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  • MIT Blossoms
ATP: The Fuel of Life
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The goal of this lesson is to introduce students who are interested in human biology and biochemistry to the subtleties of energy metabolism (typically not presented in standard biology and biochemistry textbooks) through the lens of ATP as the primary energy currency of the cell. Avoiding the details of the major pathways of energy production (such as glycolysis, the citric acid cycle, and oxidative phosphorylation), this lesson is focused exclusively on ATP, which is truly the fuel of life. Starting with the discovery and history of ATP, this lesson will walk the students through 8 segments (outlined below) interspersed by 7 in-class challenge questions and activities, to the final step of ATP production by the ATP synthase, an amazing molecular machine. A basic understanding of the components and subcellular organization (e.g. organelles, membranes, etc.) and chemical foundation (e.g. biomolecules, chemical equilibrium, biochemical energetics, etc.) of a eukaryotic cell is a desired prerequisite, but it is not a must. Through interactive in-class activities, this lesson is designed to spark the students’ interest in biochemistry and human biology as a whole, but could serve as an introductory lesson to teaching advanced concepts of metabolism and bioenergetics in high school depending on the local science curriculum. No supplies or materials are needed.

Subject:
Life Science
Biology
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Christian Schubert
Date Added:
02/13/2015
Antioxidant Enzymes: Three or Four Veggies a Day Keeps Aging Away
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The purpose of this video lesson is to expand the student's knowledge about enzymes by introducing the antioxidant enzymes that are intimately involved in the prevention of cellular damage and eventual slowing of the aging process and prevention of several diseases. Students will learn that natural antioxidant enzymes are manufactured in the body and provide an important defense against free radicals. The topic of free radical action is introduced, covering how they are constantly generated in living cells both by ''accidents of chemistry'' and also by specific metabolic processes.

Subject:
Nutrition
Chemistry
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Sawsan F. Karadsheh
Date Added:
06/16/2015
Arabesque: Where Art Meets Mathematics
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The main objective of this lesson is to illustrate an important application of mathematics in practical life -- namely in art. Most of the pictures selected for this lesson are visible on the walls of Al-Hambra – Granada (Spain), which is one of the most important landmarks in the Islamic civilization. There are three educational goals for this lesson: (1) establishing the concept of isometries; (2) giving real-life examples of groups; (3) demonstrating the importance of matrices and their applications. As background for this lesson, students just need some familiarity with the concept of a group and a limited knowledge about matrices and the inverse of a non-singular matrix.

Subject:
Arts and Humanities
Mathematics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Dr. Jawad Abuhlail
Date Added:
02/13/2015
Are Random Triangles Acute or Obtuse?
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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.

Subject:
Geometry
Statistics and Probability
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Gilbert Strange
Date Added:
06/02/2012
The Art of Approximation in Science and Engineering: How to Whip Out Answers Quickly
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The purpose of this learning video is to show students how to think more freely about math and science problems. Sometimes getting an approximate answer in a much shorter period of time is well worth the time saved. This video explores techniques for making quick, back-of-the-envelope approximations that are not only surprisingly accurate, but are also illuminating for building intuition in understanding science. This video touches upon 10th-grade level Algebra I and first-year high school physics, but the concepts covered (velocity, distance, mass, etc) are basic enough that science-oriented younger students would understand. If desired, teachers may bring in pendula of various lengths, weights to hang, and a stopwatch to measure period. Examples of in- class exercises for between the video segments include: asking students to estimate 29 x 31 without a calculator or paper and pencil; and asking students how close they can get to a black hole without getting sucked in.

Subject:
Engineering
Algebra
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Stephen M. Hou
Date Added:
06/02/2015
The Art of Making Layer Cakes: Proper Construction of Bituminous Roads and Highways
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The aim of this video is to introduce high school students to the engineering concept of road construction and to the reasons why problems might arise in road construction. Presentation of this concept is made more accessible to students by comparing road construction to the art of baking a layer cake. This simple comparison can serve to emphasize how important it is to follow proper procedures and to use proper materials for successful road construction. The approach used is highly correlated with the common knowledge of baking layer cakes in Malaysia. Students should be able to relate the procedure of baking a layer cake to the importance of following the correct methods of road construction. An understanding of basic statistics is necessary before starting this lesson. This lesson will take almost 60 minutes to complete. During activity breaks, students are required to answer questions and complete assigned tasks related to the subject.

Subject:
Engineering
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Dr Norhidayah Abdul Hassan, Dr Mariyana Aida Ab. Kadir, Dr Sarimah Shamsudin
Date Added:
02/12/2015
Averages: Still Flawed
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This learning video continues the theme of an early BLOSSOMS lesson, Flaws of Averages, using new examples—including how all the children from Lake Wobegon can be above average, as well as the Friendship Paradox. As mentioned in the original module, averages are often worthwhile representations of a set of data by a single descriptive number. The objective of this module, once again, is to simply point out a few pitfalls that could arise if one is not attentive to details when calculating and interpreting averages. Most students at any level in high school can understand the concept of the flaws of averages presented here. The essential prerequisite knowledge for this video lesson is the ability to calculate an average from a set of numbers. Materials needed include: pen and paper for the students; a blackboard or equivalent; and coins (one per student) or something similar that students can repeatedly use to create a random event with equal chances of the two outcomes (e.g. flipping a fair coin). The coins or something similar are recommended for one of the classroom activities, which will demonstrate the idea of regression toward the mean. Another activity will have the students create groups to show how the average number of friends of friends is greater than or equal to the average number of friends in a group, which is known as The Friendship Paradox. The lesson is designed for a typical 50-minute class session.

