# 41 Results

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• Probability and statistics
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This learning video deals with a question of geometrical probability. A key idea presented is the fact that a linear equation in three dimensions produces a plane. The video focuses on random triangles that are defined by their three respective angles. These angles are chosen randomly subject to a constraint that they must sum to 180 degrees. An example of the types of in-class activities for between segments of the video is: Ask six students for numbers and make those numbers the coordinates x,y of three points. Then have the class try to figure out how to decide if the triangle with those corners is acute or obtuse.

الموضوع:
هندسة الشكل
الإحصائيات والاحتمالات
نوع المادة:
Lecture
Provider:
MIT
Provider Set:
أزهار معهد ماساتشوستس للتكنولوجيا MIT
المؤلف:
Gilbert Strange
06/02/2012
Unrestricted Use
CC BY
Rating

This this task about mixing paint requires students to graph ratios on a coordinate plane. It is a standard language in ratio problem.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
Unrestricted Use
CC BY
Rating

This this task about mixing paint requires students to graph ratios on a coordinate plane. It is a standard language in ratio problem.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
Some Rights Reserved
Rating

Explore the origin of energy bands in crystals of atoms. The structure of these bands determines how materials conduct electricity.

Subject:
Physics
Material Type:
Simulation
Provider:
Provider Set:
PhET Interactive Simulations
Author:
Carl Wieman
Chris Malley
Kathy Perkins
Sam McKagan
07/02/2010
Unrestricted Use
CC BY
Rating

This module contains the basic operations with real numbers from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.

الموضوع:
علم الجبر
نوع المادة:
القراءة
Provider:
جامعة رايس
Provider Set:
صلات
المؤلف:
Denny Burzynski
02/16/2011
Only Sharing Permitted
CC BY-NC-ND
Rating

This activity explores the main algorithms that are used as the basis for searching on computers, using different variations on the game of battleships. This activity demonstrates three search methods for finding information in data: linear searching, binary searching and hashing. It also includes an optional introductory activity as well as a video showing a fun demonstration related to the same content.

Subject:
Computer Science
Engineering
Education
Mathematics
Geometry
Material Type:
Activity/Lab
Game
Lesson Plan
Simulation
Provider:
Computer Science Unplugged
Science and Math Informal Learning Educators (SMILE)
Provider Set:
Computer Science Unplugged
SMILE Pathway: Science and Math Activities in One Search
Author:
Brian Mason Scientific and Technical Trust
Computer Science Unplugged
Ian Witten
Jane McKenzie
Mike Fellows
Tim Bell
01/02/2002
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CC BY-NC-SA
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This learning video is designed to develop critical thinking in students by encouraging them to work from basic principles to solve a puzzling mathematics problem that contains uncertainty. Materials for in-class activities include: a yard stick, a meter stick or a straight branch of a tree; a saw or equivalent to cut the stick; and a blackboard or equivalent. In this video lesson, during in-class sessions between video segments, students will learn among other things: 1) how to generate random numbers; 2) how to deal with probability; and 3) how to construct and draw portions of the X-Y plane that satisfy linear inequalities.

الموضوع:
القياس والبيانات
نوع المادة:
Lecture
Provider:
MIT
Provider Set:
أزهار معهد ماساتشوستس للتكنولوجيا MIT
المؤلف:
Richard C. Larson
10/31/2014
Conditional Remix & Share Permitted
CC BY-NC-SA
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This task was developed by high school and postsecondary mathematics and design/pre-construction educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

Subject:
Architecture and Design
Geometry
Statistics and Probability
Material Type:
Activity/Lab
Assessment
Homework/Assignment
Lesson Plan
Provider:
National Association of State Directors of Career Technical Education Consortium
Provider Set:
Career Technical Education
03/05/2012
Conditional Remix & Share Permitted
CC BY-NC-SA
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This task was developed by high school and postsecondary mathematics and health sciences educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

