Example JiTT WarmUp Exercises
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Symmetry and Tilings: An Exploration part of Examples
Students are directed to read through a Web-based tutorial on Symmetry and Tilings in the form of an short and colorful article entitled Tilings and Tesselations; afterwards, they answer several questions on tilings (tessellations), tiling terminology, types of symmetry (isometries), periodic tilings and Penrose tilings.
Pythagorean Theorem Investigations part of Examples
Secondary Math Ed majors or Geometry students are directed to a Web site where they read through a rich and extensive collection of proofs of the Pythagorean Theorem, some accompanied by Java applets. Each student then selects two proofs to prepare to present to the class-a geometric proof and a visual proof-and writes a detailed outline of each proof. The student also indicates one additional proof that was of particular interest and the reason(s) for its selection.
History of Pi and Buffon's Needle part of Examples
Students are directed to visit the MacTutor History of Mathematics Archive and read an extensive online article entitled History of Pi; in addition, they make use of an interactive simulation of Buffon's Needle experiment. Afterwards, they answer several questions on how mathematicians calculated approximations for the value of pi and on the formulas that they used; they also discuss and analyze Buffon's experiment.
Economic Statistics: Hypothesis Testing part of Examples
This activity helps a student recognize the consequences of Type I and Type II errors in hypothesis testing.