VI. Probability and Discrete Mathematics

 
  1. Probability
  2. Discrete Mathematics

 

Additional Links to General Mathematics Sites

 

High School

  1. Benchmark 1. "Develop an understanding of randomness and chance variation and describe chance and certainty in the language of probability."
    1. Fire - Probability (VI.1.HS.1&4)
      In this site the student picks the probabilty that a tree will catch fire and where in the forest a fire will start. This lesson utilizes concepts of probability, graphing and graph interpretation, mean, and variance in analyzing a simulation of a forest fire. A complete lesson plan is included and a student interactive applet is provided. The simulation then shows what happen to the forest until the fire burns out.
    2. Frankfurter High: Hot Dog Sales - Probability (VI.1.HS.1,2,3,4&5)
      Students use probability and simulation to determine an optimum ordering policy. The website is not interactive but contains student worksheets, teacher notes and case studies.
    3. Guru Math- Probability and Statistics - Probability (VI.1.HS.1&2)
      A tutorial site that is quite informative with respect to probability and statistics. Different graphs are utilized and there is student interaction provided.
    4. Probability - Probability (VI.1.HS.1,2,3,4&5)
      An on-line multimedia unit with interactive applets and questions for assesment with explanations given. The unit starts with basic concepts of probability and continues through the binomial distribution and Bayes' Theorem.
    5. Probability Central: Learning Section - Probability (VI.1.HS.1,2&3)
      This is an explanation of basic probability, with vocabulary and examples that will be easily understood by high school students. The "Learning Section" is where all the information about probability can be found. It is broken into six different sections in order to simplify browsing it. There are five lesson sections and one exercise section. The "Lesson Section" include: 1. Introduction to Probability, 2. Probability Theory, 3. Probability Model, 4. Probability Properties, 5. Rules of Probability. The explanations are clear and concise and the exercises at the end access well the student's knowledge of what has been taught. You can also download the learning section for use off of the Web.
    6. Random Birthdays - Probability (VI.1.HS.1)
      This site is an applet that will randomly generate from 10 to 100 birthdays and show the number of times people share the same birthday.
    7. The Winning Edge: Probability in Basketball - Probability (VI.1.HS.1,2,4&5)
      Students perform an activity to determine what player they would have make the last two free throws of a tied game based on their percentage of shots made using an interactive probability simulator. Follow the link to lesson #4 for an extension activity.
  2. Benchmark 2. "Give a mathematical definition of probability and determine the probabilities of more complex events, and generate and interpret probability distributions."
    1. Frankfurter High: Hot Dog Sales - Probability (VI.1.HS.1,2,3,4&5)
      Students use probability and simulation to determine an optimum ordering policy. The website is not interactive but contains student worksheets, teacher notes and case studies.
    2. Guru Math- Probability and Statistics - Probability (VI.1.HS.1&2)
      A tutorial site that is quite informative with respect to probability and statistics. Different graphs are utilized and there is student interaction provided.
    3. Probability - Probability (VI.1.HS.1,2,3,4&5)
      An on-line multimedia unit with interactive applets and questions for assesment with explanations given. The unit starts with basic concepts of probability and continues through the binomial distribution and Bayes' Theorem.
    4. Probability Central: Learning Section - Probability (VI.1.HS.1,2&3)
      This is an explanation of basic probability, with vocabulary and examples that will be easily understood by high school students. The "Learning Section" is where all the information about probability can be found. It is broken into six different sections in order to simplify browsing it. There are five lesson sections and one exercise section. The "Lesson Section" include: 1. Introduction to Probability, 2. Probability Theory, 3. Probability Model, 4. Probability Properties, 5. Rules of Probability. The explanations are clear and concise and the exercises at the end access well the student's knowledge of what has been taught. You can also download the learning section for use off of the Web.
    5. The Winning Edge: Probability in Basketball - Probability (VI.1.HS.1,2,4&5)
      Students perform an activity to determine what player they would have make the last two free throws of a tied game based on their percentage of shots made using an interactive probability simulator. Follow the link to lesson #4 for an extension activity.
    6. The World Series Problem - Probability (VI.1.HS.2&3)
      This project uses the Internet, and other student activities to explore the concept of expected value (ie: How many games do we expect the World Series to last?). This project has students explore the probability for how many games we expect the World Series to last.
  3. Benchmark 3. "Analyze events to determine their dependence or independence and calculate probabilities of compound events."
    1. Conditional Probability and Independence - Probability (VI.1.HS.3&5)
      This site is a tutorial for conditional probability, trees, independent events. It includes quizzes with answers and explanations.
    2. Frankfurter High: Hot Dog Sales - Probability (VI.1.HS.1,2,3,4&5)
      Students use probability and simulation to determine an optimum ordering policy. The website is not interactive but contains student worksheets, teacher notes and case studies.
    3. Probability - Probability (VI.1.HS.3)
      This site is a student interactive tutorial with examples, animations, and quizzes. They are introduced to probability through simple and compound experiments.
    4. Probability - Probability (VI.1.HS.1,2,3,4&5)
      An on-line multimedia unit with interactive applets and questions for assesment with explanations given. The unit starts with basic concepts of probability and continues through the binomial distribution and Bayes' Theorem.
    5. Probability Central: Learning Section - Probability (VI.1.HS.1,2&3)
