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Adjacent Circles

Adjacent Circles. An activity on data analysis and probability concepts and skills. Lindsay Moore. SMTE 4382 . History of Probability Theory . The mathematical theory of probability first came about in 1654 Blaise Pascal and Pierre de Fermat fundamental principles of probability theory

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Adjacent Circles

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  1. Adjacent Circles

    An activity on data analysis and probability concepts and skills Lindsay Moore SMTE 4382
  2. History of Probability Theory The mathematical theory of probability first came about in 1654 Blaise Pascal and Pierre de Fermat fundamental principles of probability theory 1657, ChristianHuygenspublished the first book on probability; De Ratiociniis in Ludo Aleae,analysis on games of chance 1812, Pierre de Laplacebook, Théorie Analytique des Probabilitésconcerned with using probability for scientific and practical problems 1933, Russian mathematician, A. Kolmogorov outlined an axiomatic approach that forms the basis for the modern theory we use today.
  3. Aspects of Probability-Cultural, psychological, social actually cultural differences in the perception of risk and there is a cultural difference in the attitude towards perceived risk. the German accountants are more conservative as compared to American accountants. Chinese participants are more risk seeking than American participants. Many theories and beliefs and psychological studies are supported by probability statistics. Attribution Theory Men are more likely to take risks than women.
  4. Importance of probability: Connections with other math topics very different from the normal addition, subtraction, multiplication, division problems data analysis and probability are highly compatible Helps develop good number sense Connected to future topics Encounter probability problems throughout high school, undergraduate studies and graduate studies for many different careers. Many jobs rely on or use the study of statistics dailyto predict outcomes of a future event. Bayesian probability is the process of using probability to try to predict the likelihood of certain events occurring in the future. Relativity to the real world Games jobs
  5. Jobs that use probability statistics: weather forecasting baseball business’ sales forecast study of genetics science experiments and much more!
  6. Objective Predict the number of ways a pattern can be colored with a given amount of colors, following certain rules. Generalize the possible number of combinations that can be made. Discover all the combinations of a simple event.
  7. Directions Each student will need colored crayons and an activity sheet. Five circles are connected as shown. Each of the five circles must be colored solidly with one of three colors: red, blue, or yellow. For example: Two circles connected by a line segment may NOT be the same color!
  8. Solution We need to organize the data in some way:

    Case 1 — B and C are the same color.

    Case 2 — B and C are different colors.
  9. Why is my activity cool……. concrete evidence earlier grade’s math curricula usually leave probability all but untouched until high school even adults aren't great at understanding probability a great example on the types of probability problems that let students learn through exploration
  10. For extra practice: A Die generator: http://nces.ed.gov/nceskids/chances/index.asp Demonstrates how increasing or decreasing the number of dice rolls affects an outcome. Red fish vs. Yellow fish: http://www.bbc.co.uk/education/mathsfile/shockwave/games/fish.html Come up with your own calculations for the probability of catching fish of a certain color. A game of Pig: http://www.pleasanton.k12.ca.us/pleasanton/MathWeb/Grade7/Probability/PIG/PIG.html Find rules and score cards for the popular game using probability.
  11. Resources: http://math-and-reading-help-for-kids.org/teaching_probability_to_kids.html http://www.faqs.org/periodicals/201004/2040416851.html http://www.cc.gatech.edu/classes/cs6751_97_winter/Topics/stat-meas/probHist.html http://en.wikipedia.org/wiki/History_of_probability http://www.teacherlink.org/content/math/interactive/probability/numbersense/numbersense/home.html http://www.nctm.org/about/content.aspx?id=13822 http://www.experiment-resources.com/bayesian-probability.html http://mathforum.org/dr.math/faq/faq.prob.world.html http://illuminations.nctm.org/LessonDetail.aspx?id=L615 http://www.cognitionandculture.net/Hugo-s-blog/cross-cultural-differences-in-risk-taking.html http://findarticles.com/p/articles/mi_hb3538/is_4_52/ai_n28958299/pg_7/ http://www.jstor.org/pss/2634710
  12. Thank you very much!!
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