4. Statistics and Probability

 
  1. Exploring Univariate and Bivariate Data (S1)
  2. Sampling and Study Design (S2)
  3. Probability Models (S3)
  4. Sampling Distributions (S4)
  5. Point and Interval Estimation (S5)
  6. Significance Testing (S6)
  7. Inference for Regression (S7)
  8. Assessing Assumptions of Statistical Models (S8)

 

Additional Links to General Mathematics Sites

 

3. Probability Models (S3)

Students understand and apply sampling and various sampling methods, examine surveys and experiments, identify bias in methods of conducting surveys, and learn strategies to minimize bias. They understand basic principles of good experimental design.

 

High School

  1. Probability Models
    1. Analysis of Human Population Growth
      This 3-part activity is designed to introduce students to human population growth. Several online sources are used in this activity, including a World Population Clock that is a real time data site. In Parts 1 and 2 students make a variety of mathematical calculations designed to illustrate the current size and growth rate of the human population. In Part 3 students analyze a graph that shows human population growth over time and complete a written assessment that requires them to demonstrate their level of understanding of population size, growth rate, factors that have led to current levels of growth, and predictions for the future.  The site includes three activities, rubrics for assessment, and suggestions for accomodations for special needs.
    2. Conditional Probability and Independence
      This site is a tutorial for conditional probability, trees, independent events. It includes quizzes with answers and explanations.
    3. Fire
      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.
    4. Frankfurter High: Hot Dog Sales
      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.
    5. Global Warming Statistics
      This site is a good resource for teachers and contains an activity for the students to collect data on the Internet about changing climates. The students then analyze the data with statistics as well as plot graphs and extrapolate.
    6. Let's Make a Deal
      Interactive student activity based on the game show "Let's Make a Deal".
    7. Mystery Liquids
      Teacher lesson plan that focuses on a student project that requires students to make and test a hypothesis about the density of liquids, do an experiment, collect data, and then represent the data collected in a graph.
    8. Polling: Sampling Variation and the Margin of Error
      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.
    9. Probability
      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.
    10. Probability Central: Learning Section
      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.
    11. Probability Simulator-Dice and Spinners
      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.
    12. Probability With a Spinner
      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.
    13. Put the Heart into Mathematics
      Outstanding      ! This NCTM (Illuminations) activity is geared for students in grades 9-12. This unit contains four different teacher lesson plans with reproducible student worksheets, and interactive graphing and data collection capabilities. The lessons provided explore cardiac output by measuring the amount of blood being pumped by an experimental heart. Students will explore rates of change and accumulation in the context of cardiac output and accumulation using hands on experimentation, data collection, "pencil and paper" activities, etc.
    14. Random Birthdays
      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.
    15. Running to Conclusions and Exponential Fit
      Using spreadsheets, this lesson explores the process of finding the best fitting exponential curve to sets of statistical data.
    16. Sampling Distribution
      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.
    17. Shedding Light on the Subject: Function Models of Light Decay
      Presented by NCTM (Illuminations), this website provides the teacher with a four lesson unit on the decay of light as an exponential model. Teachers will appreciate the printer friendly lesson plans accompanied by student objectives, worksheets, and references. The site includes an interactive grapher and downloadable movie clips (quick time required) for students.
    18. The Birthday Problem: A short lesson in probability
      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.
    19. The Cereal Box Problem - A Lesson in Expected Value
      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.
    20. The Hermit Problem
      This project tracks the spread of a disease on a desert island inhabited by hermits. It uses the Internet and other student activities to explore the concept of expected value (ie: How many hermits do we expect to get the disease?).
    21. The Winning Edge: Probability in Basketball
      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.
    22. The World Series Problem
      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.
    23. What Percentage of your Class is Right or Left Handed?
      Cythia Lanius provides this lesson for high school students to determine the percentage of students that are right or left handed in a classroom. Students perform experiments, collect data, graph the data, and analyze their findings. Worksheets, spreadsheets and teacher notes are available.
    24. What's the City Mileage of a Typical American Car?
      The goals of this lesson are to teach the methods of finding confidence intervals and tests for differences using the bootstrap method. Many statistical ideas will be investigated such as randomness, how to sample from a data set and how to make decisions based on statistical evidence. The activities use car mileage and sports topics. The class level that this lesson is geared towards are high school mathematics or statistics classes who have an interest in investigating statistical decision making.

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