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Flood Frequency Analysis
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The Flood Frequency Analysis module offers an introduction to the use of ...

The Flood Frequency Analysis module offers an introduction to the use of flood frequency analysis for flood prediction and planning. Through use of rich illustrations, animations, and interactions, this module explains the basic concepts, underlying issues, and methods for analyzing flood data. Common concepts such as the 100-year flood and return periods as well as issues affecting the statistical representation of floods are discussed. Common flood data analysis methods as well as an overview of design events are also covered. As a foundation topic for the Basic Hydrologic Science course, this module may be taken on its own, but it will also be available as a supporting topic providing factual scientific information to support students in completion of the case-based forecasting modules.

Subject:
Hydrology
Material Type:
Module
Provider:
COMET MetEd Collection
Author:
COMET
Flood Frequency Analysis: International Edition
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Flood frequency analysis uses historical flow records to both estimate the frequency ...

Flood frequency analysis uses historical flow records to both estimate the frequency with which floods of a certain magnitude may occur and predict the possible flood magnitude over a certain time period. This module offers a thorough introduction to appropriately constructing the necessary historical data series, calculating the flooding probabilities, and gauging the reliability of the resulting probability values. Methods for assessing flood frequency in basins with limited data are also discussed.

Subject:
Atmospheric Science
Hydrology
Material Type:
Module
Provider:
COMET MetEd Collection
Author:
COMET
Math, Grade 7, Unit 6
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Samples and ProbabilityType of Unit: ConceptualPrior KnowledgeStudents should be able to:Understand the ...

Samples and ProbabilityType of Unit: ConceptualPrior KnowledgeStudents should be able to:Understand the concept of a ratio.Write ratios as percents.Describe data using measures of center.Display and interpret data in dot plots, histograms, and box plots.Lesson FlowStudents begin to think about probability by considering the relative likelihood of familiar events on the continuum between impossible and certain. Students begin to formalize this understanding of probability. They are introduced to the concept of probability as a measure of likelihood, and how to calculate probability of equally likely events using a ratio. The terms (impossible, certain, etc.) are given numerical values. Next, students compare expected results to actual results by calculating the probability of an event and conducting an experiment. Students explore the probability of outcomes that are not equally likely. They collect data to estimate the experimental probabilities. They use ratio and proportion to predict results for a large number of trials. Students learn about compound events. They use tree diagrams, tables, and systematic lists as tools to find the sample space. They determine the theoretical probability of first independent, and then dependent events. In Lesson 10 students identify a question to investigate for a unit project and submit a proposal. They then complete a Self Check. In Lesson 11, students review the results of the Self Check, solve a related problem, and take a Quiz.Students are introduced to the concept of sampling as a method of determining characteristics of a population. They consider how a sample can be random or biased, and think about methods for randomly sampling a population to ensure that it is representative. In Lesson 13, students collect and analyze data for their unit project. Students begin to apply their knowledge of statistics learned in sixth grade. They determine the typical class score from a sample of the population, and reason about the representativeness of the sample. Then, students begin to develop intuition about appropriate sample size by conducting an experiment. They compare different sample sizes, and decide whether increasing the sample size improves the results. In Lesson 16 and Lesson 17, students compare two data sets using any tools they wish. Students will be reminded of Mean Average Deviation (MAD), which will be a useful tool in this situation. Students complete another Self Check, review the results of their Self Check, and solve additional problems. The unit ends with three days for students to work on Gallery problems, possibly using one of the days to complete their project or get help on their project if needed, two days for students to present their unit projects to the class, and one day for the End of Unit Assessment.

Subject:
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Mathematics
Statistics and Probability
Material Type:
Unit of Study
Provider:
Pearson
Introduction to Verification of Hydrologic Forecasts
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This module offers a comprehensive description of a set of common verification ...

