Angle of Elevation and Depression!

I want to put out a special thanks to John Scammell for providing me with this lesson!  It was amazing and quite honestly, very entertaining!  Some of the images are his, one of them is Dan Meyer's, and I sort of mashed everything together to recreate a lesson that John taught to a class somewhere here in Alberta! It was fantastic!


Here is a link to the notebook file I used: honestly, the activity was not tech based at all and the students still loved it!



Finally, the activity sheet I used so students could record their observations, measurements, and calculations!



Was this activity successful?  Absolutely.  One student said “it managed to be applicable to real life.”  Another said it was “interactive, engaging, and inquiry based.”  Yet another said that it “showed an application that 20-3’s will be excited to complete and learn.”  However, in my opinion, the most useful comments are the ones that will make this lesson stronger and more memorable for students.  One of my peers pointed out that “in order to be [more] accurate you need to be farther away” when using the clinometers. “A thorough discussion of error” is needed, and “spending more time on some of the strategies and how to measure more accurately using the clinometers” both came up several times in the feedback.  Quite frankly, I agree with them.


The time provided to introduce this activity to my peers was not quite enough to fully appreciate what they encountered.  Our opening exercise would have included more than identifying trigonometric ratios and the introduction to the clinometers would have included building them and measuring the angle to an object at varying distance had there been more time available to enjoy the activity.  With more hands-on experience and more time to explore the use of the clinometers students would have observed the rules of the clinometers on their own and would have begun to think about how else these tools could have been used.  I have often felt pressured to perform while teaching in a classroom and the results during these times are always poor.  When teaching my grade eight class last year I was told that I was speaking far to fast for anyone to keep up.  Making a small leap in logic here, I can assume that it is also possible to move a class too fast through an activity.  Without the proper amount of time available to students they will have trouble making connections.


A lot of the students forgot to add their own height to their estimate while measuring the height of the Education Cafeteria.  Others didn’t use angles at all, preferring to measure the height of the windows and multiply that by three, estimating for the difference in height of the windows.  What is really interesting though is that some students preferred to use meters in their answers instead of feet.  When the answer was given in meters some of the groups cheered about how close they came and others ran to google to convert the measurement into meters.  Kieren talks a lot about teaching mathematics with a focused, yet open mind.  Not looking for a specific answer and yet keeping the class moving towards the final goal, ie. the program of studies.  We need to think about teaching with respect to how our students are thinking about the subject.  A good discussion to add to this lesson is one that explores the way that different groups found their answer and the strategies that they used.

While teaching during my IPT, I gave students an assignment to explore the NASA website.  However, after looking at the assignment, two of my students decided to write their own fictional story and base their calculations on the scenario that they described.  Their zeal for the assignment went from nearly no interest to extremely interested when they were allowed to explore the material in a manner that appealed to them.  I find the same thing often happens to me while completing assignments.  Pedagogically, this lesson became an inner argument of control in the classroom.  Allowing the students the freedom to leave the classroom and giving them the responsibility to return to the designated meeting spot can motivate students who would otherwise feel micromanaged and creates an atmosphere of open ideas and solutions.  This can be the basis for building mathematically confident and inspired learners.  Students who feel empowered within a classroom are more likely to share, communicate, and practice the skills that they’ve learned; which will in turn creates a healthy student/teacher relationship with my students!