Subject:
Mathematics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Dan Livengood, Rhonda Jordan
Date Added:
02/13/2015
Biotechnology: Can It Help in Making the Desert Green?
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This learning video introduces high school students to a topic they would not ordinarily study in school, biotechnology, and to different applications of biotechnology that relate to the main theme of the module - making the desert greener. After reviewing traditional methods used for manipulating plants to produce desired traits, students will learn about the methods of making transgenic plants. Dr. Ziad discusses a real world problem that is critical in his country, Jordan, where much of the land is desert. A prerequisite to this video lesson is some background in biology.

Subject:
Botany
Genetics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Ziad W. Jaradat, PhD
Date Added:
09/09/2015
Blood: The Stuff of Life
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The purpose of this lesson is to teach students about blood and its components while instilling an appreciation of its importance for survival. The lesson takes a step-by-step approach to determining the recipe for blood while introducing students to important laboratory techniques like centrifugation and microscopy, as well as some diseases of cell types found in blood. It also highlights the importance of donating blood by explaining basic physiological concepts and the blood donation procedure.

Subject:
Biology
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Melis Anahtar
Date Added:
10/31/2014
The Broken Stick Experiment: Triangles, Random Numbers and Probability
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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.

Subject:
Measurement and Data
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Richard C. Larson
Date Added:
10/31/2014
Building Cryptosystems
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This video module presents an introduction to cryptography - the method of sending messages in such a way that only the intended recipients can understand them. In this very interactive lesson, students will build three different devices for cryptography and will learn how to encrypt and decrypt messages. There are no prerequisites for this lesson, and it has intentionally been designed in a way that can be adapted to many audiences. It is fully appropriate in a high school level math or computer science class where the teacher can use it to motivate probability/statistics or programming exercises. nteractive lesson, students will learn to build the cryptography devices and will learn how to send and ''crack'' secret messages.

Subject:
Computer Science
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Daniel J. Sturtevant
Date Added:
05/07/2015
Can Earthquakes Be Predicted?
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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:
Zach Adam
Date Added:
06/11/2012
The Case of the Stolen Painting: A Forensic Mystery
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This video will help students, particularly those not in AP-level classes, have a practical application for knowing about the major divisions between plants, particularly about the details of plant anatomy and reproduction. Students will be able to :Identify the major evolutionary innovations that separate plant divisions, and classify plants as belonging to one of those divisions based on phenotypic differences in plants. Classify plants by their pollen dispersal methods using pollen dispersal mapping, and justify the location of a _„ƒcrime scene_„Ž using map analysis. Analyze and present their analysis of banding patterns from DNA fingerprinting done using plants in a forensic context.

Subject:
Botany
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
MIT BLOSSOMS
Sydney Bergman
Date Added:
10/11/2012
Catalytic Converter
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This video lesson aims to motivate students about chemistry and to raise their awareness about how chemistry helps in solving certain environmental problems. In this lesson, the air pollution problem created by cars and other vehicles is presented. The lesson will highlight causes of this problem, harmful products from it and possible solutions. There will also be discussion of ways to convert the pollutants produced by burning oil in vehicles into more friendly products.

Subject:
Environmental Science
Chemistry
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Prof. Mohammad El-Khateeb
Date Added:
06/11/2012
Classifying Animals by Appearance Versus DNA Sequence
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The topic of this video module is how to classify animals based on how closely related they are. The main learning objective is that students will learn how to make phylogenetic trees based on both physical characteristics and on DNA sequence. Students will also learn why the objective and quantitative nature of DNA sequencing is preferable when it come to classifying animals based on how closely related they are. Knowledge prerequisites to this lesson include that students have some understanding of what DNA is and that they have a familiarity with the base-pairing rules and with writing a DNA sequence.

Subject:
Biology
Genetics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Megan E. Rokop
Date Added:
06/11/2012
Discovering Genes Associated with Diseases and Traits in Dogs
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In this video module, students learn how scientists use genetic information from dogs to find out which gene (out of all 20,000 dog genes) is associated with any specific trait or disease of interest. This method involves comparing hundreds of dogs with the trait to hundreds of dogs not displaying the trait, and examining which position on the dog DNA is correlated with the trait (i.e. has one DNA sequence in dogs with the trait but another DNA sequence in dogs not displaying the trait). Students will also learn something about the history of dog breeds and how this history helps us find genes.

Subject:
Biology
Genetics
Zoology
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Elinor Karlsson
Date Added:
06/02/2015
Discovering Medicines, Using Robots and Computers
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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.