This module offers a comprehensive description of a set of common verification measures for hydrologic forecasts, both deterministic and probabilistic. Through use of rich illustrations, animations, and interactions, this module explains how these verification measures can provide valuable information to users with varying needs. In addition to providing a measure of how well a forecast matches observations, verification measures can be used to help forecasters and users learn about the strengths and weaknesses of a forecast.

Subject:
Atmospheric Science
Material Type:
Module
Provider:
COMET MetEd Collection
Author:
COMET
Collaborative Statistics: Custom Version modified by R. Bloom
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No Strings Attached
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Collaborative Statistics was written by Barbara Illowsky and Susan Dean, faculty members ...

Collaborative Statistics was written by Barbara Illowsky and Susan Dean, faculty members at De Anza College in Cupertino, California. The textbook was developed over several years and has been used in regular and honors-level classroom settings and in distance learning classes. This textbook is intended for introductory statistics courses being taken by students at two– and four–year colleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite. The book focuses on applications of statistical knowledge rather than the theory behind it. This custom textbook collection has been modified by R. Bloom for her classes at De Anza College; the homework content for the custom collection is now contained in a separate homework collection.

Subject:
Statistics and Probability
Material Type:
Full Course
Reading
Provider:
Rice University
Provider Set:
Connexions
Author:
Roberta Bloom
Collaborative Statistics Homework Book: Custom Version modified by R. Bloom
Conditions of Use:
No Strings Attached
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This is a custom collection (by R. Bloom) of homework and review ...

This is a custom collection (by R. Bloom) of homework and review problems to accompany Collaborative Statistics textbook custom collection by R. Bloom. Content is derived from Collaborative Statistics written by Barbara Illowsky and Susan Dean, faculty members at De Anza College in Cupertino, California. The textbook by S. Dean and B. Illowsky was developed over several years and has been used in regular and honors-level classroom settings and in distance learning classes. This textbook is intended for introductory statistics courses being taken by students at two– and four–year colleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite. The book focuses on applications of statistical knowledge rather than the theory behind it. This custom version of their collection has been modified by R. Bloom for her classes at De Anza College.

Subject:
Statistics and Probability
Material Type:
Full Course
Homework/Assignment
Provider:
Rice University
Provider Set:
Connexions
Author:
Roberta Bloom
Statistical Method in Economics, Fall 2006
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The course introduces statistical theory to prepare students for the remainder of ...

The course introduces statistical theory to prepare students for the remainder of the econometrics sequence. The emphasis of the course is to understand the basic principles of statistical theory. A brief review of probability will be given; however, this material is assumed knowledge. The course also covers basic regression analysis. Topics covered include probability, random samples, asymptotic methods, point estimation, evaluation of estimators, Cramer-Rao theorem, hypothesis tests, Neyman Pearson lemma, Likelihood Ratio test, interval estimation, best linear predictor, best linear approximation, conditional expectation function, building functional forms, regression algebra, Gauss-Markov optimality, finite-sample inference, consistency, asymptotic normality, heteroscedasticity, and autocorrelation.

Subject:
Statistics and Probability
Economics
Material Type:
Assessment
Full Course
Homework/Assignment
Lecture Notes
Syllabus
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Chernozhukov, Victor
QPF Verification: Challenges and Tools
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This module looks at the common challenges and tools with respect to ...

This module looks at the common challenges and tools with respect to verification of quantitative precipitation forecasts (QPF). Through the use of rich illustrations, animations, and interactions, this module provides an introduction to a variety of methods and approaches for assessing the quality of QPFs. The module examines the need for, and the challenges of verifying precipitation forecasts. An overview is then presented of three verification programs available to most NWS forecast offices: the Hydrometeorological Prediction Center (HPC) verification, the National Precipitation Verification Unit (NPVU), and the Boise Verify Program (BOI Verify). For each of these programs, an introduction is provided covering the strengths and weaknesses as well as specific products available. Case examples are provided where appropriate to illustrate the application of the products in the field. Additional NWS verification tools under development are introduced: the Interactive Verification Program (IVP) and the Ensemble Verification System (EVS).

