Educational Activities (Lesson Plans) The Winnipeg School Division No. 1
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Mathematics - Outdoor Trigonometry S1

Math
Yes

Description
Students will construct a simple measuring device and find the height and distances for   large outdoor objects using sin, cos and tan ratios.

MultiClassPlan
Yes

Tech Skills
none

Software
none

SpecificGrade
Yes

T1
S1 Trigonometry unit

SubmittedBy
Jacqueline Morrison

Acknowledgments
Thanks to Harold Neufled and Risto Pussa for the measuring instrument prototypes.   Thank you to Barb Hall for doing all the work on this diagram and for her wonderful drawing of the measuring device.

Details:

Construction of Measuring Device

1.  Use a protractor and a sheet of stiff cardboard to trace the outline of the protractor.

2.  Starting at the 90 degree mark, students should draw a line to mark every 5 degrees on their  of the protractor.

3.  Extend the line where 90 degrees would be on the protractor so that it cuts through the entire tracing of the protactor.  Label this line 0 degrees.

4.  Begin to label the degrees on the curved edge of the protractor shape.   Label the first lines on either side of 0 degrees as 5 degrees.  The second lines on either side of 0 degrees should be labeled 10 degrees.  The third lines should be labeled 15 degrees and so on up to 90 degrees.

5.  Tape a thread to the straight edge of the protractor shape at the zero degree mark.  The thread should be long enough to hang below the curved edge of the protractor shape.  Tie a washer to the thread.  The washer and thread should be able to swing freely alond the entire range of the protractor shape.

6.  Tape a large bore drinking straw (the ones from McDonald's work well) to the straight edge of the protractor shape.

A diagram of the measuring instrument is available as an attachment.  If you wish to download these files, click on these links: protractor.gif and protrWstraw.gif.   

Measuring Outdoor Objects

1.  The straw is the sight.  Students can look through the straw and their partner can read the angle of elevation or depression of any point/object.

2.  Use a metre stick to measure the distance from the student taking the sighting to the object.

The Assignment

I pick several objects in the school area that students could not measure using a metre stick alone(the school itseld, trees, hydro poles, the diagonal of the school yard, etc.)   Student pairs must find the height or distance  and "prove" their claim by drawing an accurate to scale diagram that includes their measurements and their sin, cos or tan calculations (all work shown).  With small classes  I have had students present their arguments to classmates.  A surpising number forget to factor in the height of the student sighting!!