Subject:
Biology
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Anne Carpenter
Date Added:
05/07/2015
The Ecological Cost of Dinner
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This lesson is about the flow of energy in ecosystems. The setting is Plimoth Plantation, a living history museum in Plymouth, Massachusetts, USA, where students will learn about the first Thanksgiving meal in America, celebrated in 1621 by early American settlers and Wampanoag Indians. By examining this meal and comparing it to a modern day Thanksgiving celebration, students will be able to explore the way in which food energy moves and is transformed in an ecosystem. The learning goals focus on the movement of energy from one feeding level to the next within a food web, the way in which energy changes form, and the inefficiency of energy transfer, which in turn affects the availability of food energy for organisms at the highest feeding level. The lesson is directed at high school level biology students. Students should be familiar already with food webs, food chains, and trophic (feeding) levels. They should also be familiar with the general equations for photosynthesis (CO2 + H2O => C6H12O6) and cell respiration (C6H12O6 => CO2 + H2O), and understand the basic purpose of these processes in nature. This lesson can be completed during one long classroom period, or can be divided over two or more class meetings. The duration of the lesson will depend on prior knowledge of the students and on the amount of time allotted for student discussion. There are no supplies required for this lesson other than the downloadable worksheets (accessed on this BLOSSOMS site), paper and some glue or tape.

Subject:
Life Science
Ecology
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Leslie Reinherz
Date Added:
02/12/2015
Ecological Tipping Points: When Is Late Too Late?
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The major goal of this lesson is to provide students with some of the tools they will need to analyze and solve the many complex problems they will face during their lifetimes. In the lesson, students learn to use Flow Charts and Feedback Diagrams to analyze a very complex problem of ecological sustainability. The lesson looks at a specific case study—from my home town in the Philippines—of the Live Reef Fish Trade now threatening survival of the Coral Reef Triangle of Southeast Asia. Live reef fish have long been traded around Southeast Asia as a luxury food item, but in recent decades trade in fish captured on coral reefs has expanded rapidly. Although the trade has provided communities with additional income, these benefits are unsustainable and have come at considerable cost to the environment. This lesson begins by having students analyze a familiar or personal problem, using Flow Charts and Feedback Diagrams, and then moves on to the application of those tools to a complex environmental problem. The lesson could be completed in a 50-minute class session, but using it over two class sessions would be preferable. Everything needed for the lesson is downloadable from the BLOSSOMS website, including blank Flow Charts and Feedback Diagrams, as well as articles on the Philippines case study from the World Wildlife Fund and the United States Agency for International Development.

Subject:
Ecology
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Fred Pontillas
Date Added:
02/12/2015
Electrochemistry: Electroplating
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The aim of this lesson is to introduce the concepts of Electrochemistry and Electroplating and to present their applications in our daily lives. Students are encouraged to construct their knowledge of Electroplating through brainstorming sessions, experiments and discussions. This video lesson presents a series of stories related to Electroplating and begins with a story about house gates as an example of the common items related to the Electroplating topic. Prerequisites for this lesson are knowledge of the basic concepts of electrolysis and chemical equations. The lesson will take about 60 minutes to complete, but you may want to divide the lesson into two classes if the activities require more time.

Subject:
Chemistry
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Hafizah Binti Nasir, Mohd Fared Bin Samin
Date Added:
02/12/2015
Engineering Innovation and Entrepreneurship
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This video lesson introduces students to the worlds of engineering innovation and entrepreneurship. It seeks to encourage students to see the world with a fresh perspective for innovation through interactive classroom brainstorming activities and real life stories. Students will build self-efficacy in their own entrepreneurial potential by developing their perspective for innovation, developing a prototype solution for a problem they have recognized, and delivering an elevator pitch. The video will familiarize students with all the steps in the innovation process: from conception to launch. By the end of this lesson, students will be prepared for an optional long-term innovation project.

Subject:
Business and Communication
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Diane Amanti
Date Added:
09/09/2015
Fabulous Fractals and Difference Equations
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This learning video introduces students to the world of Fractal Geometry through the use of difference equations. As a prerequisite to this lesson, students would need two years of high school algebra (comfort with single variable equations) and motivation to learn basic complex arithmetic. Ms. Zager has included a complete introductory tutorial on complex arithmetic with homework assignments downloadable here. Also downloadable are some supplemental challenge problems. Time required to complete the core lesson is approximately one hour, and materials needed include a blackboard/whiteboard as well as space for students to work in small groups. During the in-class portions of this interactive lesson, students will brainstorm on the outcome of the chaos game and practice calculating trajectories of different equations.

Subject:
Geometry
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Laura Zager
Date Added:
07/12/2014
Fantastic Factorials
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The aim of this video lesson is to introduce the concept of factorials, and to show students that everyday events in their lives have so much to do with factorials - even if they do not realize it! During this video, students will learn about the large number of ways to arrange people and objects using the mathematical concept of factorials. This video lesson will begin with a story of a family vacation to Pulau Pinang, an island located 330 km from the city of Kuala Lumpur in Malaysia. In this video, lessons about using factorials are demonstrated through several challenges this family encounters during their vacation. A prerequisite for this lesson is knowledge of the multiplication rule of counting. During the classroom activities, students are asked to carry out collaborative learning challenges in groups of 6. These activities require students to arrange cards to show different factorial arrangements that can be made. The materials needed for this activity are very simple. We only need to provide a few pieces of blank or colored paper for each student. The lesson will take about 40 – 50 minutes to complete.