Subject:
Atmospheric Science
Material Type:
Module
Provider:
COMET MetEd Collection
Author:
COMET
The Flaws of Averages
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This learning video presents an introduction to the Flaws of Averages using ...

This learning video presents an introduction to the Flaws of Averages using three exciting examples: the ''crossing of the river'' example, the ''cookie'' example, and the ''dance class'' example. Averages are often worthwhile representations of a set of data by a single descriptive number. The objective of this module, however, is to simply point out a few pitfalls that could arise if one is not attentive to details when calculating and interpreting averages. The essential prerequisite knowledge for this video lesson is the ability to calculate an average from a set of numbers. During this video lesson, students will learn about three flaws of averages: (1) The average is not always a good description of the actual situation, (2) The function of the average is not always the same as the average of the function, and (3) The average depends on your perspective. To convey these concepts, the students are presented with the three real world examples mentioned above.

Subject:
Education
Mathematics
Numbers and Operations
Material Type:
Lecture
Provider:
M.I.T.
Provider Set:
M.I.T. Blossoms
Author:
Daniel Livengood
MIT BLOSSOMS
Rhonda Jordan
Statistical Methods in Brain and Cognitive Science, Spring 2004
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Descriptive and inferential statistics for the behavioral and neurological sciences are considered. ...

Descriptive and inferential statistics for the behavioral and neurological sciences are considered. Techniques such as t-tests, factorial analysis of (co)variance, correlation, multiple regression, and nonparametric tests are introduced. Subject provides an introductory overview of some advanced methods such as path analysis, factor analysis, discriminant analysis, and analysis of functional MRI data. Basic issues of research design and methodology intimately associated with data analysis are discussed.

Subject:
Statistics and Probability
Psychology
Material Type:
Full Course
Textbook
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Rosenholtz, Ruth
Sticks and Stones
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Students will play Sticks and Stones, a game based on the Apache ...

Students will play Sticks and Stones, a game based on the Apache game "Throw Sticks," which was played at multi-nation celebrations. Students will collect data, investigate the likelihood of various moves, and use basic ideas of expected value to determine the average number of turns needed to win a game. Students work with tree diagrams to see the probabilities in a new way. All teaching steps and game rules are illustrated.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Samuel E. Zordak
Communicating With Data, Summer 2003
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Introduces students to the basic tools in using data to make informed ...

Introduces students to the basic tools in using data to make informed management decisions. Covers introductory probability, decision analysis, basic statistics, regression, simulation, and linear and nonlinear optimization. Computer spreadsheet exercises and examples drawn from marketing, finance, operations management, and other management functions. Restricted to Sloan Fellows.

Subject:
Business and Communication
Finance
Marketing
Statistics and Probability
Material Type:
Full Course
Textbook
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Carroll, John S.
Combinations
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This 2-lesson unit focuses on combinations, a subject related to probability. Students ...

This 2-lesson unit focuses on combinations, a subject related to probability. Students develop strategies for discovering all the possible combinations in two given situations. They learn to collect and organize data and then use the results to generalize methods for determining possible combinations. They discuss how the number of possible outcomes is affected by decisions about the order of choices, or whether choices may be repeated. The unit includes student activity sheets, questions and extensions for students, and a link to an interactive applet.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Marcy Cook (adapted from "Ideas: Combinations", The Arithmetic Teacher Vol. 36, No. 1, September 1988)
Quantum Theory I, Fall 2002
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Topics include uncertainty relation, observables, eigenstates, eigenvalues, probabilities of the results of ...

