MIT Massachusetts Institute of Technology

How Tall Is That?

Fei Liang 
Teacher of Mathematics 
Verakin High School of Chongqing
Chongqing, China 

梁菲 数学老师,中国重庆第二外国语学校

This lesson is a practical lesson about measuring the height of different objects in daily life. Through this lesson, we hope that students will learn how to use simple tools to measure the height of objects whose height cannot be measured directly. In addition, students should get more understanding about how to use mathematical models to solve the problems in our lives. As a prerequisite to this lesson, students need to have some familiarity with the Pythagorean theorem, trigonometric functions and similar triangles -- which are the theoretical basis for the lesson. It would be better to teach this video in two lessons. In the first lesson, the teacher raises the questions and asks students to prepare for the solutions. The teacher would also explain the working principles of a protractor and the steps to use it. In the second lesson, the students would do the actual measurements using the tools they have prepared and discuss their proposals and results with each other. After that class, the teacher could lead the students to improve their current proposals or even to come out with new ones. 

Watch supporting video: How to Make a Protractor (Mandarin, Flash).

这节课是关于测量生活中物体的高度的一节实践操作课。通过这节课,希望学生了解对于那些不能直接通过测量得出高度的物体,如何利用我们手头的工具去间接得到它们的高度,并进一步体会数学模型在实际生活中的应用。

 

课前学生需掌握勾股定理,相似三角形定理以及三角函数等知识,为模型的建立提供理论支持。这节课最好分为两个课时进行。第一节课提出问题,让学生根据所学的知识设计方案,并可在此介绍侧倾器的制作和使用原理。第二节课,学生可以到室外使用已准备好的侧倾器和卷尺进行实地测量,并对测量方案的可操作性和结果的准确性进行交流。课后教师可引导学生对已有的方案进行讨论和改进,在此基础上思考设计其它测量方案。

I like mathematics. I think that the thinking methods for mathematics are the same as for many principles in our life. Math comes from life and should also serve life. 

喜欢数学,感觉数学中蕴含的思想方法和生活中很多原理是相通的,数学来源于生活,更应服务于生活。

This resource is a Wikipedia article on the Pythagorean Theorem.
https://en.wikipedia.org/wiki/Pythagorean_theorem

This site is a Wikipedia article on trigonometric functions.
https://en.wikipedia.org/wiki/Trigonometric_functions

This page, sponsored by SOPHIA, provides several resources related to using similar triangles to make indirect measurements.
https://www.sophia.org/concepts/using-similar-triangles-to-make-indirect-measurements

This site, sponsored by Connecting Geometry, features the method of indirect measurement known as “Shadow Reckoning”.
http://mathforum.org/sanders/connectinggeometry/ch_09Similar.html

This site is sponsored by Math Is Fun and provides an introduction to trigonometry.
https://www.mathsisfun.com/algebra/trigonometry.html

This site provides an introduction to trigonometric functions and is sponsored by Universal Class
https://www.universalclass.com/articles/math/pre-calculus/introduction-to-trigonometric-functions.htm

Watch optional video: How to Make a Protractor (Mandarin, Flash)
http://blossoms.mit.edu/videos/files/mandarin/how_make_protractor_mandarin_flash

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This Lesson is in the following clusters: Pythagorean Theorem