Creating Problems for Solution with Technology

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

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

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

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

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

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

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

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

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

Questions:

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

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

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

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

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 http://cedarpoint.com/thrill/millennium/mffacts2.htm

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

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