The Culver Academies

        My name is Daniel Tobert. Currently I am a senior at the Culver Academies finishing up Precalculus taught by Mr. Haynes. For the final project grade, I will be compiling the previous three projects and providing links so they can all be accessible. The projects consist of various topics that test and exercise the subjects we have studied throughout the two terms. The concepts and standards for these projects are outlined on the NCTM site. 

PROJECT 1:

The first project consisted of explaining and visually representing ten different types of functions. It was a group project, and my group included Lulu Zhang, Megan Ulery, and Gregory Couch. Each member was assigned two or three different functions used in Precalc to define and provide a graph for. Gregory did Even, Odd and Inverse functions. Megan did Step, Greatest/Least Integer functions. Lulu explained Onto and One-to-One functions. I defined Piecewise Defined and Constant functions. The definitions for these functions were largely facilitated by the following website: Wolfram. As organizer, I compiled the data, which can be accessed here: Functions Project. 

PROJECT 2:

The second project was done alone and involved fitting a model to data. During this project I took the carbon dioxide levels over different years and found a model that accurately represented the model. However the trick to the project in the later half was when it asked to find an equation to model a sinusoidal line. I am proud to say I was one of few who accurately found a model that fit the oscillating line. In addition I predicted what carbon dioxide levels would be as well as what such a model can do for society. The link to this project is found here: Fitting a Model to Data.

PROJECT 3:

The third project consisted gathering data about two different media interfaces from our hometowns. Our group included Max Sills, Whitney Breidenbaugh and Andrew Parlin. The first part of the project was to get population figures and maps of our hometowns. Mine for example was Houston, Texas with a population of about 2 million people. The second part of the project was to get readership data for a magazine and the number of viewers for a local TV station. From those figures we estimated the trend of viewers and readership. We then assigned different tasks to each member and picked up one person's data to create a group web page. The link to our page can be found here: Map Project.

CONCLUSION

These projects have taught our class a number of things. They have taught us how to organize data on a web page, extrapolate figures from the data and present data to a group of listeners. Although sometimes a hard task, they have helped us learn a skill that will be invaluable in the information age.

NCTM STANDARDS

The NCTM standards provide a chance to reflect on how closely they relate to the concepts we did during the three projects. Here is the link to the website.

NUMBERS AND OPERATIONS: A student must understand numbers, know how to represent them, their relationships with other numbers and number systems. In addition, students must know how numbers interact and relate with each other. In the FITTING A MODEL TO DATA project (link can be found above), we took carbon dioxide levels and represented them in a graph, along with formulating a relationship between them. Through doing this, we demonstrated how we met the NCTM Standard for understanding numbers and their operations. For further information on Numbers and Operations, visit the link.

DATA ANALYSIS AND PROBABILITY: According to NCTM, a student must know how to question data, analyze that data through organization, and finally answer the initial questions through this analysis. In addition, students must use statistical methods to analyze data. They also must make predictions and inferences on the data, and use basic concepts of probability. In the MAP PROJECT (link can be found above), we took the number of viewers or listeners of entertainment sources and organized them into graphs and formulas. Also, we predicted the future number of  listeners, viewers, or readers for the source. By both analyzing and predicting this number, we demonstrated the NCTM Standard for Numbers and Operations. More information on this standard can be found at the previous link.

ALGEBRA: NCTM specifies that for a student to be proficient in Algebra, he/she must understand patterns, relations, and functions. In addition, one must represent mathematical situations, use mathematical models, and analyze change in different contexts. During the FUNCTIONS (link can be found above) project, we defined 10 different functions. By doing this, we demonstrated a proficiency and understanding of various types of functions used in algebra. More information on the Algebra standard by NCTM can be be found at the link.

COMMUNICATION: Students must organize and consolidate mathematical thinking to meet the NCTM standard on Communication. Further, the student must analyze the mathematical thinking of his/her peers and use mathematical language when communicating mathematical thinking to others. We demonstrated this standard in the FINAL PROJECT (link can be found above). Using mathematical language, we summarized and illustrated various mathematical concepts. This demonstrated the Communication Standard, and further information can be found at the link.