Curso Capinzal 2024

Jorge Cássio, 7 Jun 2024

Table of Contents

  1. Atividades sobre áreas e perímetros de figuras planas
    1. Área do Retângulo
    2. Área do triângulo
    3. Área do trapézio
    4. Área do Losango
    5. Área do Círculo
    6. Tangram
    7. Perímetro de um polígono
    8. Área e perímetro no PHET
    9. Área do Paralelogramo
  2. Atividades de Álgebra
    1. Algeplan
    2. Equação do 2º Grau
    3. Sistema 2 x 2 possível e determinado
    4. Problemas Resolvidos
  3. Atividades de Geometria espacial
    1. As formas Geométricas Espaciais -Poliedros
  4. Atividades sobre pontos notáveis do triângulo
    1. Incentro
    2. Circuncentro
  5. Atividades de trigonometria no triângulo retângulo
    1. TRIGONOMETRIA NO TRIÂNGULO RETÂNGULO
    2. Exercícios envolvendo Trigonometria no Triângulo Retângulo
    3. Problemas de Trigonometria
  6. Tarefas sobre frações
    1. Régua das Frações
    2. Frações equivalentes com modelo de área
    3. Frações equivalentes no PHET
    4. Visualizando frações com vários modelos
    5. Adicionando frações com um modelo de área
    6. Multiplicando Frações - Modelo de Área
  7. Como fazer?
    1. Como criar atividades na plataforma GeoGebra? (atualizado em 2023)
    2. Como copiar e editar uma atividade?
    3. Como criar um livro na plataforma GeoGebra
    4. Como criar um livro na plataforma GeoGebra
    5. Como copiar e editar um livro na plataforma GeoGebra

1.

Atividades sobre áreas e perímetros de figuras planas

  • 1. Área do Retângulo
  • 2. Área do triângulo
  • 3. Área do trapézio
  • 4. Área do Losango
  • 5. Área do Círculo
  • 6. Tangram
  • 7. Perímetro de um polígono
  • 8. Área e perímetro no PHET
  • 9. Área do Paralelogramo

1.1.

Área do Retângulo

Área do retângulo
Para deduzirmos a fórmula da área do retângulo, vamos explorar a construção seguinte.[br](ps.: esta construção foi adaptada de uma feita por Jayrton Carvalho)
Reflexão 1
Altere o controle deslizante n observe os quadradinhos preenchendo o retângulo. Quantos quadradinhos cabem no retângulo?
Reflexão 2
Altere os valores da base (B) para 10 e da altura (H) para 5. Altere o controle deslizante n e observe os quadradinhos preenchendo o retângulo. Quantos quadradinhos cabem no retângulo?
Reflexão 3
Qual a relação entre o número de quadradinhos (n) que cabem no retângulo com a altura (H) e a base (B) do retângulo?
Reflexão 4
Intuitivamente, o número de quadradinhos que cabem no retângulo pode ser considerado como a área do retângulo. Dessa forma, escreva uma equação que representa a área de um retângulo de base B e altura H.
E se o quadradinho fosse menor?
– Jorge Cássio, Jayrton Carvalho

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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2.

Atividades de Álgebra

  • 1. Algeplan
  • 2. Equação do 2º Grau
  • 3. Sistema 2 x 2 possível e determinado
  • 4. Problemas Resolvidos

2.1.

Algeplan

– Jorge Cássio

2.2.

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2.3.

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2.4.

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3.

Atividades de Geometria espacial

  • 1. As formas Geométricas Espaciais -Poliedros

3.1.