Subject:
Mathematics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Bashirah Seleman
Date Added:
02/13/2015
The Flaws of Averages
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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.

Subject:
Education
Mathematics
Numbers and Operations
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Daniel Livengood
MIT BLOSSOMS
Rhonda Jordan
Date Added:
06/02/2012
Flu Math Games
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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
Provider Set:
MIT Blossoms
Author:
Mai Perches
Richard C. Larson
Sahar Hashmi
Date Added:
07/12/2014
Forces and Angles
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The goal of this lesson is to assist students to relate the forces acting upon particular objects and the “unseen” resolution of those forces. The video begins with a story line involving Adam, who helps his father in the garden by disposing of a garbage bag of leaves—the very act that involves resolution of forces. This lesson includes embedded video clips, animations, diagrams and inquiry-based experiments where students are required to work collaboratively and answer thought-provoking questions. The experiments will involve the study of the resolution of forces on objects placed on varying planes or on platforms of different angles, using materials that are easily found. Finally, students are required to discuss and apply what they have learned to determine whether it is easier to push or to pull a luggage bag with wheels. The lesson will take about 50 minutes to complete.

Subject:
Physics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Bahtiar Afandi, Jong Kah Yin, Hussaini Abdul Rahman
Date Added:
02/12/2015
Free Fall
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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.

Subject:
Physics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
John Bookston
Date Added:
09/09/2015
From Psychology to Logic: Learning Computer Programming in the Kitchen
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This lesson focuses on the biggest problem faced by any young programmer - i.e. the LOGIC BUILDING required while solving a particular problem. With programming, the solution to a particular problem lies in the head, but one is unable to convert it into a computer program. This is because the thought processes of a human are much faster than the sense of observation. If this thought process could be slowed down, logic to solve a programming problem could be found very easily. This lesson focuses on converting this psychological thought process in a step-by -step logic fashion that a computer program can understand. This lesson is recorded in a kitchen where the basic programming concepts are taught by giving examples from the process of making a mango milk shake. This lesson teaches the 4 following techniques: 1) Swapping two variables by swapping a glass of milk with a glass of crushed ice; 2) Finding max from an array by finding the biggest mango; 3) Sorting an array by arranging the jars; and 4) Understanding the concept of a function, parameters and return type by comparing it with the blender/juicer. The lesson targets those students who know the syntax of programming in any language (C or GWBASIC preferred), but are unable to build the logic for a program. It can be taught in a class of 45 to 50 minutes.

This lesson is also available in Mandarin Chinese.

Subject:
Engineering
Psychology
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Tanzeela Ali
Date Added:
02/13/2015
Galaxies and Dark Matter
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This video lesson has the goal of introducing students to galaxies as large collections of gravitationally bound stars. It explores the amount of matter needed for a star to remain bound and then brings in the idea of Dark Matter, a new kind of matter that does not interact with light. It is best if students have had some high school level mechanics, ideally Newton's laws, orbital motion and centripetal force. The teacher guide segment has a derivation of centripetal acceleration. This lesson should be mostly accessible to students with no physics background. The video portion of this lesson runs about 30 minutes, and the questions and demonstrations will give a total activity time of about an hour if the materials are all at hand and the students work quickly. However, 1 1/2 hours is a more comfortable amount of time. There are several demonstrations that can be carried out using string, ten or so balls of a few inches in diameter, a stopwatch or clock with a sweep second hand and some tape. The demonstrations are best done outside, but can also be carried out in a gymnasium or other large room. If the materials or space are not available, there are videos of the demonstrations in the module and these may be used.

Subject:
Astronomy
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Peter Fisher
Date Added:
06/03/2015
The Genetic Basis of Inheritance and Variation
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The topic of this video module is genetic basis for variation among humans. The main learning objective is that students will learn the genetic mechanisms that cause variation among humans (parents and children, brothers and sisters) and how to calculate the probability that two individuals will have an identical genetic makeup. This module does not require many prerequisites, only a general knowledge of DNA as the genetic material, as well as a knowledge of meiosis.

Subject:
Biology
Genetics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Amjad Mahasneh
Date Added:
06/16/2015
Geologic Time: The Ticking of Our Planet's 4.6 Billion Year Clock
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This BLOSSOMS lesson will help students conceptualize the enormity of geologic time and learn about important events in Earth s history. Students will also learn how geologic time can help explain seemingly incomprehensible processes, like the formation of the Himalayan Mountains from a flat plain to their current height, and the evolution of a tiny group of reptiles into enormous dinosaurs. During the breaks, students will construct a geologic timeline of their own in the classroom and do simple calculations to determine how long amounts of time can lead to impressive changes in the height of the Himalayan Mountains and the size of a group of reptiles.

