Motivating MobilesAuthor(s): Paul CarterSource: The Mathematics Teacher, Vol. 75, No. 1 (January 1982), pp. 39-40Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/27962746 .

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sharing teaching ideas

Motivating Mobiles In order to illustrate some mathematical

concepts in a relatively simple manner, I have created four mobiles. The Universe of

Complex Numbers (fig. 1) and the Quad mobile (fig. 2) are modifications of Venn

Fig. 1. The Universe of Complex Numbers

Fig. 2. The Quadmobile

diagrams. The Discriminating Flowmobile

(fig. 3) is a modified flowchart. The Pla tonic Mobile (fig. 4) is more conventional.

The Universe of Complex Numbers

(fig.l) was constructed from a twenty three-inch square piece of one-eighth-inch

plywood. The width of the discarded por tion was adjusted to allow the proper spac ing dependent on the length of the modi fied fishing swivels used to connect the

parts. This design could be modified by us

ing ellipses ot rectangles rather than circles and would then hang closer to the ceiling. Another suggestion would be to use numer als or symbols on one side and names for the systems on th? other. The Quadmobile (fig. 2) illustrates how

restrictions on the definitions produce dif ferent classes of figures. A quadrilateral is a

polygon of four sides. I used the definition that a trapezoid is a quadrilateral with at least one pair of parallel sides so that a par allelogram and other figures appear as sub sets. A rectangle is a parallelogram with one right angle. A square is a rectangle whose adjacent sides are congruent. An al ternative is to define a rhombus as a paral lelogram with adjacent sides congruent and a square as a rhombus with a right angle.

The Quadmobile was constructed from

three-eighths-inch wood purchased at a

hobby shop. Again, fishing swivels were used with small screw eyes to suspend the various components.

The Discriminating Flowmobile (fig. 3) is a modified flowchart that illustrates the na ture of roots of a quadratic equation as de

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

January 1982 39

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termin?e! by the value of the discriminant. These relationships can best be understood

by studying the picture of this mobile. The term "discriminant" appears on one side of the top card and on the reverse side is "?2 ?

4ac." On one side of the decision diamond is "negative, zero, positive," and on the re verse side, "-, 0, +." If the roots are real and unequal, then a check is made to see if the discriminant is the square root of some

integer /; if so, then the roots are rational

ip/q), and if not, they are irrational &p/q). The necessary restrictions on the coeffi

cients are not included on the mobile itself.

During the class discussion of the quadratic

Fig. 3. The Discriminating Flowmobile

formula, it is a pleasure to see the students

think and reason through the nature of the

solutions to the equations as the restrictions are changed from the reals to the rationals

and integers. It depends on the mathemati

cal maturity of the students, but the think

ing process can be expanded further as

complex coefficients are used. The quadratic symbol was bent from a

strip of aluminum. The balance of the mo

bile was constructed from poster board, one-fourth-inch dowel rod, and yarn.

The Platonic Mobile (fig. 4) displays the five Platonic solids. Each solid was con

structed by the rubber band construction

method (McGowan 1978). Again, one

fourth-inch dowels were used for cross

members and nylon thread was used to

hang the solids. This thread is almost invis ible and gives the illusion of suspension in

midair of the solids. Care must be given in the adjustment on the arms of the model to

Fig. 4. The Platonic Mobile

distribute the weight of the models to es tablish the cross members in a horizontal

position. It helps to start hanging the mo bile by beginning with the cross pieces at the bottom to find the balancing position. The balancing of the arm provides an illus tration for certain lever-fulcrum problems in the textbook. The air current from the

heating system keeps these moving gently. The first three of these mobiles (in modi

fied form) have been used for bulletin board displays, whereas the fourth has been used in a hallway display case. These mobiles have added to the decor of the

classroom, created interesting and informa tive discussions, and?it is hoped?helped students understand some mathematical

concepts.

Paul Carter Haworth High School

Kokomo, IN 46901

REFERENCE McGowan, William E. "A Recursive Approach to the

Construction of the Deltahedra." Mathematics Teacher 71 (March 1978):204-10.

40 Mathematics Teacher

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