As formas Geométricas Espaciais -Poliedros

Ao observarmos a natureza e os objetos feitos pelo homem podemos perceber diferentes formas. Algumas delas tem características comuns que chamamos, na matemática, de [b]Formas Geométricas Espaciais[/b]. Nesta tarefa, exploraremos os Poliedros.
O que são os Poliedros ?
Formas Poliédricas
Formas Não Poliédricas
Questão 1
Compare as formas poliédricas e não poliédricas. Qual a principal diferença entre elas?
Paralelepípedo
Um objeto bastante comum que é usado para transporte de mercadorias é a caixa de papelão. Veja alguns exemplos:[br][img]https://cdn.geogebra.org/material/MVGCAAishKwUHoAt9iaKPbqiTM1UgSFE/material-B6bCFGCJ.png[/img][img]https://cdn.geogebra.org/material/8TvS4URBrMnzbCLgHxOgecaYgLseo2g0/material-nznSUsuW.png[/img][br]Essas caixas têm formato de [b]Paralelepípedo[/b].
PARALELEPÍPEDO
QUESTÃO 2
Na construção anterior, para visualizar melhor os elementos do paralelepípedo, marque ou desmarque as caixas "Destacar vértices", "Esconder/Mostrar arestas" e "Esconder/Mostrar Faces". Quantos vértices tem paralelepípedo?
QUESTÃO 3
Na construção anterior, para visualizar melhor os elementos do paralelepípedo, marque ou desmarque as caixas "Destacar vértices", "Esconder/Mostrar arestas" e "Esconder/Mostrar Faces". Quantas faces tem paralelepípedo?
QUESTÃO 4
Na construção anterior, para visualizar melhor os elementos do paralelepípedo, marque ou desmarque as caixas "Destacar vértices", "Esconder/Mostrar arestas" e "Esconder/Mostrar Faces". Quantas arestas tem paralelepípedo?
Dimensões do Paralelepípedo
O Paralelepípedo possui 3 dimensões: comprimento, largura e altura. [br][img 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[/img][br]
Questão 5
No paralelepípedo seguinte, quanto mede a altura, largura e comprimento?[br][img]data:image/png;base64,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[/img]
Planificação
QUESTÃO 6
Na construção anterior, mova o seletor "mova" para ver a planificação do paralelepípedo. Qual polígono que forma as faces do paralelepípedo?
Quando o Paralelepípedo será um Cubo?
QUESTÃO 7
Na construção anterior, mova os seletores "largura", "comprimento" e "altura", buscando fazer combinações até que apareça a frase "Este Paralelepípedo é um Cubo". Como devem ser as dimensões do paralelepípedo para que ele seja um Cubo?
QUESTÃO 8
Na construção anterior, mova os seletores "largura", "comprimento" e "altura" até que se obtenha um cubo. Após isso mova o seletor "mova" para planificar o Cubo. Qual polígono compõe as faces do Cubo?
Dado
QUESTÃO 9
Na construção anterior, altere o ponto "Girar" para ver as diferentes posições do dado. Qual das figuras seguintes representa a planificação do dado?
PRISMAS E PIRÂMIDES
Alguns outros objetos que podem ser vistos no nosso dia a dia e que se assemelham com formas geométricas. Tais objetos se assemelham com os [b]Prismas [/b]e as [b]Pirâmides[/b]. [br][img]https://www.geogebra.org/resource/FbpUrGv8/JChZEdfRdc2yqjkt/material-FbpUrGv8.png[/img][img]https://www.geogebra.org/resource/nfa6MGK3/YlGocrV5H43BXkU3/material-nfa6MGK3.png[/img][img]https://www.geogebra.org/resource/KaUAeRpu/GGiLyqlIPxBy7oiO/material-KaUAeRpu.png[/img][br]
PRISMAS
QUESTÃO 10
Na construção anterior, clique com o botão direito, segure e arraste para ver os prismas em diferentes posições. Quais são os polígonos que formam o prisma vermelho?
Elementos do Prisma
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[/img]
QUESTÃO 11
Um prisma de base hexagonal, possui:
Pirâmides
ELEMENTOS DA PIRÂMIDE
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[/img][/center]
QUESTÃO 12
Qual polígono que forma as faces laterais da pirâmide?
– Jorge Cássio

4.

Atividades sobre pontos notáveis do triângulo

  • 1. Incentro
  • 2. Circuncentro

4.1.

