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Introduction: Keep track of the counter at you favorite site for several months. Is it increasing, decreasing, or staying the same in popularity? Can you find an equation that will allow you to predict the amount of visitors your site will have in the months to come?
Prior Knowledge: Some knowledge of curve fitting.
Grade Level: 7-12
Task: This lesson will actually be done sometime after the first semester in the class. However, students will have been gathering data for the project for the entire year. Students will plot their data, try to fit a equation to their data, and speculate on why the data shows the pattern it does and project its future growth.
Resources: I encourage using your favorite site that has a counter, but here are some potential addresses.
http://kingsnet.kings.k12.ca.us/index.asp
Process: The students will visit their favorite site weekly throughout the semester/year and keep track of the number of visitors each time they go. After the students have acquired a collection of data they will plot the data on a graph. Next the students will analyze the growth pattern of their data. Is it linear, exponential, logarithmic, etc.? If the students are sophisticated enough, they can try to find an equation which fits their collection of data. Lastly the students will speculate about future data and why they see the trend that they do.
Learning Advice: It is important to note whether the counter resets itself periodically or is purely cumulative as this will affect the way they analyze the data.
Evaluation: The following items could be assessed: quality and accuracy of their graph, correctness of the type of growth pattern they describe and how well they fit the curve, and their analysis of potential causes for their growth/decline pattern and predictions of future trends.
Extensions: Have your students set up their own counted home page to track.
Conclusion: Students will have had an opportunity to have fun on the web and had practice in analyzing data trends.
California Mathematics Academic Standards:
Grade 7:
Algebra and Functions
1.0 Students express quantitative relationships using algebraic terminology, expressions, equations, inequalities and graphs1.5 represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in terms of the situation represented by the graphGrade 8-12:
Algebra I
16.0 Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functionsAlgebra II
12.0 Students know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay.Probability and Statistics
8.0 Students organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line and bar graphs, stem-and-leaf displays, scatterplots, and box-and-whisker plots.
NCTM 9-12:
STANDARD 1: MATHEMATICS AS PROBLEM SOLVING
STANDARD 3: MATHEMATICS AS REASONING
STANDARD 4: MATHEMATICAL CONNECTIONS
STANDARD 5: ALGEBRA
STANDARD 6: FUNCTIONS
August 1996 / Revised June 16,
2000
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