At the Cathy Battles "Great Tasks" mathematics workshop that was presented at ESHS on July 29, 2015, the ESHS and ESMS math department members were provided with a wide variety of mathematical tasks that are free and available to all students. Cathy did a phenomenal job of showing us numerous techniques for allowing the students to take control of their learning as well as analyzing how other tasks can be improved to better engage and challenge our students. I was very impressed with the "hands-on" nature of these tasks and felt like many of them would be extremely applicable for my Geometry students.
One such task that I decided to use was to take my Geometry classes into the ESHS Commons and provide them with only a weighted protractor and calculator while asking them to determine the height of various objects in the Commons. This activity allowed my students to gain a deeper understanding of the concept of angle of elevation and how it can be utilized to find missing lengths by solving trigonometric ratios. My students quickly realized that they were able to form right triangles by using the weighted protractors to find the angle of elevation from eye level to whatever object they chose in the Commons. Also, they immediately realized that a tape measure was unnecessary since the base of each right triangle could be calculated by simply using the knowledge that each tile in the Commons is a square with a side length of 1 foot. Lastly, it was fascinating to watch as my kids performed their trig calculations and realized that the answer produced was not correct for the actual height until they added in their eye level body height to the calculated value.
One of the big takeaways from this activity that my students acquired was that this method could be used to find the height of virtually any object as long as they had access to the angle of elevation. Consequently, we discussed various jobs that would perform these types of calculations. Furthermore, my students were able to develop a strong comprehension of why the angles of elevation and depression are congruent as well as seeing how applicable trigonometric ratios are in numerous aspects of life.
Post by | Jeff Meyer | High School Mathematics
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