الموضوع:
Health, Medicine and Nursing
علم الجبر
Ratios and Proportions
الإحصائيات والاحتمالات
نوع المادة:
Activity/Lab
Lesson Plan
Provider:
National Association of State Directors of Career Technical Education Consortium
Provider Set:
التعليم المهني التقني
07/27/2012
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

This learning video uses a simple analog setup to explore why earthquakes are so unpredictable. The setup is simple enough that students should be able to assemble and operate it on their own with a teacher's supervision. The teaching approach used in this module is known as the 5E approach, which stands for Engagement, Exploration, Explanation, Elaboration, and Evaluation. Over the course of this lesson, the basic mechanisms that give rise to the behavior of the simple analog system are explained, and further elaboration helps the students to apply their understanding of the analog system to complex fault systems that cause earthquakes

Subject:
Geology
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
06/11/2012
Unrestricted Use
CC BY
Rating

This task presents a real world situation that can be modeled with a linear function best suited for an instructional context.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
Unrestricted Use
CC BY
Rating

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:
Provider Set:
PhET Interactive Simulations
Author:
Michael Dubson
Patricia Loblein
08/02/2012
Conditional Remix & Share Permitted
CC BY-NC-SA
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Scientists who are working to discover new medicines often use robots to prepare samples of cells, allowing them to test chemicals to identify those that might be used to treat diseases. Students will meet a scientist who works to identify new medicines. She created free software that ''looks'' at images of cells and determines which images show cells that have responded to the potential medicines. Students will learn about how this technology is currently enabling research to identify new antibiotics to treat tuberculosis. Students will complete hands-on activities that demonstrate how new medicines can be discovered using robots and computer software, starring the student as ''the computer.'' In the process, the students learn about experimental design, including positive and negative controls.

الموضوع:
علم الأحياء
نوع المادة:
Lecture
Provider:
MIT
Provider Set:
أزهار معهد ماساتشوستس للتكنولوجيا MIT
المؤلف:
Anne Carpenter
05/07/2015
Unrestricted Use
CC BY
Rating

Explore tunneling splitting in double well potentials. This classic problem describes many physical systems, including covalent bonds, Josephson junctions, and two-state systems such as spin 1/2 particles and ammonia molecules.

Subject:
Physics
Material Type:
Simulation
Provider:
Provider Set:
PhET Interactive Simulations
Author:
Carl Wieman
Chris Malley
Kathy Perkins
Sam McKagan
10/04/2006
Only Sharing Permitted
CC BY-NC-ND
Rating

This lesson unit is intended to help you assess how well students are able to: solve simple problems involving ratio and direct proportion; choose an appropriate sampling method; and collect discrete data and record them using a frequency table.

Subject:
Education
Geometry
Measurement and Data
Ratios and Proportions
Material Type:
Assessment
Lecture Notes
Lesson Plan
Teaching/Learning Strategy
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Author:
http://map.mathshell.org/
04/26/2013
Only Sharing Permitted
CC BY-NC-ND
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This lesson unit addresses common misconceptions relating to probability of simple and compound events. The lesson will help you assess how well students understand concepts of: Equally likely events; randomness; and sample sizes.

Subject:
Statistics and Probability
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
04/26/2013
Unrestricted Use
CC BY
Rating

Subject:
Mathematics
Material Type:
Textbook
Provider:
Siyavula
04/12/2012
Restricted Use
Rating

This web site offers families, teachers, and tutors 80 mathematical challenges helpful for encouraging problem solving with students in grades 6 to 8. The math challenges focus on concepts and objects found in everyday life, such as how fast your heart beats, what shape container holds the most popcorn, and how much of me shows in a mirror. Each challenge contains an initial problem with a solution hint, a complete explanation of the answer, and additional problems related to the same challenge. Resources for further investigations are suggested as well. From the Printing the Challenges link on the homepage, PDF files are available for all 80 challenges in English, the first 15 challenges in Spanish, and the family resource materials in English and Spanish.

