news
____________________
"off the wall" facts
Interesting quotes
__________________________________
Warning: take care lifting questions from existing text books

6. Writing the Questions
Begin with ________________________ that grab the students' interest
Alternatively …
Present _________________________________, students come up with all of solution
Lead students through derivation of ____________ formulas, functions, relationships
Occasionally state questions _______________
Ask for preliminary _____________________, reassessment

7. Use a Variety of Viewpoints
Numeric
tables of ___________
dimensions
distances
___________________
View results of _________________
max, min, roots, intersections
combining functions (arithmetically, composition)
Can give clues as to the ______________ required to graph a function

8. Use a Variety of Viewpoints
Symbolic representation
manipulated with technology
enables ________________________
necessary for communication
Pictures, diagrams
for description of original problem
may be to scale or purposefully ____________
may be _________________ as part of solution

9. Describe Solutions Written format Verbal presentations Post web pages
require full ______________
well formed paragraphs
______________________ diagrams
Verbal presentations
use of _____________________
encourage presentation technology
Post web pages

10. Problem Categories Find real data
plot the data points
use regression for a __________________ function
Given two functions graphed together, what questions can be asked?

11. Questions:

12. Problem Categories Use _____________________ equations
Model objects moving on the graph as a function of __________________
straight line, spirals, circular
Model two objects that _______________________________
Measure distance between the moving objects

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

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

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

16. Roller Coaster Questions
Which is the best seat?
see better in front seat
pull higher g's in back (assume, 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

17. 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

18. Teams Note your team number
Person in group with first letter of family name closest to end of alphabet is the scribe
Write/type up your problem, print out
Another group will use checklist to evaluate your submission