Subject:
Geology
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Phoebe Cohen
Date Added:
10/31/2014
Gravity at Work
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This video lesson highlights how science can be learned from daily life experiences. It emphasizes the ways in which simple laws of physics can be understood from personal observations and experiences, and in fact it demonstrates that we use these laws as if they were built into our instincts. The video also introduces Newton's laws of motion. The title, Gravity at Work, comes from a fascinating example of two laborers working at a construction site in Pakistan. In this lesson, Newtonian equations of motion are used to determine the velocities and height achieved by the projectile in a very simple and basic manner.

Subject:
Physics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Arshad Saleem Bhatti
Date Added:
06/17/2015
Guess the Last Ball
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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.

Subject:
Mathematics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Fakhar Lohdi
Date Added:
09/09/2015
How Big Is a Mole? Do We Really Comprehend Avogadro’s Number?
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The unit “mole” is used in chemistry as a counting unit for measuring the amount of something. One mole of something has 6.02×1023 units of that thing. The magnitude of the number 6.02×1023 is challenging to imagine. The goal of this lesson is for students to understand just how many particles Avogadro's Number truly represents, or, how big is a mole. This lesson is meant for students currently enrolled in a first or second year chemistry course. This lesson is designed to be completed within one approximately 1 hour class; however, completion of optional activities 4 and 5 may require a longer class period or part of a second class period. This lesson requires only pencil and paper, as the activities suggested in this video place an emphasis on helping students develop their “back of the envelope” estimation skills. In fact, calculators and other measuring devices are explicitly discouraged. However, students may require additional supplies (poster board, colored pencils, markers, crayons, etc.) for the final optional/assessment activity, which involves creating a poster to demonstrate the size of a mole of their favorite macroscopic object.

Subject:
Chemistry
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Dr. Jessica Silverman, Alan D. Crosby
Date Added:
02/12/2015
How Cold Is Cold: Examining the Properties of Materials at Lower Temperatures
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This video is the second lesson in the How Cold Is Cold? BLOSSOMS series and examines the properties of materials under low temperature conditions. The video consists of a series of fascinating demonstrations with liquid nitrogen, which boils at 77K (-196 C -321 F). These demonstrations include the following: What goes up, may not come down; Is that supposed to be cold? - thermal insulation; Some properties of liquid nitrogen; Making ice cream - the slow way and the fast way; Try not to explode: expansion of liquid nitrogen and the ideal gas law; Making the air cold: phase changes and the affect on volume; No frozen fingers: the changes in mechanical properties; Resistivity at 77K; The magic magnet: the Meissner Effect; Cautions in using liquid nitrogen

Subject:
Chemistry
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Rick McMaster_
Date Added:
06/02/2012
How Cold Is Cold: What Is Temperature?
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This video lesson is part of a two-part series and introduces the concept of temperature. Temperature can be a challenging concept to convey since our perception is tied to words that are relative to our own experience, which varies quite a lot. A short activity to be performed in the classroom shows the need for a temperature scale since qualitative descriptions are not adequate. Temperatures that vary from the hottest to coldest recorded temperatures on earth are shown in advance of introducing the boiling temperatures of a number of cryogenic liquids.

Subject:
Physics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Rick McMaster
Date Added:
09/09/2015
How Hot Is Hot? Heat versus Temperature
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The aim of this lesson is to introduce the concepts of heat and temperature, which many students find confusing. During the lesson, students will be asked to explore and discuss situations where even though the same amount of heat is absorbed by several substances, the increase in temperature of the substances is different. This video lesson presents a series of stories relating to heat and temperature, beginning with a visit to a factory where gamat oil is produced. In the video, a man dips his finger into boiling gamat oil yet feels no pain. The scene will draw students’ attention and raise their curiosity about how this is possible. Students will also carry out several experiments to compare and relate the situations where the same amount of heat absorbed by substances will result in different temperatures. By the end of this lesson, students will understand the term “specific heat capacity” and will recognize the difference between a high or low specific heat capacity. They will also understand the term “thermal diffusivity” and how this relates to the topic of the lesson. This lesson offers some authentic learning experiences where students will have the opportunity to relate the concept of heat and temperature to everyday situations. It will take about 50 minutes to complete - however, you may want to divide the lesson into two classes if the activities require more time.

Subject:
Physics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Mohd Zah Ismail, Mohd Suhaimi Mohd Ghazali
Date Added:
02/12/2015
How Mosquitoes Can Fly in the Rain
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In this lesson, we learn how insects can fly in the rain. The objective is to calculate the impact forces of raindrops on flying mosquitoes. Students will gain experience with using Newton's laws, gathering data from videos and graphs, and most importantly, the utility of making approximations. No calculus will be used in this lesson, but familiarity with torque and force balances is suggested. No calculators will be needed, but students should have pencil and paper to make estimations and, if possible, copies of the graphs provided with the lesson. Between lessons, students are recommended to discuss the assignments with their neighbors.