Subject:
Algebra
Geometry
Statistics and Probability
Material Type:
Activity/Lab
Homework/Assignment
Provider:
National Council of Teachers of Mathematics
Provider Set:
Figure This!
01/01/2002
Conditional Remix & Share Permitted
CC BY-NC-SA
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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.

الموضوع:
التعليم
الرياضيات
الأعداد والعمليات الحسابية
نوع المادة:
Lecture
Provider:
MIT
Provider Set:
أزهار معهد ماساتشوستس للتكنولوجيا MIT
المؤلف:
Daniel Livengood
MIT BLOSSOMS
Rhonda Jordan
06/02/2012
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

This video lesson shows students that math can play a role in understanding how an infectious disease spreads and how it can be controlled. During this lesson, students will see and use both deterministic and probabilistic models and will learn by doing through role-playing exercises. The primary exercises between video segments of this lesson are class-intensive simulation games in which members of the class 'infect' each other under alternative math modeling assumptions about disease progression. Also there is an occasional class discussion and local discussion with nearby classmates.

الموضوع:
علم الأحياء
علم الإجتماع
نوع المادة:
Lecture
Provider:
MIT
Provider Set:
أزهار معهد ماساتشوستس للتكنولوجيا MIT
المؤلف:
Mai Perches
Richard C. Larson
Sahar Hashmi
07/12/2014
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

This video lesson shows students that math can play a role in understanding how an infectious disease spreads and how it can be controlled. During this lesson, students will see and use both deterministic and probabilistic models and will learn by doing through role-playing exercises. The primary exercises between video segments of this lesson are class-intensive simulation games in which members of the class 'infect' each other under alternative math modeling assumptions about disease progression. Also there is an occasional class discussion and local discussion with nearby classmates.

Subject:
Biology
Sociology
Material Type:
Lecture
Provider:
MIT Learning International Networks Consortium
Provider Set:
M.I.T. Blossoms
Author:
Mai Perches
Richard C. Larson
Sahar Hashmi
06/02/2012
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

This video lesson is an example of ''teaching for understanding'' in lieu of providing students with formulas for determining the height of a dropped (or projected) object at any time during its fall. The concept presented here of creating a chart to organize and analyze data collected in a simple experiment is broadly useful. During the classroom breaks in this video, students will enjoy timing objects in free fall and balls rolling down ramps as a way of learning how to carefully conduct experiments and analyze the results. The beauty of this lesson is the simplicity of using only the time it takes for an object dropped from a measured height to strike the ground. There are no math prerequisites for this lesson and no needed supplies, other than a blackboard and chalk. It can be completed in one 50-60-minute classroom period.

الموضوع:
الفيزياء
نوع المادة:
Lecture
Provider:
MIT Learning International Networks Consortium
Provider Set:
M.I.T. Blossoms
المؤلف:
John Bookston
06/02/2012
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

This video lesson uses the technique of induction to show students how to analyze a seemingly random occurrence in order to understand it through the development of a mathematical model. Using the medium of a simple game, Dr. Lodhi demonstrates how students can first apply the 'rules' to small examples of the game and then, through careful observation, can begin to see the emergence of a possible pattern. Students will learn that they can move from observing a pattern to proving that their observation is correct by the development of a mathematical model. Dr. Lodhi provides a second game for students in the Teacher Guide downloadable on this page. There are no prerequisites for this lesson and needed materials include only a blackboard and objects of two different varieties - such as plain and striped balls, apples and oranges, etc. The lesson can be completed in a 50-minute class period.

نوع المادة:
Lecture
Provider:
MIT Learning International Networks Consortium
Provider Set:
M.I.T. Blossoms
المؤلف:
Fakhar Lohdi
06/02/2012
Only Sharing Permitted
CC BY-NC-ND
Rating

This lesson unit is intended to help teachers assess how well students are able to: interpret data and evaluate statistical summaries; and critique someone elseŐs interpretations of data and evaluations of statistical summaries. The lesson also introduces students to the dangers of misapplying simple statistics in real-world contexts, and illustrates some of the common abuses of statistics and charts found in the media.

