Star Trek: A Construction Problem Using Compass and Straightedge

Star Trek: A Construction Problem Using Compass and StraightedgeAuthor(s): Bee EllingtonSource: The Mathematics Teacher, Vol. 76, No. 5 (May 1983), pp. 329-332Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/27963519 .

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sharing teaching ideas

Star Trek: A Construction Problem Using Compass and Straightedge

Teacher's Guide

Grade level: 8-12

Materials: A set of the directions and two copies of the map should be made for each student. Each student should have a

compass and a straightedge.

Objectives: The students are to find

Sp?ck, who is lost in space, by performing a series of consecutive geometric construc tions. This activity requires cognitive be haviors at the Knowledge, Techniques and

Skills, Comprehension, and Application levels of Wood's heirarchy of cognitive be havior (1968).

Directions: This activity should be used toward the end of a unit in geometric con

structions. Distribute copies of the direc tions and two copies of the map to each student. Be sure each student has a com

pass and a straightedge. Explain that the

points are to be found consecutively and that none of the ten points are necessarily indicated on the map, although all the

points needed to find the hidden points are

indicated by a circled dot on the map. If students cannot find a particular point, suggest that they guess its location in order to proceed with the remainder of the as

signment. The following construction skills are needed to find the indicated points:

Point 1. Bisection of a line segment

Point 2. Bisection of a line segment or di vision of a line segment into a

given number of congruent seg ments

Point 3. Construction of a perpendicular at a point on a line; bisection of an angle

Point 4. Duplication of a given distance

Point 5. Location of a point equidistant from three given points (center of the circle circumscribed about a

triangle)

Point 6. Dropping a perpendicular from a

point to a line

Point 7. Division of a line segment into a

given number of congruent line

segments

Point 8. Construction of a parallel line at a point not on the line

Point 9. Dropping a perpendicular from a

point not on a line to a given line

Point 10. Finding a point equidistant to three lines (center of the circle in scribed in a triangle). Spock's lo cation should be just above the

M-5 computer.

Additional problems: A more challenging problem can be made by substituting the

following directions for points 7 and 9:

Sharing Teaching Ideas offers practical tips on the teaching of topics related to the secondary school curriculum. We hope to include classroom-tested approaches that offer new slants on familiar subjects for the

beginning and the experienced teacher. Please send an original and four copies of your ideas to the managing editor for review.

May 1983 329



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These are the voyages of the starship Enterprise. Its five-year mission?to

explore strange new worlds, to seek out new life and new civilizations, to boldly go where no man has gone before.

Wait a minute... Where's Sp?ck? Sp?ck? Sp?ck? We've got to find Sp?ck !

Your assignment, as Captain of this starship, is to help the crew of the Enterprise find its first officer, Sp?ck. To do this, you must find ten new points on the

accompanying chart. To find these points, follow in order the directions given. You have only fifty minutes before your command is revoked and you are reassigned to menial work. In following the directions, use the circled dots that are part of each

object pictured. The Romulan neutral zone should be considered as a line.

1. Warp out of orbit to find point 1 midway between the Klingon ship and Earth.

2. To find point 2, proceed three-fourths of the distance from point 1 to Apollo's hand. (The point on Apollo's hand is on the watchband.)

3. To find point 3, change course by 45? in a counterclockwise direction, heading toward the Romulan neutral zone until you intersect the line that bisects the

angle formed by the planet killer, the Tribble asteroid, and the Jupiter 2.

4. Take an immediate course change heading directly for the nova from point 3. You will find point 4 at a distance equal to three times the distance between the

edge of the galaxy and the Enterprise. 5. The nova's heat drives your crew berserk, and they lose control of the ship. You

find yourself at point 5 when you regain control. Point 5 is an equal distance from point 4, the time portal, and the planet killer.

6. From point 5, under sealed orders, proceed to point 6, which is at the edge of the Romulan neutral zone. Be sure to take the shortest route. (To keep your worksheet from getting too cluttered, you may want to move point 6 to a clean

copy of the sheet.) 7. After accomplishing your mission at the edge of the Romulan neutral zone,

return toward the Enterprise. To avoid a space radiation belt, you stop at point 7, which is one-third of the distance between point 6 and the Enterprise.

8. Starfleet Command instructs you to proceed to point 8 along a line that is

parallel to the line between the time portal and the asteroid belt. You find point 8 on this line at a distance equal to the distance between point 7 and the Tribble asteroid.

9. Meteor shower! You veer off course to find point 9. It is where the perpendicu lar line from point 8 intersects the line between the Klingon ship and the planet killer.

10. You find Sp?ck at point 10, which is equidistant from the three lines that connect point 9, the Tholian web, and the asteroid belt.

CONGRATULATIONS to those of you who found Sp?ck! You will proceed to advanced mathematics where you will pick up your commissions. The rest of you ... get your brooms and get to work.



7. To find point 7 after completion of your mission at the Romulan neutral zone, return toward the Enterprise. Go a dis tance equal to the fourth proportional -

a, the distance from the Jupiter 2 to the M-5 computer,

b. the distance from the M-5 computer to the Klingon ship,

c. the distance from the Jupiter 2 to the rock.

(Do this construction on the back of

your map.)

9. Meteor shower! To find point 9, veer off course toward the Jupiter 2 at a distance

equal to the mean proportional between?

a. the edge of the galaxy and the shut

tlecraft,

b. the Klingon ship and the Asteroid belt.

(Do this construction on the back of

your map.)

Cognitive behavior at the Inventiveness

(highest) level of Wood's taxonomy can be obtained by encouraging students to devel

op their own construction problems of the "treasure hunt" type.

REFERENCE

Wood, R. "Objectives in the Teaching of Mathemat ics." Educational Research X (1968):83-98.

Bee Ellington Shawnee Mission North and

Shawnee Mission West High Schools

Olathe, KS 66061

Assistance with Star Trek lore and art were given

by Randy Hamilton and Andy Ellington.

A Simplified Approach to

Scattergrams are a source of valuable mathematical experience for middle school students. They can use data collected from their own class to investigate the existence of a connection between two variables. This article outlines an effective way in

which they can analyze their scattergrams and suggests the use of a simplified corre

lation coefficient.

Examples of pairs of variables recently

investigated successfully by a class of

thirty-two 11- and 12-year-olds follow.

1. Height in cm and area of foot in

cm?do the taller students tend to have

larger feet? The scattergram in figure 1 sug

gests a positive correlation between these two variables. Most of the dots are clus tered in an upward-sloping band.

2. Length of leg in cm and time to run

100 m to the nearest tenth of a second?do the students with longer legs tend to have

shorter times? The scattergram in figure 2

suggests such a negative correlation. Most

332 Mathematics Teacher

Correlation

Fig. 1. A positive correlation

of the dots are clustered in a downward

sloping band.

3. Guess of the mass of an object in grams and guess of the length of a time interval in

seconds?are good guessers of mass also

good guessers of time? The scattergram in

figure 3 suggests no connection between

these variables. The dots do not seem to lie

in a band at all.



Documents

Star Trek: A Construction Problem Using Compass and Straightedge