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
- Probability Models
- Conditional Probability and Independence
This site is a tutorial for conditional probability, trees, independent events. It includes quizzes with answers and explanations. - El Nino or El No-no
Student interactive site where the students collect data (Water temperatures from ocean buoys.) and present it using different statistical methods. They will then predict what the future weather patterens will be from their collected data. This is a Webquest site - 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. - Frankfurter High: Hot Dog SalesStudents use probability and simulation to determine an optimum ordering policy. The website is not interactive but contains student worksheets, teacher notes and case studies.
- 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. - 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. - ProbabilityAn 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.
- 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. - Probability Simulator-Dice and SpinnersThis 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.
- Probability With a SpinnerStudents 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.
- Put the Heart into MathematicsOutstanding! 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.
- Random BirthdaysThis site is an applet that will randomly generate from 10 to 100 birthdays and show the number of times people share the same birthday.
- 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. - Sampling DistributionThis 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.
- Shedding Light on the Subject: Function Models of Light DecayPresented 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.
- 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. - 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?). - 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. - 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.
- 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.
- Conditional Probability and Independence