Writing Problems for Solution
with Technology
Dr. Steve Armstrong
LeTourneau University
Longview, TX
SteveArmstrong@letu.edu
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New Attraction
Writing Problems for Solution
with Technology
Dr. Steve Armstrong
LeTourneau University
Longview, TX
SteveArmstrong@letu.edu
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
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graphical
numerical
symbolic
textual
Motivation
Develop students' abilities to think
mathematically
Need for good judgment about mathematical
claims

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advertisers
government
media
Problems should …
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require thought and analysis
development ability to communicate results
Sources for Problems
World Almanac
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population figures
finance figures
sports results
Amusement parks
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physics
motion
business strategies
Sources for Problems
World Wide Web
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science news
graphs
"off the wall" facts
NCTM Mathematics
Teacher Media Clips
Interesting quotes
Warning: take care
lifting questions from existing text books
Writing the Questions
Begin with statements that grab the students'
interest
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"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:

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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
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tables of values
dimensions
distances
profit, loss
Can give clues as to
the window required
to graph a function
View results of graphs

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max, min, roots, intersections
combining functions
(arithmetically, composition)
Use a Variety of Viewpoints
Symbolic representation
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manipulated with technology
enables proofs
necessary for communication
Pictures, diagrams
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for description of original problem
may be to scale or purposefully generic
may be required as part of solution
Presenting Solutions
Written format
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What expectations
would you want for
written reports?
State the problem
Describe the solution
Give all formulas used
Use full sentences, well formed
paragraphs
Diagrams with labels
Screen shots from calculator
Presenting Solutions
Verbal presentations
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What elements
Use of visuals
should be included
in verbal
Encourage presentation technology
presentations?
All members of group participate
Speak plainly, avoid "verbal commas"
Give points for "dressing up"
Presenting Solutions
Describe
recommendations you
Post web pages
would give for a sequence
 Consistent backgrounds, fonts
of web pages.
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Logical sequence of ideas
Easily used links
Links to other relevant pages
Diagrams, screen shots from calculator
Problem Categories
Find real data
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http://lib.stat.cmu.edu/DASL/DataArchive.html
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
•
•
0
time
Problem Categories
Use parametric equations
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
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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
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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 …
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extra elegance portions of the problem
early or first submission
A Project for this Workshop
A problem for solution with technology concerning a roller coaster.
Roller Coaster Questions
Which is the best seat?

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see better in front seat
pull higher g's in back
(100 feet from front)
Millennium Force facts
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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

www.letu.edu/people/SteveArmstrong/NCTM/Web2