Incentro

Incentro
O incentro de um triângulo é o ponto de encontro das bissetrizes dos ângulos internos do triângulo.
Construção do Incentro do Triângulo
[list][*]Ative a ferramenta POLÍGONO (Janela 5) e clique em três lugares distintos para formar um triângulo. Para fechar o triângulo clique novamente no primeiro ponto. Naturalmente que os pontos não podem estar alinhados. Um triângulo com vértices nos pontos A, B e C será criado.[/*][*]Ative a ferramenta BISSETRIZ (Janela 4) e clique sobre os vértices: A, C e B (nessa ordem). Posteriormente sobre os vértices C, B e A (nessa ordem). Duas bissetrizes foram criadas com os nomes “d” e  “e”.[/*][*]Ative a ferramenta INTERSEÇÃO DE DOIS OBJETOS (Janela 2) e crie o ponto D de interseção das retas “d” e “e”. [br][/*][*]Queremos traçar a terceira bissetriz. A pergunta é: será que ela também passará pelo ponto D? Ative a ferramenta BISSETRIZ (Janela 4) e clique nos pontos B, A e C (nessa ordem).[br][/*][/list]
Construção do círculo inscrito
[list][*]Ative a ferramenta EXIBIR/ESCONDER OBJETO (Janela 11), clique sobre as retas d, e, f e aperte ESC posteriormente. [br][/*][*]Vamos modificar o nome do ponto D para Incentro. Para tal, clique com o botão do lado direito do mouse sobre o ponto D e selecione a opção RENOMEAR. Na nova janela que aparecerá, escreva Incentro e clique em OK.[/*][*]Ative a ferramenta RETA PERPENDICULAR (Janela 4), clique no ponto Incentro e no lado c do triângulo (que liga os pontos A e B). [br][/*][*]Ative a ferramenta INTERSEÇÃO DE DOIS OBJETOS (Janela 2), clique na reta g e, posteriormente, no lado c que liga os pontos A e B. Um ponto D será criado[1]. [br][/*][*]Nosso interesse é apenas no pé da perpendicular (ponto D). Assim, podemos esconder a reta g, usando a ferramenta EXIBIR/ESCONDER OBJETO (Janela 11). Feito isto, aperte a tecla ESC. [br][/*][*]Ative a ferramenta CÍRCULO DEFINIDO PELO CENTRO E UM DE SEUS PONTOS (Janela 6), clique no ponto Incentro e posteriormente no ponto D. Uma circunferência h será criada.[/*][/list]
Reflexão 1
Altere as posições dos pontos A, B ou C. Por que os lados do triângulo tangenciam o círculo?
Reflexão 2
Meça as distâncias de um dos vértices do triângulo a dois pontos de tangência e observe que são iguais. Por que?[br][br] [img 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[/img]
Propriedade
As três bissetrizes internas de um triângulo interceptam-se num mesmo ponto que equidista dos 3 lados do triângulo.
Demonstração
– Jorge Cássio

4.2.

–

5.

Atividades de trigonometria no triângulo retângulo

  • 1. TRIGONOMETRIA NO TRIÂNGULO RETÂNGULO
  • 2. Exercícios envolvendo Trigonometria no Triângulo Retângulo
  • 3. Problemas de Trigonometria

5.1.