Subject:
Statistics and Probability
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
04/26/2013
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

This learning video addresses a particular problem of selection bias, a statistical bias in which there is an error in choosing the individuals or groups to make broader inferences. Rather than delve into this broad topic via formal statistics, we investigate how it may appear in our everyday lives, sometimes distorting our perceptions of people, places and events, unless we are careful. When people are picked at random from two groups of different sizes, most of those selected usually come from the bigger group. That means we will hear more about the experience of the bigger group than that of the smaller one. This isn't always a bad thing, but it isn't always a good thing either. Because big groups ''speak louder,'' we have to be careful when we write mathematical formulas about what happened in the two groups. We think about this issue in this video, with examples that involve theaters, buses, and lemons. The prerequisite for this video lesson is a familiarity with algebra. It will take about one hour to complete, and the only materials needed are a blackboard and chalk.

الموضوع:
التعليم
الرياضيات
علم الإجتماع
نوع المادة:
Lecture
Provider:
MIT
Provider Set:
أزهار معهد ماساتشوستس للتكنولوجيا MIT
المؤلف:
Anna Teytelman
Arnold Barnett
MIT BLOSSOMS
06/02/2012
Only Sharing Permitted
CC BY-NC-ND
Rating

This lesson unit is intended to help you assess how well students are able to: Calculate the mean, median, mode, and range from a frequency chart; and to use a frequency chart to describe a possible data set, given information on the mean, median, mode, and range.

الموضوع:
التعليم
الرياضيات
الفيزياء
نوع المادة:
Activity/Lab
التقييم
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
المؤلف:
Shell Center Team
01/17/2013
Only Sharing Permitted
CC BY-NC-ND
Rating

This lesson unit is intended to help teachers assess how well students are able to: make sense of a real life situation and decide what math to apply to the problem; understand and calculate the conditional probability of an event A, given an event B, and interpret the answer in terms of a model; represent events as a subset of a sample space using tables, tree diagrams, and Venn diagrams; and interpret the results and communicate their reasoning clearly.

الموضوع:
الإحصائيات والاحتمالات
نوع المادة:
التقييم
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
04/26/2013
Only Sharing Permitted
CC BY-NC-ND
Rating

This lesson unit is intended to help teachers assess how well students are able to: Understand conditional probability; represent events as a subset of a sample space using tables and tree diagrams; and communicate their reasoning clearly.

الموضوع:
الإحصائيات والاحتمالات
نوع المادة:
التقييم
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
04/26/2013
Only Sharing Permitted
CC BY-NC-ND
Rating

This lesson unit is intended to help teachers assess how well students understand conditional probability, and, in particular, to help teachers identify and assist students who have the following difficulties: representing events as a subset of a sample space using tables and tree diagrams; and understanding when conditional probabilities are equal for particular and general situations.

الموضوع:
الإحصائيات والاحتمالات
نوع المادة:
التقييم
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
04/26/2013
Unrestricted Use
CC BY
Rating

How did scientists figure out the structure of atoms without looking at them? Try out different models by shooting light at the atom. Check how the prediction of the model matches the experimental results.

Subject:
Physics
Material Type:
Simulation
Provider:
Provider Set:
PhET Interactive Simulations
Author:
Carl Wieman
Chris Malley
Kathy Perkins
Michael Dubson
Mindy Gratny
Sam McKagan
01/01/2007
Unrestricted Use
CC BY
Rating

In this group task students collect data and analyze from the class to answer the question "is there an association between whether a student plays a sport and whether he or she plays a musical instrument? "

الموضوع:
الرياضيات
الإحصائيات والاحتمالات
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
10/09/2012
Only Sharing Permitted
CC BY-NC-ND
Rating

This activity lets learners participate in the process of reconstructing a phylogenetic tree and introduces them to several core bioinformatics concepts, particularly in relation to evolution. Groups of learners (at least 10) repeat a secret message (five to seven similar-sounding words) like the game "Telephone". In this version of the game, however, learners write and then code what they hear, creating a model of a phylogenetic tree and using a species distance matrix. This resource includes background information about phylogenetic trees, maximum parsimony, and matrix theory (see page 6-7 of PDF).