Subject:
Physics
Material Type:
Activity/Lab
Lecture Notes
Lesson Plan
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
David Hu
Date Added:
10/29/2012
How to Estimate the Value of Pi
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This lesson is about the estimation of the value of Pi. Based on previous knowledge, the students try to estimate Pi value using different methods, such as: direct physical measurements; a geometric probability model; and computer technology. This lesson is designed to stimulate the learning interests of students, to enrich their experience of solving practical problems, and to develop their critical thinking ability. To understand this lesson, students should have some mathematic knowledge about circles, coordinate systems, and geometric probability. They may also need to know something about Excel. To estimate Pi value by direct physical measurements, the students can use any round or cylindrical shaped objects around them, such as round cups or water bottles. When estimating Pi value by a geometric probability model, a dartboard and darts should be prepared before the class. You can also use other games to substitute the dart throwing game. For example, you can throw marbles to the target drawn on the floor. This lesson is about 45-50 minutes. If the students know little about Excel, the teacher may need one more lesson to explain and demonstrate how to use the computer to estimate Pi value. Downloadable from the website is a video demonstration about how to use Excel for estimating Pi.

Subject:
Mathematics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Renyong Feng
Date Added:
02/12/2015
Is Bigger Better? A Look at a Selection Bias that Is All Around Us
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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.

Subject:
Education
Mathematics
Sociology
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Anna Teytelman
Arnold Barnett
MIT BLOSSOMS
Date Added:
06/02/2012
Is There A Connection Between Computer Network Topologies And A Malaysian Wedding?
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The aim of this video lesson is to teach students about the different topologies of computer networks and how they function. The approach that is used is highly correlated with common knowledge about weddings and the local Malay culture associated with weddings. Students should be able to relate the act of delivering food to a large crowd of people to the basic principles of network topologies and the method of data transfer within each type of topology. The lesson will begin in a classroom with students working in small groups, answering assigned questions. Teaching aids such as color cards will be used. One student from each group will be appointed as the wedding event manager, and she/he will have to discuss and act out with group members in order to answer more challenging questions. At the end of the lesson, students will be asked to come up with their own version of a hybrid computer network topology. The lesson concept taught here not only educates students on computer topologies, but also introduces students to an important cultural perspective of Malaysia. Above all, this video is designed to assist students with their study of Computer Literacy in schools. The lesson will take up to 60 minutes to complete. Materials needed include: 10 red cards representing waitresses; 10 green cards representing waiters; 10 blue cards representing tables in the hall; a sketch book; and classroom tables and chairs.

Subject:
Computer Science
Engineering
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Dr. Zaleha Abdullah Juhazreen, Juhazreen Junaidi, Norah Md. Noor, Dr. Noor Azean Atan, Dr. Mohd Nihra Haruzuan Mohamad Said, Dr. Shaharuddin Md Salleh
Date Added:
02/13/2015
The King of Dinosaurs or a Chicken Dinner? One Paleontologist’s Quest to Activate Atavistic Genes and Create a Dinosaur
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This lesson uses the fundamentals of protein synthesis as a context for investigating the closest living relative to Tyrannosaurus rex and evaluating whether or not paleontologist and dinosaur expert, Jack Horner, will be able to "create" live dinosaurs in the lab. The first objective is for students to be able to access and properly utilize the NIH's protein sequence database to perform a BLAST, using biochemical evidence to determine T rex's closest living relative. The second objective is for students to be able to explain and evaluate Jack Horner's plans for creating live dinosaurs in the lab. The main prerequisite for the lesson is a basic understanding of protein synthesis, or the flow of information in the cell from DNA to RNA during transcription and then from RNA to protein during translation

Subject:
Genetics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Justin Lessek and Diana Aljets
Date Added:
10/11/2012
Kite Flying: Fun, Art and Science
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This lesson presents the basics of aerodynamics by using kite flying as an example, i.e., forces acting on a flying object. Students will measure the net force acting on a kite due to blowing air and will learn how a simple instrument like a spring can be used to measure such force. They will also examine and experience how the force on the kite is transferred to the string in the form of tension and will again measure that tension with a simple spring. This lesson will take about 30 minutes to complete. One will need a calibrated spring to measure forces, as well as a few springs to study the coplanar forces.

Subject:
Physics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Date Added:
02/12/2015
The Mathematics of Voting
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The goal of this video lesson is to teach students about new and exciting ways of holding an election that they may not be aware of. Students will learn three different methods of voting: plurality, instant runoff, and the Borda count. They will be led through a voting experiment in which they will see the weakness of plurality when there are three or more candidates. This lesson will show that not every voting system is perfect, and that each has its strengths and weaknesses. It will also promote thought, discussion, and understanding of the various methods of voting.

Subject:
Political Science
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Dr. Andy Felt
Date Added:
06/04/2015
Measuring Distances in the Milky Way
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The main aim of this lesson is to show students that distances may be determined without a meter stick—a concept fundamental to such measurements in astronomy. It introduces students to the main concepts behind the first rung of what astronomers call the distance ladder. The four main learning objectives are the following: 1) Explore, in practice, a means of measuring distances without what we most often consider the “direct” means: a meter stick; 2) Understand the limits of a method through the exploration of uncertainties; 3) Understand in the particular method used, the relationship between baseline and the accuracy of the measurement; and 4) Understand the astronomical applications and implications of the method and its limits. Students should be able to use trigonometry and know the relation between trigonometric functions and the triangle. A knowledge of derivatives is also needed to obtain the expression for the uncertainty on the distance measured. Students will need cardboard cut into disks. The number of disks is essentially equal to half the students in the class. Two straight drink straws and one pin per disk. Students will also need a protractor. The lesson should not take more than 50 minutes to complete if the students have the mathematical ability mentioned above. This lesson is complimentary to the BLOSSOMS lesson, "The Parallax Activity." The two lessons could be used sequentially - this one being more advanced - or they could be used separately.

