Abordagem da Matemática na Logomarca da Mercedes-Benz
Autor: Carla | Publicado: 2012-11-19T07:34:00-08:00

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ACADÊMICAS: Carla Juliana Princival.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp; Joaide Bughay

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 

NÚMERO DE AULAS: Uma h/a.



PLANO DE AULA DESTINADO AO ENSINO
FUNDAMENTAL: 8º e 9º Ano.



TEMA: Arco de Circunferência e Ângulo
Central.



OBJETIVOS:

<!--[if !supportLists]-->·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->Reconhecer e diferenciar um arco de circunferência
e um ângulo central;

<!--[if !supportLists]-->·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<!--[endif]-->Conhecer algumas de suas propriedades;



METODOLOGIA: Resolução de Problemas,
Aula Expositiva Dialogada e TICs.



RECURSOS DIDÁTICOS: Laboratório de
informática para uso do software Geogebra
e X-Logo.



DESENVOLVIMENTO:



Inicia-se a aula solicitando que os alunos observem
da figura que representa a logomarca da fabricante de caminhões e ônibus
Mercedes-Benz, uma estrela de três pontas inscrita em um círculo conforme a figura
abaixo.





Fonte:
http://autos.vocedeolhoemtudo.com.br/carros/mercedez-benz/



Com o auxilio do software GeoGebra, solicita-se que os alunos reproduzam a estrela
da Mercedes-Benz, sabendo que o ângulo formado pelos braços da estrela são
iguais e utilizando apenas as seguintes ferramentas: Círculo definido pelo
centro e um de seus pontos, Ângulo com amplitude fixa e Segmento definido por
dois pontos, utilizando apenas três segmentos.

Neste momento os alunos terão que pensar em
uma maneira de reproduzir a estrela com as ferramentas dadas, espera-se que
seja utilizado então, o conceito de ângulo central. Portanto ao fim desta etapa
o professor poderá interferir e formalizar o conceito de ângulo central, que
segundo Giovanni e Giovanni Jr (2000), é qualquer ângulo que tenha o vértice no
centro de uma circunferência. Também é possivel apresentar o conceito de arco,
que neste caso espera-se que todos encontrem os arcos medindo 120°.

Solicita-se que os alunos liguem as pontas da
estrela, então forma-se um triângulo inscrito na circunferência. E define-se o
que é um ângulo inscrito, que segundo Giovanni e Giovanni Jr (2000), é todo
ângulo que têm o vértice na circunferência e seus lados são secantes a ela.

Ainda é apresentada a seguinte relação: a
medida de um ângulo inscrito é igual a metade da medida do ângulo central correspondente.


&nbsp;Com
isso pede-se aos alunos que descubram a medida dos ângulos do triângulo formado
BB’B’’, sem utilizar a ferramenta Ângulo, apenas utilizando a relação entre a
medida do ângulo inscrito com a medida do ângulo central e as observações da
figura, só após as conjecturas feitas e a apresentação das mesmas para o grande
grupo os alunos utilizam a ferramenta ângulo para a verificação.

Com isso faz-se os alunos observarem que o
triângulo BB’B’’ formado contém os três ângulos iguais, portanto é um triângulo
eqüilátero, possui os lados iguais. 

Faz-se também o aluno perceber os triângulos
ABB’, AB’B’’ e ABB’’ e que estes são triângulos isósceles, pois seus dois lados
são formados pelos raios da circunferência. Sabendo desta informação e
utilizando a soma interna de ângulos de um triângulo pede-se para que o aluno
descubra a medida dos ângulos destes três últimos triângulos.&nbsp; Neste momento o professor pode indicar/relembrar
a propriedade dos triângulos isósceles com relação aos seus ângulos internos
bem como a soma dos ângulos internos de qualquer triângulo da geometria plana.
Então depois das conjecturas feitas confere-se as medidas com a ferramenta
Ângulo, do GeoGebra. Neste último passo indagam-se os alunos com relação à
medida de B’B’’B e AB’’B e consequentemente o que o segmento B’A é de B’B’’B.

Após a indicação da bissetriz, é solicitado
que tracem as bissetrizes dos ângulos AB’’B e ABB’’ do triângulo AB’’B e
marquem a interseção das mesmas, e logo após escondam as retas ficando apenas o
ponto de interseção, repetindo o processo análogo para os outros dois
triângulos semelhantes. Agora se solicita que liguem estes pontos por segmentos
de retas desde a ponta de cada braço do esboço inicial da estrela e observe que
formará novos triângulos, CBB’’, B’B’’E e B’BD. 

Solicita-se que descubram as medidas dos ângulos
C, D e E dos triângulos dos triângulos CBB’’, B’B’’E e B’BD, para isso
espera-se que utilizem novamente soma de ângulos internos de um triângulo, uma
vez que irão saber os valores dos outros dois ângulos dos triângulos. Após as
conjecturas novamente confere-se os resultados através da ferramenta Ângulo.

Para finalizar utiliza-se a ferramenta Exibir
Objeto para esconder os segmentos B’’B, B’’B’ e B’B, todos os ângulos, e
pontos.&nbsp; Por fim com a ferramenta Exibir
Rótulo esconde-se os rótulos dos segmentos e da circunferência. Então obtem-se
a figura a seguir.



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 height:258.75pt;z-index:1;visibility:visible;mso-wrap-style:square;
 mso-wrap-distance-left:9pt;mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
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 mso-position-vertical-relative:text'>
 <v:imagedata src="file:///C:\Users\Usuario\AppData\Local\Temp\msohtmlclip1\01\clip_image003.png"
  o:title=""/>
<![endif]--><!--[if !vml]-->
Fonte: a autora, 2012.


Para a segunda atividades utiliza-se o software X-Logo ou o KTurtle, onde os
alunos deveram reproduzir novamente o símbolo da Mercedes-Benz, a estrela de
três pontas inscrita em um círculo, porém agora elaborando individualmente uma
estratégia&nbsp; para a construção, uma vez
que já obterão as medidas dos ângulos advindos da atividade anterior.









REFERÊNCIAS



GIOVANNI J. R., GIOVANNI, J. R. J. Matemática: Pensar e Descobrir. São
Paulo: Editora FT.