The following is a list of thirty open-ended project ideas (in no particular order). You may work by yourself or with a partner. You will present an update on your progress and this will be a chance for you to seek critique and suggestions from your peers. Choose a topic that you find interesting and challenging.
Families of Curves Project. Continue work on the Family of Curves Project we began last semester. Use the same equation, choose a new family, or explore several different ones.
Graphing Activity. Continue work on the Graphing Activity where you design a picture and then write the directions for someone else to follow. Make the pictures more complex. This time use equations of lines and parabolas to draw your designs.
Algebra Book. Write your own book about how to factor, graph lines, or solve equations. Choose an audience and write the book for them. Include examples, diagrams, exercises, and whatever else you think will make it interesting, informative, and fun.
Linear Systems. Research some consumer issue and analyze it mathematically. For example, research different rental car offers or cellular phone plans for the best deal. See Section 7.10 “Systems of Equations: Word Problems” for other examples.
Balance Puzzles. Solve and design several “balance” puzzles. For (a simple) example, if 2 red marbles balance 3 white marbles, how many red marbles balance 18 white marbles? You may want to put your collection together as a book. See me for more examples.
2-Dimensional Graphing. We are studying Cartesian Coordinates in class. What other types of 2-dimensional coordinate systems are there? What do the equations look like? What do the graphs look like? Create your own system. You should find some very interesting graphs.
3-Dimensional Graphing. How do we assign coordinates to points in 3-dimensions? What other types of 3-dimensional coordinate systems are there? Perhaps you could design and build a 3-D model using what you learn. You may want to use computer graphics programs as well.
Quadratic Systems. We study how to find the intersection of two lines in class. How do you find the intersection of two parabolas (quadratic equations)? This lends itself nicely to symbolic, numerical, graphical, and verbal explorations.
Quadratic Applications. Problems where objects are thrown or dropped. See, for example, Section 6.9. Create your own models and extensions of a problem you find interesting.
Sports Research. Find a sport that you enjoy playing or watching. Research the mathematics involved. This can include statistics, management, the dynamics of play, etc. You may want to choose one particular application and explore it in depth.
Patterns. Look for patterns in number sequences, paper folding, graphic designs. Where do you see such patterns in the real world? Make your own activities and puzzles. Connect what you learn to equations and rules of algebra. Perhaps you will want to explore fractal geometry.
Rate Problems. See Section 11.10 of the book. More complex equations to describe more interesting motion situations. These equations create interesting graphs that include asymptotes.
Asymptotes. What are “asymptotes”? When do they show up in equations? What do they look like numerically and graphically? Perhaps explore word problems that result in asymptotes. See Section 11.10 of the book.
Superball Problem. Study the behavior of a bouncing ball. Analyze its motion comparing different quantities such as height vs. time bouncing, time vs. radius, accuracy vs. mass, etc.
Slope of a Curve. We study the slopes of lines in this class. How would you find the slope of a curve? What does that mean? What does it look like? Good opportunities for graphical and numerical analysis. You would be doing Calculus in Algebra I!
Area Under a Curve. How do you find the area of an unusual shape? What if you know the equation of the graph? Create a systematic method for calculating the area under a given curve.
Population. A national census was taken recently. Research national, state, and/or local statistics. Graph your findings, make predictions, study the past. Analyze various sub-populations.
Base Math. We use a base-ten number system. What would our number system look like if we only had 5 fingers? Or 8? Or 20? Or 2? How would adding, multiplying, etc. change? Historically, different cultures have used different bases. Research a few. Can you calculate in Mayan?
Class Game. Develop a game for the class that either uses or reviews the algebraic concepts we have been studying. Plan to conduct a mini-version of the game for your progress presentation.
Scientific Study. Connect algebra to your science class. Develop your own project that combines some of the key ideas. Perhaps you want to conduct an experiment and share your findings like a science fair project.
Pascal’s Triangle. What is “Pascal’s Triangle”? How is it used in Algebra? How is it constructed? What are some of the patterns found within it?
Pi. What does the symbol p (“pi”) represent? Why is it so important? What is its history?
The Parabola. What is a “parabola”? What determines its shape? What is the geometric definition? What are the properties of a parabola? What formulas are associated with these properties? When does it show up in applications?
Fibonacci Numbers. 0, 1, 1, 2, 3, 5, 8, . . .What are the “Fibonacci Numbers”? How are they found? Where in nature are Fibonacci patterns visible? Why are they interesting?
The Calculator. Who invented the calculator? What kinds of “calculators” were used before electronics? Research the history of calculators. Solve sample problems that use various types of calculators. Include some research and/or history of the issue of calculators in classrooms.
Powers of Ten. How do we represent numbers that are really, really large? What kinds of things are measured with powers of ten? Give some examples used in the study of time and space. Include graphs (linear and logarithmic) to compare values. What is a googol?
Mathematicians. Who are the people that developed the mathematics we use today? Choose a historical figure in mathematics. What were his or her contributions to the subject? Be sure to choose someone who worked with material you understand. What do professional mathematicians do today? Who are they? What kinds of work do they do on a daily basis?
Math in the News. How is math used in everyday news reports on television, in newspapers, and in magazines? Follow a particular news program and/or section of the newspaper for several days. Record how numbers are used in reporting. What kinds of math are referred to the most? Which stories generate the most mathematical analysis? Choose a story that uses math and follow it. Do your own mathematical analysis to share with the class.
Time. How did we come to use the system of time that we use today? Does everyone measure time the same way? What are different units of time? How were modern (analog and digital) clocks invented? Include a historical discussion of time and culture.
Your Own Idea. Design your own project.
Be creative. Apply the algebra you know and push the limits of your understanding to
tackle something beyond this course. The idea is to
learn something new. Enjoy the experience and share what you learn
with others.
Be sure to write down your partner's name and phone number somewhere handy.
Abby Brown -Torrey Pines High School - 2/2001 (Revised 4/2002)