Creating Problems for Solution with Technology

Necessity of Technology

Messy numbersFunctions that are difficult to graphVarieties of regression seek to find an appropriate modeling

function

Multiple views of a problem graphical numerical symbolic textual

Motivation

Develop students' abilities to think mathematicallyNeed for good judgment about mathematical claims advertisers government media

Problems should … require thought and analysis development ability to communicate results

Sources for Problems

World Almanac population figures finance figures sports results

Amusement parks physics motion business strategies

Sources for Problems

World Wide Web science news graphs "off the wall" facts

Interesting quotes

Warning: take care lifting questions from existing text books

Jail Releases Upset Judges

Writing the Questions

Begin with statements that grab the students' interestAlternatively … 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 looselyAsk for preliminary guesses, reassessment

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

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

Describe Solutions

Written format require full sentences well formed paragraphs labeled diagrams

Verbal presentations use of visuals encourage presentation technology

Post web pages

Problem Categories

Find real data plot the data points use regression for a modeling function

Given two functions graphed together, what questions can be asked?

Problem Categories

Use Parametric EquationsModel objects moving on the graph as a function of time straight line, spirals, circular

••time

0

Problem Categories

Model two objects that must (not) meetMeasure distance between the moving objects

Use parametric equations

Levels of Problems

Usually we do not write our own homework questionsMore 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

Group Project Management

Best to assign the groups randomize and manually alter as needed

Assign locations for group gatheringAssign one person to be the "scribe" who will record the official resultsProvide a handout that precisely describes the task to be performed, problem to be solved

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 gradeAward bonus points for … extra elegance portions of the problem early or first submission

A Project for this Workshop

A problem for solution with technology concerning a rollercoaster.

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 MelliniumForce.htm

Roller Coaster Questions

What comparisons/contrasts can you make?

Roller Coaster Questions

The newest coasteris 420 feet highGoes from 0 to 120 mph in 4 secMore Facts

Your Task …

Write a problem that requires technology for its solutionUse whatever portion of the facts about the ride that you chooseTry to use/require all of symbolic, numeric, graphic, textual expressionsLead students through solution stepsFinal objective must be clearly statedSuggest enrichment/elegance pursuitsSpecify level: algebra, precalc, calculus

Teams

Note small number on back of front page of handout – that is your team numberPerson in group with first letter of family name closest to end of alphabet is the scribeWrite/type up your problem, print outAnother group will use checklist to evaluate your submission

Front of room

Group 1 Group 2 Group 3

Group 4 Group 5 Group 6