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  • Statistics and Probability
Are Random Triangles Acute or Obtuse?
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Remix and Share
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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.

Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Gilbert Strange
Date Added:
06/02/2012
The Broken Stick Experiment: Triangles, Random Numbers and Probability
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Remix and Share
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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.

Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Richard C. Larson
Date Added:
10/31/2014
CTE Architecture: Storage Sheds
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Remix and Share
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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.

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
Date Added:
03/05/2012
CTE Health Sciences: BMI Calculations
Conditions of Use:
يمكن إعادة ترتيب المحتوى ومشاركته
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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.

نوع المادة:
Activity/Lab
Lesson Plan
Provider:
National Association of State Directors of Career Technical Education Consortium
Provider Set:
التعليم المهني التقني
Date Added:
07/27/2012
Curve Fitting (AR)
Conditions of Use:
Read the Fine Print
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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.

Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Michael Dubson
Patricia Loblein
Date Added:
08/02/2012
Evaluating Statements About Probability
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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.

Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
The Flaws of Averages
Conditions of Use:
Remix and Share
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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.

Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Daniel Livengood
MIT BLOSSOMS
Rhonda Jordan
Date Added:
06/02/2012
ألعاب الأنفلونزا الرياضية
Conditions of Use:
يمكن إعادة ترتيب المحتوى ومشاركته
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يُظهر هذا الفيديو التعليمي للطلاب أن الرياضيات يمكن أن تلعب دور في فهم كيفية انتشار المرض المعدي، وكيفية السيطرة عليه. وخلال هذا الدرس، سيقوم الطلاب برؤية واستخدام النموذجين الحتمي والاحتمالي، وسيتعلموا من خلال تأدية تمارين لعب الأدوار. علماً بأن التمارين الأساسية الممتدة بين مقاطع الفيديو الخاص بهذا الدرس هي عبارة عن ألعاب محاكاة مخصصة للفصول المدرسية يقوم فيها أعضاء الفصل بـ'عدوى' بعضهم البعض في ظل افتراضات نماذج رياضية بديلة حول متتالية تفاقم المرض. كذلك يكون هناك مناقشة عرضية داخل الفصل ومناقشة محلية مع زملاء الدراسة القريبين.

نوع المادة:
Lecture
Provider:
MIT
Provider Set:
أزهار معهد ماساتشوستس للتكنولوجيا MIT
المؤلف:
Mai Perches
Richard C. Larson
Sahar Hashmi
Date Added:
07/12/2014
ألعاب رياضية حول الانفلونزا
Conditions of Use:
يمكن إعادة ترتيب المحتوى ومشاركته
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يبين درس الفيديو هذا للطلاب أن الرياضيات يمكن أن تلعب دوراً في فهم كيف ينتشر مرض معد وكيف يمكن السيطرة عليه. من خلال هذا الدرس، سيرى وسيستخدم الطلاب النماذج القطعية والاحتمالية على حد سواء وسيتعلمون بالممارسة من خلال تمارين لعب الأدوار. ان التدريبات الأولية بين مقاطع الفيديو المخصصة بهذا الدرس هي ألعاب محاكاة دراسية مكثفة و التي 'يصيب' فيها أعضاء الفصل بعضهم البعض في اطار افتراضات نموذجية للرياضيات البديلة حول تطور المرض. هناك أيضا نقاش عرضي بالفصل ومناقشة محلية مع الزملاء القريبين.

نوع المادة:
Lecture
Provider:
MIT Learning International Networks Consortium
Provider Set:
M.I.T. Blossoms
المؤلف:
Mai Perches
Richard C. Larson
Sahar Hashmi
Date Added:
06/02/2012
Interpreting Statistics: A Case of Muddying the Waters
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.

نوع المادة:
التقييم
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Is Bigger Better? A Look at a Selection Bias that Is All Around Us
Conditions of Use:
Remix and Share
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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.

Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Anna Teytelman
Arnold Barnett
MIT BLOSSOMS
Date Added:
06/02/2012
Mean, Median, Mode, and Range
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.

نوع المادة:
Activity/Lab
التقييم
Lesson Plan
Provider:
Shell Center for Mathematical Education
Provider Set:
Mathematics Assessment Project (MAP)
المؤلف:
Shell Center Team
Date Added:
01/17/2013
Medical Testing
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.

نوع المادة:
التقييم
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Modeling Conditional Probabilities 1: Lucky Dip
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.

نوع المادة:
التقييم
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Modeling Conditional Probabilities 2
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.

Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Representing Data 1: Using Frequency Graphs
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.

Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Representing Data 2: Using Box Plots
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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.

Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013