Subject:
Astronomy
Physics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
The Pythagorean Theorem: Geometry’s Most Elegant Theorem
Date Added:
02/17/2015
Meet the Family: Investigating Primate Relationships
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In this lesson students will see the different types of evidence scientists use to understand evolutionary relationships among organisms. They will first practice by using shared physical characteristics to predict relationships among members of the cat family and then use this approach to predict primate relationships. They will compare their predictions to evidence provided by analyzing amino acid sequences and build a phylogenetic tree based on these sequences. Finally, they will look at the tree in the context of time in order to see divergence times.

Subject:
Life Science
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Jennifer Cross Peterson
Date Added:
02/12/2015
Methods for Protein Purification
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This Protein Purification video lesson is intended to give students some insight into the process and tools that scientists and engineers use to explore proteins. It is designed to extend the knowledge of students who are already somewhat sophisticated and who have a good understanding of basic biology. The question that motivates this lesson is, ''what makes two cell types different?'' and this question is posed in several ways. Such scientific reasoning raises the experimental question: how could you study just a subset of specialized proteins that distinguish one cell type from another? Two techniques useful in this regard are considered in the lesson.

Subject:
Biology
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Natalie Kuldell, PhD
Date Added:
06/16/2015
The Monty Hall Problem or How to Outsmart a Game Show and Win a Car
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This lesson teaches students how to make decisions in the face of uncertainty by using decision trees. It is aimed for high school kids with a minimal background in probability; the students only need to know how to calculate the probability of two uncorrelated events both occurring (ie flipping 2 heads in a row). Over the course of this lesson, students will learn about the role of uncertainty in decision making, how to make and use a decision tree, how to use limiting cases to develop an intuition, and how this applies to everyday life. The video portion is about fifteen minutes, and the whole lesson, including activities, should be completed in about forty-five minutes. Some of the activities call for students to work in pairs, but a larger group is also okay, especially for the discussion centered activities. The required materials for this lesson are envelopes, small prizes, and some things similar in size and shape to the prize.

Subject:
Statistics and Probability
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Sam Shames, Cameron Tabatabaie, Ben Kaloupek
Date Added:
02/13/2015
The Mysteries of Magnetism
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This lesson will explore the connections between magnetism in natural materials and electromagnetism. The ultimate goal will be for students to form an understanding that the source of magnetism in natural materials is moving charges. It is helpful, but not required, for the students to have some work with electricity, and other distance forces (such as gravity or the electric force). The lesson will probably take two 50-minute periods to complete. Although the video footage is brief, the activities are in depth, inquiry-based, and can take time for the students to explore. The materials are not specifically prescribed, but can include things such as bar magnets, compasses, iron filings, wire, batteries, steel bolts, coils, straws, and hot glue. The activities include drawing the magnetic fields of bar magnets and electromagnets. The activities also include making a magnet from a drinking straw and iron filings.

Subject:
Physics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Gary Garber
Date Added:
02/12/2015
The Mystery of Motion: Momentum, Kinetic Energy and Their Conversion
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In this video lesson, the concept of momentum applied to hard-body collisions is explained using a number of simple demonstrations, all of which can be repeated in the classroom. Understanding Newton's Laws is fundamental to all of physics, and this lesson introduces the vital concepts of momentum and energy, and their conservation. Only some preliminary ideas of algebra are used here, and all the concepts presented can be found in any high-school level physics book. In terms of materials required, getting hold of large steel balls may not be easy, but large ball bearings can be procured easily. On the basis of what students have learned in the video, teachers can easily generate a large number of questions that relate to one's daily experiences, or which pose new challenges: for example, in a collision between a heavy and light vehicle, why do those inside the lighter one suffer less injury?

Subject:
Physics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Hoodbhoy
Date Added:
05/29/2015
Optimizing Your Diet: What Linear Programming Can Tell You
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In this video lesson, students will learn about linear programming (LP) and will solve an LP problem using the graphical method. Its focus is on the famous "Stigler's diet" problem posed by the 1982 Nobel Laureate in economics, George Stigler. Based on his problem, students will formulate their own diet problem and solve it using the graphical method. The prerequisites to this lesson are basic algebra and geometry. The materials needed for the in-class activities include graphing paper and pencil. This lesson can be completed in one class of approximately one hour. If the teacher would like to cover the simplex algorithm by George Dantzig as an alternative solution method, an additional whole class period is suggested.

Subject:
Algebra
Geometry
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Aysegul Topcu
Date Added:
05/29/2015
The Physics of Boomerangs
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This learning video explores the mysterious physics behind boomerangs and other rapidly spinning objects. Students will get to make and throw their own boomerangs between video segments! A key idea presented is how torque causes the precession of angular momentum. One class period is required to complete this learning video, and the optimal prerequisites are a familiarity with forces, Newton's laws, vectors and time derivatives. Each student would need the following materials for boomerang construction: cardboard (roughly the size of a postcard), ruler, pencil/pen, scissors, protractor, and a stapler.

