Writing Problems for Solution with Technology Welcome to Texas

Writing Problems for Solution with Technology

Welcome to Texas

Words of Wisdom from Texas

• Always drink upstream from the herd.

Words of Wisdom from Texas

• The quickest way to double your money is to fold it over and put it back in your pocket.

Words of Wisdom from Texas

• Never order chicken fried steak in a restaurant without a juke box.

Words of Wisdom from Texas

• Never kick a cow chip on a hot day.

Words of Wisdom from Texas

• Don't squat with your spurs on.

Writing Problems for Solution with Technology

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

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

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

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."

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

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)

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 Equations

• Model objects moving on the graph as a function of time

• straight line, spirals, circular

Problem Categories

• Model two objects that must (not) meet

• 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 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 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

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

A Project for this Workshop

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

Roller Coaster Questions

• What comparisons/contrasts can you make?

Roller Coaster Questions

• The newest coaster is 420 feet high

• Goes from 0 to 120 mph in 4 sec

• More Facts

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

• 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 submission

F.Y.I.

• Technology used:

• Ink Link pen, by Seico

• This presentation available (PowerPoint and Web versions) at

• web2\index.htm