Measuring the Flag Pole
Lesson 9 of 10
Objective: SWBAT use trigonometry to measure distances indirectly. Students will understand the meaning of an angle of elevation and how it is used in indirect measurement.
The lesson opener asks students to think of a way to use trigonometry to measure the height of the flagpole in front of the school indirectly (MP5). I ask them to draw a picture and to clearly identify what they would have to measure in order to compute the height of the flag pole. Students have actually seen a method in their notes and in a homework problem, so at least one student in every team should be able think of a viable answer.
This activity follows our Team Warm-Up routine, which is described in my Strategy folder.
To make a couple of key points, I direct the attention of the class to one or more of the teams’ solutions on the front board:
- Since the observer’s eyes are actually about 5 feet above the ground while sighting on the top of the flag pole, this distance (called ‘height of eye’) must be added to the height of the right triangle formed by part of the flagpole, the distance from the base of the flagpole to the observer’s feet, and the line of sight between the observer’s eyes and the top of the flagpole.
- We need a means of measuring the angle of elevation accurately. This is the lead-in to the next activity, in which students make clinometers.
Making a Clinometer
Students make clinometers out of inexpensive materials. There are many sets of instructions on the Internet. I describe one simple method in the video that accompanies this lesson: Making a Clinometer video narrative. The handout for this activity (Measuring the Flag Pole Activity handout) has instructions on the reverse side that come from the Geometry Connections textbook by College Preparatory Mathematics. After demonstrating to the class how to make a clinometer, I distribute this handout to the students, make sure they that know where to find the supplies they need, and have them get to work.
I usually have each student make his or her own clinometer, but it is fine to have students pair up to make them. They will actually use the clinometers in pairs, since it is difficult to read the protractor scale accurately while sighting the top of the flag pole with the clinometer.
Materials required for each clinometer:
1 piece of corrugated cardboard, a rectangle measuring approximately 15 cm x 20 cm
1 plastic drinking straw
1 printed protractor scale (you can find a suitable set here)
1 piece of cotton string, between 12” and 15” long
1 large washer (plumb bob weight)
4 pieces of tape, about 1 ¼” or 1 ½” long
Before class: I print out the handout for this activity. I print out the protractor scales and cut each sheet of four scales into quarters. I cut the string into pieces 12-15 inches long and tie on the washers. (This really saves time.)
Measuring the Flag Pole
Before going outside to measure the flag pole, I have the students complete a practice problem to ensure that they know what to do. As students finish making their clinometers, I ask them to complete problem 2 in the handout for the activity. If I leave this step out, they will all sun themselves when we go outside while I run around explaining to each pair of students how to find compute the height of the flagpole. Finally, I have them measure their height of eye with a tape measure (I have a set of 6-foot tape measures for sewing in the classroom) (MP6). If time is short, I have each student estimate his or her height of eye by subtracting 3 inches from their overall height. Before leaving the classroom, I make sure that we have the materials we need:
I bring a 50-foot tape measure (on a reel). (The track coach has several.)
Each student should bring his or her clinometer, the handout for the activity, a pencil, and a scientific calculator or trig table.
A flag pole about 10 meters high makes an ideal object for indirect measurement. I hook one end of a 50-foot tape measure to the base of the flag pole (or have a student hold it) and stretch the tape measure out to about 48 feet. Then I swing the tape measure in an arc and indicate the spots where each student who is going to sight the top of the flag pole should stand. Allow 3-4 feet of space between teams.
If the weather cooperates, it is nice to have students calculate the height of the flagpole while sitting on the lawn in front of the school. I want to finish the class back in the classroom, though, so that students can return the calculators they’ve borrowed and complete the lesson close.
I display the lesson close question on the front board using the slideshow. I have the students brainstorm in pairs, then in teams, before writing their answers in their learning journals. The purpose of the learning journal is to encourage students to reflect on what they have learned (as well as to provide individual accountability). Time permitting, I also ask one student from each team to write a team answer on the white board. This gives me immediate feedback on what students learned from the lesson.
Before class is dismissed, I remind students of their homework assignment, listed on the unit syllabus.