Subject:
Physics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Zhiming Darren Tan
Date Added:
06/08/2015
The Physics of Donkey Carts
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This video lesson explores Newton's Third Law of Motion through examination of several real world examples of this law in action, including that of a donkey cart - a site common in the streets of Pakistan. Students will understand that forces act on objects even if the objects appear to be static and that certain conditions - gravity in particular - affect how two objects interact. The time needed to complete this lesson is approximately 50-60 minutes, and students should be familiar with basic mechanics such as Newton's laws, levers, etc. The materials required are a couple of spring balances, a meter rule, tape, pencil, two desks, and some lab weights (few grams each). The types of in-class activities for between the video breaks include active discussions and participation by students in activities related to the Third Law.

Subject:
Physics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Naveed A. Malik
Date Added:
06/08/2015
The Physics of Pool
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The objective of this lesson is to illustrate how a common everyday experience (such as playing pool) can often provide a learning moment. In the example chosen, we use the game of pool to help explain some key concepts of physics. One of these concepts is the conservation of linear momentum since conservation laws play an extremely important role in many aspects of physics. The idea that a certain property of a system is maintained before and after something happens is quite central to many principles in physics and in the pool example, we concentrate on the conservation of linear momentum. The latter half of the video looks at angular momentum and friction, examining why certain objects roll, as opposed to slide. We do this by looking at how striking a ball with a cue stick at different locations produces different effects.

Subject:
Geometry
Physics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Joseph A. Formaggio
Date Added:
06/02/2012
Plants and Environmental Resources
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Earth contains a variety of plants to provide food, medicine and, most importantly, energy sources for humans. In this lesson, students will categorize plants by their components and shapes. Additionally, they will learn the mechanisms behind the making of medicines and bio-fuels. It is important that the students have prior knowledge of the plant cell structures and functions. The video duration is 21 minutes, during which the students will use skills such as classification and experimentation. The students must therefore be supplied with various samples of plants. In Arabic with English subtitles.

Subject:
Life Science
Ecology
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Sara A. Alzahid
Date Added:
03/27/2015
Pollination: Saying It with Flowers
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This lesson focuses on the process of pollination. The learning objectives include learning the anatomy and physiology of flowers, the ecology of pollination, and a focus on plants as essential players in the natural world. There are no prerequisites for the lesson. The lesson will take 1½ hours, or 2 class periods or more -- depending on the areas teachers want to spend more time on or how far in depth they want their students to go. Materials needed are colored modeling clay, 8 or more assorted fresh flowers or pictures of flowers, preferably native to the local ecosystem. Dissecting microscopes or magnifying glasses are great for examining the fresh flowers, but not necessary. Additionally, pictures of different subjects/objects amongst plants are needed for the last activity. Activities for the breaks include assessing student knowledge of flowers by model building, and examining flowers to determine and distinguish between the pollination anatomy of different flowers.

Subject:
Life Science
Anatomy/Physiology
Ecology
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Naomi Volain
Date Added:
02/12/2015
The Power of Exponentials, Big and Small
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In this lesson, through various examples and activities, exponential growth and polynomial growth are compared to develop an insight about how quickly the number can grow or decay in exponentials. A basic knowledge of scientific notation, plotting graphs and finding intersection of two functions is assumed.

Subject:
Education
Functions
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
MIT BLOSSOMS
Date Added:
07/12/2014
Pythagoras and the Juice Seller
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This video lesson presents a real world problem that can be solved by using the Pythagorean theorem. The problem faces a juice seller daily. He has equilateral barrels with equal heights and he always tries to empty the juice of two barrels into a third barrel that has a volume equal to the sum of the volumes of the two barrels. This juice seller wants to find a simple way to help him select the right barrel without wasting time, and without any calculations - since he is ignorant of Mathematics. The prerequisite for this lesson includes knowledge of the following: the Pythagorean theorem; calculation of a triangles area knowing the angle between its two sides; cosine rule; calculation of a circle's area; and calculation of the areas and volumes of solids with regular bases.

Subject:
Geometry
Measurement and Data
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Ghada Sulaiman Abdullah Marmash
Date Added:
06/02/2012
The Quadratic Equation: It’s Hip to Be Squared
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This lesson aims to help students with quadratic functions y = ax2 + bx + c. This is the next step after linear functions bx + c. The lesson begins with three quadratics and their graphs (three parabolas): y = x2 - 2x + (0 or 1 or 2). The prerequisite or co-requisite is some working experience with algebra, like factoring x2 -2x into x(x-2). The objective is to connect four things: the formula for y, the graph of y (a parabola), the roots of y and the minimum or maximum of y. The particular example y = x2 – 2x could be repeated by the teacher, for emphasis. The lesson will take more than one class period (and this is deserved!). The breaks allow time to consider parabolas starting with -x2 and opening downward. A physical path would be one (dangerous?) activity.

Subject:
Mathematics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Gilbert Strang
Date Added:
02/13/2015