الموضوع:
علم الحاسوب
الهندسة
Information Science
التعليم
Life Science
الرياضيات
علم الإنسان
نوع المادة:
Activity/Lab
Game
Lesson Plan
Provider:
Computer Science Unplugged
Science and Math Informal Learning Educators (SMILE)
Provider Set:
Computer Science Unplugged
SMILE Pathway: Science and Math Activities in One Search
المؤلف:
Brian Mason Scientific and Technical Trust
Computer Science Unplugged
Jim Becker
Katrin Becker
Truman State University
01/02/2005
Unrestricted Use
CC BY
Rating

This task is part of a series presenting important foundational geometric results and constructions which are fundamental for more elaborate arguments. They are presented without a real world context so as to see the important hypotheses and logical steps involved as clearly as possible.

الموضوع:
الرياضيات
هندسة الشكل
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
01/11/2013
Unrestricted Use
CC BY
Rating

Explore the properties of quantum "particles" bound in potential wells. See how the wave functions and probability densities that describe them evolve (or don't evolve) over time.

Subject:
Physics
Material Type:
Simulation
Provider:
Provider Set:
PhET Interactive Simulations
Author:
Carl Wieman
Chris Malley
Kathy Perkins
Sam McKagan
10/02/2006
Only Sharing Permitted
CC BY-NC-ND
Rating

This lesson unit is intended to help teachers assess how well students: are able to use frequency graphs to identify a range of measures and make sense of this data in a real-world context; and understand that a large number of data points allow a frequency graph to be approximated by a continuous distribution.

الموضوع:
القياس والبيانات
الإحصائيات والاحتمالات
نوع المادة:
التقييم
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
04/26/2013
Only Sharing Permitted
CC BY-NC-ND
Rating

This lesson unit is intended to help teachers assess how well students are able to interpret data using frequency graphs and box plots. In particular this unit aims to identify and help students who have difficulty figuring out the data points and spread of data from frequency graphs and box plots. It is advisable to use the lesson: Representing Data 1: Frequency Graphs, before this one.

الموضوع:
القياس والبيانات
الإحصائيات والاحتمالات
نوع المادة:
التقييم
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
04/26/2013
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

In this activity, learners explore scale by using building cubes to see how changing the length, width, and height of a three-dimensional object affects its surface area and its volume. Learners build bigger and bigger cubes to understand these scaling relationships.

Subject:
Geometry
Material Type:
Activity/Lab
Provider:
Exploratorium
Author:
Exploratorium
Gordon and Betty Moore Foundation
National Science Foundation
The Exploratorium
12/07/2010
Rating

This online math course develops the mathematics needed to formulate and analyze probability models for idealized situations drawn from everyday life. Topics include elementary set theory, techniques for systematic counting, axioms for probability, conditional probability, discrete random variables, infinite geometric series, and random walks. Applications to card games like bridge and poker, to gambling, to sports, to election results, and to inference in fields like history and genealogy, national security, and theology. The emphasis is on careful application of basic principles rather than on memorizing and using formulas.

Subject:
Numbers and Operations
Material Type:
Homework/Assignment
Lecture
Provider:
Harvard University
Provider Set:
Harvard Extension School
Author:
Paul G. Bamberg
01/09/2013
Unrestricted Use
CC BY
Rating

This is a multi-step problem since it requires more than two steps no matter how it is solved. The problem is not scaffolded for the student, but each step is straightforward and should follow from the previous with a careful reading of the problem.

الموضوع:
الرياضيات
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012
Unrestricted Use
CC BY
Rating

Make waves with a dripping faucet, audio speaker, or laser! Add a second source or a pair of slits to create an interference pattern.

Subject:
Physics
Material Type:
Simulation
Provider: