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.
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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.
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.
يستخدم هذا الفيديو التعليمي نظام تناظري بسيط لاستكشاف السبب في كون الزلازل لا يمكن التنبؤ بها. والنظام بسيط بشكل كافي يسمح للطلاب بتجميعه وتشغيله بأنفسهم تحت إشراف المعلم. علماً بأن المقاربة التدريسية المستخدمة في هذه الوحدة تُعرف باسم مقاربة المهام الخمسة، ألا وهي: الاشتراك والاستكشاف والشرح والاسهاب والتقييم. وعلى مدار هذا الدرس، يتم شرح وتفسير الآليات الأساسية التي تثير سلوك هذا النظام التناظري البسيط، ويتم تقديم المزيد من الشرح لمساعدة الطلاب على تطبيق فهمهم للنظام التناظري على أنظمة الخطأ المعقدة التي تُحدِث الزلازل
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
موضوع التمثيل (البناء) الضوئي هو مفهوم أساسي في الأحياء والكيمياء وعلوم الأرض. وقد وجدت الدراسات التعليمية أنه وبالرغم من العروض التقديمة في الفصول المدرسية، يحتفظ معظم الطلاب بفكرتهم الساذجة بأن كتلة النبات مستمدة في أغلبها من التربة، وليس من الهواء. ولأجل لفت انتباه الطلاب إلى هذه الفكرة المغلوطة، سنقوم في بداية هذا الدرس بعرض نتيجة تجريبية مدهشة بحيث يواجه الطلاب خطأهم الفكري. تالياً، سنساعد الطلاب على امتلاك تصور أفضل لعملية البناء الضوئي من خلال عمل نموذج للمكان الذي تأتي منه الذرات في هذه العملية المهمة التي تنتج الغذاء للنبات. علماً بأنه يمكن إكمال هذا الدرس في 50-60 دقيقة، وذلك في ظل قيام الطلاب بالعمل على أنشطة الفصل خلال 20-25 دقيقة من زمن الدرس. وكشرط مسبق لهذا الدرس، يحتاج الطلاب إلى درس تعريفي لعملية البناء الضوئي، بحيث يتضمن المعادلة الكيميائية الإجمالية. فإن كان الطلاب قد درسوا بالفعل عملية البناء الضوئي داخل الخلايا بالتفصيل، يمكن لهذا الفيديو أن يظل مفيد للغاية لأن الطلاب غالباً ما يغفلون المشهد الكبير لعملية البناء الضوئي. والمواد اللازمة تشمل: قطع ليغو حمراء وبيضاء وسوداء (الأمر موصوف في ملف قابل للتنزيل)، أو شرائط من الورق الأحمر والأبيض والأسود بالإضافة إلى مشابك ورق (الإرشادات موجودة في ملف قابل للتنزيل). وبالإضافة إلى مناقشات الفصل، فإن النشاط الرئيسي لهذا الفيديو يتضمن قيام الطلاب بعمل نموذج لمصدر الذرات في عملية البناء الضوئي، وذلك باستخدام قطع الليغو أو الورق الملون.
The main objective of this video lesson is to bring the students' attention to the importance of basic and natural sciences in our lives. The lesson will introduce a topic (sustainable energy) that is related mainly to chemistry and is not usually covered directly in a high school curriculum. We hope that this lesson will show students how important and useful the natural and basic sciences are not only for our daily lives, but also for sustainable development. The lesson will present creative and challenging ideas on the topic of alternative energies. It is hoped that students will be inspired by the introduction of these ideas, and that they will develop the confidence to come up with creative ideas themselves. Background for this lesson is based on fundamental concepts in chemistry (mainly), biology, physics and environmental science.
This learning video presents an introduction to graph theory through two fun, puzzle-like problems: ''The Seven Bridges of Konigsberg'' and ''The Chinese Postman Problem''. Any high school student in a college-preparatory math class should be able to participate in this lesson. Materials needed include: pen and paper for the students; if possible, printed-out copies of the graphs and image that are used in the module; and a blackboard or equivalent. During this video lesson, students will learn graph theory by finding a route through a city/town/village without crossing the same path twice. They will also learn to determine the length of the shortest route that covers all the roads in a city/town/village. To achieve these two learning objectives, they will use nodes and arcs to create a graph and represent a real problem.
This video is meant to be a fun, hands-on session that gets students to think hard about how machines work. It teaches them the connection between the geometry that they study and the kinematics that engineers use -- explaining that kinematics is simply geometry in motion. In this lesson, geometry will be used in a way that students are not used to. Materials necessary for the hands-on activities include two options: pegboard, nails/screws and a small saw; or colored construction paper, thumbtacks and scissors. Some in-class activities for the breaks between the video segments include: exploring the role of geometry in a slider-crank mechanism; determining at which point to locate a joint or bearing in a mechanism; recognizing useful mechanisms in the students' communities that employ the same guided motion they have been studying.