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Think about the things you do, the problems you solve. Pick something that involves quantities and write an algebraic model for it.

For instance, you may track baseball statistics. Can you generalize some of the calculations that are involved? Can you derive a set of calculations on which you might base a prediction of which team will win the World Series?

If you make quilts, you use a lot of geometry and

Business and home finance, provide a lot of opportunities to use

Remember, the model works like a recipe for solving the problem. The model (equations) will have a letter for each quantity which can vary. For instance, in the interest equation above, the principle (p) can change.

In the project, you will formulate a model and then use it to solve the particular problem. However, it should be possible to use your model to solve other similar problems.

I can use I = .05p with p= $2000. Then, I = .05(2000) = $100. However, I could use any other amount in place of p.

I could also generalize this model further by using a letter for the interest rate, r. The equation becomes I = rp. Now, I can change the interest rate, too, making my model much more useful.

It is fine to work backwards through the modeling process, too. If you know how to solve the specific problem arithmetically, start there. Use that to help you to identify quantities that are constant (same number always used in this kind of problem) and those that are variable.

You may very well need more than one equation for a complete model.

If you sit down and think this through, you will probably find that it is not as hard as it appears at first.

Assignment:

Identify a problem from your own experience that can be modeled algebraically (i.e. with equation(s)). You don't need to do something super complicated but do give yourself room to show some of what you have learned about

Create the model for solving the general problem using one or more equation(s). Use your model to solve a specific problem.

Write a report that discusses the problem that you have modeled. Be sure to identify the variables; mention any assumptions that you made; show the equation(s) that model the solution; work out a solution to a particular problem using your model. Discuss why and how it all works. Discuss your model in terms of

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Create the model for solving the general problem using one or more equations. Use the model to solve a specific problem. Write a report that discusses the problem modeled. Be sure to identify the variables; mention any assumptions made; show the equations that model the solution; work out a solution to a particular problem using the model. Discuss why and how it all works. Discuss the model in terms of

For instance, the eccentricity for a circle is zero. Earth's eccentricity is only 0.0167, while Pluto, the planet with the largest eccentricity, is .25.

Visually, this is what Keplar sought to explain:

Mathematically, however, linear algebra makes the picture an easily understood, computable function.

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If I need to fax the lesson plans instead of you using them from the web site I can do that. The lessons are a combination of lecture and powerpoint. The powerpoint part might be difficult to fax. I would have to fax thumbnails of the slides.

Thank you

Judy

References

Algebra for All - Not with Today's Textbooks, Says AAAS. (2000). Retrived April 1, 2003, at http://www.prject2061.org/newsinfo/press/r1000426.htm.

Algebra: Some Common Misconceptions. (n.d.). Retrieved April 1, 2003 at http://www.quesnrecit.qc.ca/mst/mapco/pdf/algemisc.pdf.

Aziz, N., Pain, H.G., Brna, P. (1995). Modelling and Mending Students' Misconceptions in Translating Algebra Word PRoblems Using a Belief Revision System in Taps (Abstract).

Presented In the proceedings of the 7th World Conference on Artificial Intelligence in Education, AI-ED 95, Virginia, AACE. Retrieved April 1, 2003 from DAI Database.

Homework Humdingers. (n.d.). Retrieved April 1, 2003 at http://www.funmaths.com / worksheets/downloads/view.htm?ws0100_1.gif.

Making the Transition from Arithmetic to Algebra. (n.d). Retrieved April 2, 2003, at http://www.edhelper.com/arithmetic_to_algebra.htm.

Marain, Dave (2002). Reply to "misconceptions in algebra?

need input from teachers."

Retrieved April 1, 2003 at http://mathforum.org/epigone/math-teach/twirkahpald/

Positive Exponents. Retrieved March 29, 2003, from MTSU WEB SITE:

htp:/ / www.mtsu.edu/~jan2h/Lesson2.htm.

Principles for School Mathematics. (n.d.). Principles and Standards:National Council of Teachers of Mathamatics. Retrieved April 1, 2003 from ttp://standards.nctm.org / document/

Solving Equations. Retrieved March 29, 2003, from MTSU WEB SITE:

htp:/ / www.mtsu.edu/~jan2h/Lesson1.htm.

Tall, David (1992). The Transition from Arithmetic to Algebra: Number Patterns, or Proceptual

Programming? Retrieved April 3, 2003 from University of Warwick, Mathematics

Education Research Centre web site: http://www.warwick.ac.uk/staff/David.Tall pdfs/dot1993f-arith-alg-brisbane.pdf.

Translating Words Into Equations. Retrieved March 29, 2003, from MTSU WEB SITE:

htp:/ / www.mtsu.edu/~jan2h/Lesson3.htm.

Unit 16 Algebra: Linear Equations Teaching Notes. (n.d.). Retrieved April 1, 2003, at http://ex.ac.uk/cimt/mepres/book7/y7s16tn.pdf.

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1. Describe the situation

2. Translate it into an algebraic problem and

3. Explain how to use

all sources have to be from the internet

Reference:

No Authors Listed. (1996) Achieving Mathematical Power. Mathematics Curriculum Framework. Accessed via the World Wide Web on July 17, 2005 at http://www.doe.mass.edu/frameworks/math/1996/patterns.html

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