Topics include uncertainty relation, observables, eigenstates, eigenvalues, probabilities of the results of measurement, Transformation Theory, equations of motion, and constants of motion. Symmetry in Quantum Mechanics, Representations of Symmetry Groups. Variational and Perturbation Approximations. Systems of Identical Particles and Applications. Time-Dependent Perturbation Theory. Scattering Theory - Phase Shifts, Born Approximation. The Quantum Theory of Radiation. Second Quantization and Many-Body Theory. Relativistic Quantum Mechanics of One Electron. 8.321 is the first semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: Hilbert spaces, observables, uncertainty relations, eigenvalue problems and methods for solution thereof, time-evolution in the Schrodinger, Heisenberg, and interaction pictures, connections between classical and quantum mechanics, path integrals, quantum mechanics in EM fields, angular momentum, time-independent perturbation theory, density operators, and quantum measurement.

Subject:
Statistics and Probability
Physics
Material Type:
Full Course
Textbook
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Taylor, Washington
Quantum Theory II, Spring 2003
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A two-semester subject on quantum theory, stressing principles: uncertainty relation, observables, eigenstates, ...

A two-semester subject on quantum theory, stressing principles: uncertainty relation, observables, eigenstates, eigenvalues, probabilities of the results of measurement, transformation theory, equations of motion, and constants of motion. Symmetry in quantum mechanics, representations of symmetry groups. Variational and perturbation approximations. Systems of identical particles and applications. Time-dependent perturbation theory. Scattering theory: phase shifts, Born approximation. The quantum theory of radiation. Second quantization and many-body theory. Relativistic quantum mechanics of one electron. This is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.

Subject:
Statistics and Probability
Physics
Material Type:
Full Course
Textbook
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Taylor, Washington
Illuminations: Combinations
Conditions of Use:
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This 2-lesson unit focuses on combinations, a subject related to probability. Students ...

This 2-lesson unit focuses on combinations, a subject related to probability. Students develop strategies for discovering all the possible combinations in two given situations. They learn to collect and organize data and then use the results to generalize methods for determining possible combinations. They discuss how the number of possible outcomes is affected by decisions about the order of choices, or whether choices may be repeated. The unit includes student activity sheets, questions and extensions for students, and a link to an interactive applet.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Marcy Cook
Curve Fitting
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With your mouse, drag data points and their error bars, and watch ...

With your mouse, drag data points and their error bars, and watch the best-fit polynomial curve update instantly. You choose the type of fit: linear, quadratic, cubic, or quartic. The reduced chi-square statistic shows you when the fit is good. Or you can try to find the best fit by manually adjusting fit parameters.

Subject:
Mathematics
Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Dubson, Michael
Loeblein, Patricia
Michael Dubson
PhET at University of Colorado
PhET Interactive Simulations
Trish Loeblein
Plastic Packaging
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In this data collection and analysis activity students investigate the data in ...

In this data collection and analysis activity students investigate the data in connection with recyclable materials and develop plans to help the environment. Through this activity, students explore recycling plastic containers and graph the frequency of different types of recyclable plastics. The lesson includes student worksheets, extension suggestions, and student questions.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Understanding Evolution
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Your one-stop source for learning and teaching about evolution. This website includes ...

Your one-stop source for learning and teaching about evolution. This website includes information about how evolution works, how evolution impacts our lives, evidence for evolution, and the history of evolutionary thought. There's also an entire Understanding Evolution for Teachers sub-site, which includes lesson plans, a conceptual framework, and discussion of classroom situations that may arise when teaching evolution.

Subject:
Biology
Geology
Material Type:
Activity/Lab
Lesson Plan
Teaching/Learning Strategy
Provider:
University of California Museum of Paleontology and National Center for Science Education
Alike and Different
Conditions of Use:
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This lesson focuses on the observation of properties and the classification of ...

This lesson focuses on the observation of properties and the classification of objects to build ideas about variables. Learners compare buttons to identify similarities and differences. In addition, learners are introduced to Venn Diagrams by reading "The Elves and the Shoemaker" and sorting their shoes in a giant diagram.

Subject:
Mathematics
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Carol Midgett
Grace M. Burton
NCTM Illuminations
Thinkfinity/Verizon Foundation