TRIGONOMETRIA NO TRIÂNGULO RETÂNGULO

O que é?
Trigonometria (do grego [i]trigōnon [/i]"triângulo" + [i]metron [/i]"medida") é um ramo da matemática que estuda as relações entre os comprimentos de 2 lados de um triângulo retângulo (triângulo onde um dos ângulos mede 90 graus), para diferentes valores de um dos seus ângulos agudos. A abordagem da trigonometria penetra outros campos da geometria, como o estudo de esferas usando a trigonometria esférica.[b] (fonte wikipédia)[/b]
Trigonometria no triângulo retângulo
1.       Altere a posição do ponto D e observe o resultado da razão [math]\frac{DF}{AF}[/math]. Ele muda?
2.       Altere a posição do ponto D e observe o resultado da razão [math]\frac{AD}{AF}[/math]. Ele muda?
3.       Altere a posição do ponto D e observe o resultado da razão [math]\frac{DF}{AD}[/math]. Ele muda?
4. Por que os resultados das razões [math]\frac{DF}{AF}[/math] e [math]\frac{EG}{AG}[/math] são sempre iguais? Por que os resultados das razões [math]\frac{AD}{AF}[/math] e [math]\frac{AE}{AG}[/math] são sempre iguais? Por que os resultados das razões [math]\frac{DF}{AD}[/math] e [math]\frac{EG}{AE}[/math] são sempre iguais?
5. Por que os triângulos ADF e AEG são semelhantes?
6. Movimente o ponto C, diminuindo e aumentando o ângulo [math]\alpha[/math] . O resultado da razão [math]\frac{DF}{AF}[/math] muda?[code][/code]
7. Movimente o ponto C, diminuindo e aumentando o ângulo [math]\alpha[/math] . O resultado da razão [math]\frac{AD}{AF}[/math] muda?
8. Veja que na figura temos 2 triângulos retângulos. Os lados do triângulo retângulo são chamados de catetos e hipotenusa. Chamamos a razão entre a medida do cateto oposto ao ângulo e a medida da hipotenusa de [b]Seno[/b][b] do ângulo[/b]. Na figura, temos sen([math]\alpha[/math]). O que acontece com o sen([math]\alpha[/math]) quando diminuímos o ângulo [math]\alpha[/math] fazendo ficar próximo de 0 (zero) ?
9. Chamamos a razão entre a medida do cateto adjacente ao ângulo e a medida da hipotenusa de [b]Cosseno[/b][b] do ângulo[/b]. Na figura, temos cos([math]\alpha[/math]). O que acontece com o cos([math]\alpha[/math]) quando diminuímos o ângulo [math]\alpha[/math] fazendo ficar próximo de 0 (zero) ?
10. Chamamos a razão entre a medida do cateto oposto e a medida do cateto adjacente ao ângulo de [b]Tangente [/b][b]do ângulo[/b]. Na figura, temos tan([math]\alpha[/math]). O que acontece com o tan([math]\alpha[/math]) quando diminuímos o ângulo [math]\alpha[/math] fazendo ficar próximo de 0 (zero) ?
11. O que acontece com o sen([math]\alpha[/math]) quando aumentamos o ângulo [math]\alpha[/math] fazendo ficar próximo de 90º ?
12. O que acontece com o cos([math]\alpha[/math]) quando aumentamos o ângulo [math]\alpha[/math] fazendo ficar próximo de 90º ?
13. O que acontece com a tan([math]\alpha[/math]) quando aumentamos o ângulo [math]\alpha[/math] fazendo ficar próximo de 90º ?
Trigonometria no triângulo retângulo
– Jorge Cássio

5.2.

–

5.3.

–

6.

Tarefas sobre frações

  • 1. Régua das Frações
  • 2. Frações equivalentes com modelo de área
  • 3. Frações equivalentes no PHET
  • 4. Visualizando frações com vários modelos
  • 5. Adicionando frações com um modelo de área
  • 6. Multiplicando Frações - Modelo de Área

6.1.

Régua das Frações

A figura seguinte representa um conjunto de Régua de Frações feito no GeoGebra.[br][br][img]data:image/png;base64,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[/img]
Exercício 1
No applet seguinte represente frações que são equivalentes a [math]\frac{1}{2}[/math]
Exercício 2
No applet seguinte represente frações de [math]\frac{1}{5}[/math] que sejam equivalentes a [math]\frac{6}{10}[/math]
Exercício 3
No applet seguinte temos uma régua que está sem indicação de fração. Determine duas frações equivalentes que possam ser usadas como indicação de fração para a régua.
– Jorge Cássio, Duane Habecker

6.2.

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6.3.

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6.4.

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6.5.

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6.6.

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7.

Como fazer?

  • 1. Como criar atividades na plataforma GeoGebra? (atualizado em 2023)
  • 2. Como copiar e editar uma atividade?
  • 3. Como criar um livro na plataforma GeoGebra
  • 4. Como criar um livro na plataforma GeoGebra
  • 5. Como copiar e editar um livro na plataforma GeoGebra

7.1.

Como criar atividades na plataforma GeoGebra? (atualizado em 2023)

O vídeo seguinte mostra como criar uma atividade que contém texto, questões abertas e fechadas, vídeo, figura e página da web.
No próximo vídeo mostro como configurar a barra de ferramentas do GeoGebra para podermos fazer atividades contendo applets com menos ferramentas.
Atividade 1
Crie uma pequena atividade (com vídeo, applet e perguntas) e coloque o link aqui
– Jorge Cássio

7.2.

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7.3.

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7.4.

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7.5.

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Information