      This is an explanation of basic probability, with vocabulary and examples that will be easily understood by high school students. The "Learning Section" is where all the information about probability can be found. It is broken into six different sections in order to simplify browsing it. There are five lesson sections and one exercise section. The "Lesson Section" include: 1. Introduction to Probability, 2. Probability Theory, 3. Probability Model, 4. Probability Properties, 5. Rules of Probability. The explanations are clear and concise and the exercises at the end access well the student's knowledge of what has been taught. You can also download the learning section for use off of the Web.
    6. The Birthday Problem: A short lesson in probability - Probability (VI.1.HS.3&4)
      This activity surveys the possibility of birthdays occurring on the same day in as small a group as 28 students. It also extends the problem to using a computer to simulate this problem to see what the probability generated by a random list of birthdays would be.
    7. The World Series Problem - Probability (VI.1.HS.2&3)
      This project uses the Internet, and other student activities to explore the concept of expected value (ie: How many games do we expect the World Series to last?). This project has students explore the probability for how many games we expect the World Series to last.
  4. Benchmark 4. "Use sampling and simulations to determine empirical probabilities and, when appropriate, compare them to the corresponding theoretical probabilities; understand and apply the law of large numbers."
    1. Fire - Probability (VI.1.HS.1&4)
      In this site the student picks the probabilty that a tree will catch fire and where in the forest a fire will start. This lesson utilizes concepts of probability, graphing and graph interpretation, mean, and variance in analyzing a simulation of a forest fire. A complete lesson plan is included and a student interactive applet is provided. The simulation then shows what happen to the forest until the fire burns out.
    2. Frankfurter High: Hot Dog Sales - Probability (VI.1.HS.1,2,3,4&5)
      Students use probability and simulation to determine an optimum ordering policy. The website is not interactive but contains student worksheets, teacher notes and case studies.
    3. Let's Make a Deal - Probability (VI.1.HS.4&5)
      Interactive student activity based on the game show "Let's Make a Deal".
    4. Polling: Sampling Variation and the Margin of Error - Probability (VI.1.HS.4)
      This site is a good resource for teachers to set up a polling activity for students to understand random sampling and margin of error. They get to look at real poll results so they can compare them to others and understand just how accurate they are.
    5. Probability - Probability (VI.1.HS.1,2,3,4&5)
      An on-line multimedia unit with interactive applets and questions for assesment with explanations given. The unit starts with basic concepts of probability and continues through the binomial distribution and Bayes' Theorem.
    6. Probability Simulator-Dice and Spinners - Probability (VI.1.HS.4)
      This site is for middle to high school students studying experimental probability. Multiple spinners and variation of dice are available in an applet for student use or teacher modeling.
    7. Probability With a Spinner - Probability (VI.1.HS.4)
      Students have the ability to generate a large number of trials that are automatically recorded in a table. The spinner can be adjusted to generate different probabilities.
    8. Sampling Distribution - Probability (VI.1.HS.4)
      This Java applet lets you explore various aspects of sampling distributions. When the applet begins, a histogram of a normal distribution is displayed at the topic of the screen.
    9. The Birthday Problem: A short lesson in probability - Probability (VI.1.HS.3&4)
      This activity surveys the possibility of birthdays occurring on the same day in as small a group as 28 students. It also extends the problem to using a computer to simulate this problem to see what the probability generated by a random list of birthdays would be.
    10. The Cereal Box Problem - A Lesson in Expected Value - Probability (VI.1.HS.4&5)
      This activity addresses the NCTM Standard for Probability for grades 9-12 through it's use of simulations and the cereal box random variable. It includes online simulation of the problem in addition to a hands-on activity using dice and a pencil and paper.
    11. The Winning Edge: Probability in Basketball - Probability (VI.1.HS.1,2,4&5)
      Students perform an activity to determine what player they would have make the last two free throws of a tied game based on their percentage of shots made using an interactive probability simulator. Follow the link to lesson #4 for an extension activity.
  5. Benchmark 5. "Conduct probability experiments and simulations, to model and solve problems, including compound events."
    1. Area Probability (Throw Darts!) - Probability (VI.1.HS.5)
      Students manipulate the size of a circle and a rectangle to explore the probability that a dart thrown into a rectangle will land in the circle. They simulate throwing 100 or 1000 darts and compare the results with the probability. This site provides a 30 day free trail period.
    2. Conditional Probability and Independence - Probability (VI.1.HS.3&5)
      This site is a tutorial for conditional probability, trees, independent events. It includes quizzes with answers and explanations.
    3. Frankfurter High: Hot Dog Sales - Probability (VI.1.HS.1,2,3,4&5)
      Students use probability and simulation to determine an optimum ordering policy. The website is not interactive but contains student worksheets, teacher notes and case studies.
    4. Let's Make a Deal - Probability (VI.1.HS.4&5)
      Interactive student activity based on the game show "Let's Make a Deal".
    5. Probability - Probability (VI.1.HS.1,2,3,4&5)
      An on-line multimedia unit with interactive applets and questions for assesment with explanations given. The unit starts with basic concepts of probability and continues through the binomial distribution and Bayes' Theorem.
    6. The Cereal Box Problem - A Lesson in Expected Value - Probability (VI.1.HS.4&5)
      This activity addresses the NCTM Standard for Probability for grades 9-12 through it's use of simulations and the cereal box random variable. It includes online simulation of the problem in addition to a hands-on activity using dice and a pencil and paper.
    7. The Winning Edge: Probability in Basketball - Probability (VI.1.HS.1,2,4&5)
      Students perform an activity to determine what player they would have make the last two free throws of a tied game based on their percentage of shots made using an interactive probability simulator. Follow the link to lesson #4 for an extension activity.

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