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Writing Problems for Solution with Technology. Dr. Steve Armstrong LeTourneau University Longview, TX. [email protected] Welcome to Texas. Words of Wisdom from Texas. Always drink upstream from the herd. Words of Wisdom from Texas.

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Writing problems for solution with technology

Writing Problems for Solution with Technology

Dr. Steve ArmstrongLeTourneau UniversityLongview, TX

[email protected]

Welcome to texas
Welcome to Texas

Words of wisdom from texas
Words of Wisdom from Texas

  • Always drink upstream from the herd.

Words of wisdom from texas1
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 texas2
Words of Wisdom from Texas

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

Words of wisdom from texas3
Words of Wisdom from Texas

  • Never kick a cow chip on a hot day.

Words of wisdom from texas4
Words of Wisdom from Texas

  • Don't squat with your spurs on.

Writing problems for solution with technology1

Writing Problems for Solution with Technology

Dr. Steve ArmstrongLeTourneau UniversityLongview, TX

[email protected]

Necessity of 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


  • 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
Sources for Problems

  • World Almanac

    • population figures

    • finance figures

    • sports results

  • Amusement parks

    • physics

    • motion

    • business strategies

Sources for problems1

Jail Releases Upset Judges

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
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 questions1
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

Can give clues as to the window required to graph a function

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 viewpoints1
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
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
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 categories1
Problem Categories

Use Parametric Equations

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

    • straight line, spirals, circular



Problem categories2
Problem Categories

Use parametric equations

  • Model two objects that must (not) meet

  • Measure distance between the moving objects

Levels of problems
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
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
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
A Project for this Workshop

A problem for solution with technology concerning a rollercoaster.

Roller coaster questions
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 questions1
Roller Coaster Questions

  • What comparisons/contrasts can you make?

Roller coaster questions2
Roller Coaster Questions

  • The newest coasteris 420 feet high

  • Goes from 0 to 120 mph in 4 sec

  • More Facts

Your task
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


  • 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