TEACHER'S GUIDE

Dear Teacher, if you have any question of any kind,do not hesitate to contact us by email:

conteudosdigitais@im.uff.br



DESCRIPTION

At the beginning of the 20th century, one of the issues confronting scientists at the time was the possibility of building large and stable flying devices to take a man to the sky and bring him back safely. Alexander Graham Bell proposed a flying machine (a kite) that, in fact, managed to transport a man. The idea of Bell: to use regular tetrahedrons as cells of the structures of his kites. In this activity we present a detailed script for the construction of Alexander Graham Bell's tetrahedral kites with low cost material. The activityis filled by 3D computer models. The subject is very opportune to explore counting, similarity, proportionality, areas, and volumes.


GOALS

To explore counting, similarity, proportionality, areas, and volumes related to the juxtaposition of tetrahedrons; to explore the Galileo Galilei's principle of similitude.


WHEN TO USE?

We suggest that it be used during the presentation of the theory of platonic solids, in spatial geometry.


HOW TO USE?

It could be used in classroom, as a science fair project, or as arecreation activity. We highly recommend that the student fill some kind of questionnaire, for later evaluation. We suggest the following model (feel free to modified it according to your needs):

pgb-aluno.rtf.

This student accompaniment form will also be accessible at the main page through this icon:

.

The answers to the questions proposed in this form are not included with the activity, but they can be requested through the email conteudosdigitais@im.uff.br.


METHODOLOGICAL OBSERVATIONS

Experience reports (proven in our tests) show that students have resistance in completing the accompaniment form. Moreover, these reports show that students are often able to argue correctly verbally, but face difficulties in writing their ideas.

Even with the complaints and resistance of the students, our suggestion is that you, teacher, insist on completing the form. After all, for many reasons, it is very important that the student gets the ability to correctly compose a mathematical text that can be understood by other people.


TECHNICAL OBSERVATIONS

The activity can be accessed using the internet through the link http://www.uff.br/cdme/pgb/ (alternative adress: http://www.cdme.im-uff.mat.br/pgb/). If you prefer, ask the school lab person to install the activity for offline access.

The game can run on any operating system: Windows, Linux and Mac OS. However, to run it, the computer must have JAVA language installed. The installation of the JAVA language can be done following the guidelines available in the following link http://www.java.com/.

Warning: if you are using this activity offline através de uma cópia local em seu computador, é importante que os arquivos não estejam em um diretório cujo nome contenha acentos ou espaços.

Importante: algumas distribuições Linux vêm com o interpretador JAVA GCJ Web Plugin que não é compatível com o applet da atividade. Neste caso, recomendamos que você solicite ao responsável pelo laboratório da escola que instale o interpretador nativo da Sun, disponível no link http://www.java.com/pt_BR/.

Acessibilidade: a partir da Versão 2 do Firefox e da Versão 8 do Internet Explorer, é possível usar as combinações de teclas indicadas na tabela abaixo para ampliar ou reduzir uma página da internet, o que permite configurar estes navegadores para uma leitura mais agradável.

Combinação de Teclas Efeito
Ampliar
Reduzir
Voltar para a configuração inicial

Vantagens deste esquema: (1) além de áreas de texto, este sistema de teclas amplia também figuras e aplicativos FLASH e (2) o sistema funciona para qualquer página da internet, mesmo para aquelas sem uma programação nativa de acessibilidade.


TIPS

In the classroom, we suggest that small groups of four or five students. Each group can assemble a kite with 4 tetrahedral structures, following the steps described in the activity. This kite, can already take flight by itself. Then, students can combine these kites to build larger kites, with 16 or even 64 tetrahedral cells.


DISCUSSION QUESTIONS AFTER ACTIVITY REALIZATION

We highly suggest that a discussion be held with the students after the task is completed. If you chose to take them to the laboratory, this can be done in the laboratory itself, right after the activity ends. If you have opted for an extraclass exercise, the discussion can be made upon return of the questionnaire. This discussion may include the different strategies for solving the exercises adopted by each student, comparing students' answers, difficulties encountered in performing exercises, emphasizing important properties and results, supplementary information, etc.


EVALUATION

As an assessment tool, we encourage you to have students write a report describing the questions and answers presented in the classroom discussion. In this report, the teacher will be able to evaluate the student's comprehension, argumentation and organization skills. We recommend that the questionnaire completed during the activity be attached to the report.


REFERENCES

Bell, A. G. The Tetrahedral Principle in Kite Structure. National Geographic Magazine, vol. 14, pp. 219-251, 1903.

Bender, E. A. An Introduction to Mathematical Modeling. John Wiley & Sons, Inc., 1978.

de Bock, D.; van Dooren, W.; Janssens, D.; Verschaffel, L. The Illusion of Linearity from Analysis to Improvement. Mathematics Education Library, Springer-Verlag, 2007.

Newcomb, S. Is The Airship Coming? McClure’s Magazine, vol. 17, pp. 432-435, 1901.

Niklas, K. J. Plant Allometry – The Scaling of Form and Process. University Of Chicago Press, 1994.

Schmidt-Nielsen, K. Scaling: Why is Animal Size so Important?. Cambridge University Press, 1984.

Schultz, S. A.; Schultz, M. J. The Tarantula Keeper's Guide – Comprehensive Information on Care, Housing, and Feeding. Barron's Educational Series, 1998.

Thompson, D. W. On Growth and Form. Cambridge at the University Press, 1942.

Vogel, S. Cats' Paws and Catapults – Mechanical Worlds of Nature and People. W. W. Norton & Company, 1998.


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Problems? Suggestions? We give technical support! Please, contact us by the e-mail:
conteudosdigitais@im.uff.br.