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Writing Problems for Solution with TechnologyPowerPoint Presentation

Writing Problems for Solution with Technology

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### Writing Problems for Solution with Technology

### Writing Problems for Solution with Technology

Dr. Steve ArmstrongLeTourneau UniversityLongview, TX

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.

Dr. Steve ArmstrongLeTourneau UniversityLongview, TX

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

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 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

•

•

time

0

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
- 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

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
- Facts about the Millennium Force

Roller Coaster Questions

- What comparisons/contrasts can you make?

Roller Coaster Questions

- The newest coasteris 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

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