A LAB APPROACH FOR TEACHING BASIC GEOMETRYAuthor(s): Joan L. LennieSource: The Mathematics Teacher, Vol. 79, No. 7 (OCTOBER 1986), pp. 523-524Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/27965049 .

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A LAB APPROACH FOR TEACHING BASIC GEOMETRY This past spring semester I taught two sec

tions of a class called "Survey of Geome

try." A class comprised students who had either failed or performed very poorly during the first semester of plane geometry. For some students this course would be their last high school mathematics class, whereas others would take intermediate al

gebra the following year. The challenge for me was to let them be successful in a modi

fied, less formal geometry course; to let them enjoy the class and the subject; to

give them some practical applications of ge ometry that they might use again; and to motivate them to work.

I quickly discovered that activities that involved them directly and concretely achieved my four goals. One example is a

trigonometry lab. After studying certain basic ideas about right triangles and scale

drawings, the students constructed a device for measuring angles and then proceeded to use it to make indirect measurements. The idea for the tool came from Paul Schuette, a

retired mathematics teacher.

Teacher's Guide

Prerequisites: Students should be familiar with right triangles and the Pythagorean theorem, methods of constructing scale

drawings, the definition of the tangent function, the u?e of trigonometric tables, and solutions of simple trigonometric equa tions.

Grade levels: 10-12

Materials: Yardstick or meterstick, pro tractor, fishing line and weight, plastic straw, ruler, trigonometric tables; a calcu lator for arithmetic solutions is optional.

Time: Four days to study trigonometry; a half day to explain the lab and the sight ing device, one day to complete the

measurements, and one day to complete computations, construct scale drawings, and discuss results

Objectives: Students will (1) assemble their own sighting device (fig. 1); (2) mea sure linear distances along the ground and

angles of elevation; (3) solve trigonometric equations using their data indirectly to find other distances; (4) construct scale draw

ings to represent each problem; (5) compare results and analyze sources of errors.

Tape?trawon

iweight

Fig. 1. The sighting device. In the zero position, the

weight hangs on 90 degrees.

Activity: The teacher should determine four or five objects that could be indirectly measured by the students, for example, the

heights of a tree, a flagpole, or a building in

"Sharing Teaching Ideas "

offers practical tips on the teaching of topics related to the secondary school cur

riculum. We hope to include classroom-tested approaches that offer new slants on familiar subjects for the

beginning and the experienced teacher. See the masthead page for details on submitting manuscripts for review.

October 1986 523

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the vicinity of the school. For each prob lem, the student sights the top of the struc ture or object through the straw (fig. 2) and reads the angle measure at the point where the fishing line crosses the protractor. As

long as the object is taller than the individ ual making the measurement, the angle will be obtuse. Since the weight hangs at 90 de

grees in the horizontal position, the angle of elevation is determined by subtracting 90

degrees from the angle measure read.

Fig. 2. The angle of elevation is determined by read

ing the obtuse angle and then subtracting 90 degrees.

The student then measures the distance

(d) along the ground from the point of the sighting to the base of the object (fig. 3). It is assumed that the object is perpendicular to the ground. The tangent function is used to determine the height (x). This height will have to be adjusted for the final answer by

adding it to the height (p) of the person's eye above the ground.

In my class, the students worked well in

pairs. One person sighted and one read the

angle. Each student should do his or her own computations and completion of the lab write-up. I required a scale drawing of

each sighting (fig. 3) ; a trigonometric equa tion with its solution; and a discussion of

any possible sources of error in their measurements. Appropriate rounding of an swers was discussed and expected in the

write-ups. Although making up the work

sheet is fairly easy, one may want to refer to Kullman (1976) for ready-to-use sheets.

Keep in mind that for basic students, it is

Fig. 3. = d tan a, and h = + p.

necessary to have a very structured lab worksheet that is easy for them to follow. I included a map of the school area and

marked specifically what was to be mea

sured.

Alternative activities: The students may want to investigate other measuring de vices. They may want to make several

sightings for one problem and average the results.

Kullman, David E. "Activities: Mission?Measure ment." Mathematics Teacher 69 (February 1976) :135 38.

Joan L. Lennie Oak Park and River Forest

High School Oak Park, IL 60302

CAN YOUR STUDENTS GIVE EXAMPLES? Give an example of a number that is prime. What number is divisible by 10? Give an

example of a rational number. Draw a graph of a function that is decreasing everywhere.

Asking students to provide examples stimulates class participation and produces an active atmosphere. This article discusses some of the experiences I have had when

524 - -~-Mathematics Teacher

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