Algebra gives us the means to write an equation or set of equations that model the solution to a problem. Once we have the equations, we have the means of solving all problems of a given type. It’s like the way my husband cooks. He has one recipe from which he can make pancakes, waffles, and muffins. Likewise, the equation, I= .05p allows us to calculate simple interest at 5% for any amount of principal.
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 algebra. Can you write some equations for what you do? For instance, can you describe the yardage needed in a set of equations? How about the area of each block and the area of the quilt? Is one a function of the other?
Business and home finance, provide a lot of opportunities to use algebra, too. Can you model a business decision algebraically? How about the value of a stock portfolio?
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 algebra.
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 algebra: are you using functions; is your model linear or non-linear; etc. ? You may include a chart and/or graph, and you should if it backs up your mathematics.
