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Mini caso de estudio: “Visitando una comunidad mapuche en Purén”. Conociendo nuestra cultura ancestral.

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La realización de un viaje académico a diferentes localidades de la región de la Araucanía, es una de las actividades interesantes que nuestros alumnos pueden desarrollar, ya que les permite estar en contacto con el medio social que les rodea, así como comprender y valorar las características. . . de dichas comunidades.

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Sandra es profesora de un octavo básico del Colegio Gabriela Mistral ubicado en la comuna de Hualpén y realizará un viaje de estudio a la comuna de Purén, con el fin de conocer la realidad de algunas comunidades mapuches. Para esto, la profesora deberá organizar varios aspectos relacionados con el viaje, de modo de tener claridad respecto de las condiciones y actividades que realizarán durante su estadía en dicha comuna.

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Dentro de los aspectos a considerar en la actividad se destacan las rutas del posible viaje, las características físicas del lugar, las visitas a realizar, entre otras.
La profesora realizará el viaje con un grupo de $\\var{apmaph}$ alumnos que tienen apellidos de origen mapuche y $\\var{aptradh}$ de apellidos tradicionales.

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El colegio que visitarán en la comuna de Purén es el Colegio Tranaman, donde serán recibidos por los alumnos del octavo año básico. Este curso, a diferencia del curso visitante, tiene $\\var{apmapp}$ alumnos con apellido originario y solo $\\var{aptradp}$ con apellido tradicional.

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$\\color{naranja}{\\mbox{ ACTIVIDAD 1}}$

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Como parte de las justificaciones del proyecto, Sandra buscara que sus alumnos tomen conciencia de los orígenes familiares que tienen los alumnos que participarán en el intercambio cultural. La idea es destacar la diferencia entre los orígenes familiares de ambas comunidades educativas. A partir de lo anterior:

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a) Si comparamos la cantidad de alumnos que tienen apellido mapuche con aquellos de apellido tradicional en el Colegio Tranaman podemos decir que la razón que representa dicha comparación es: [[0]](escribir razón de la forma a/b) .

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b) Si comparamos la cantidad de alumnos que tienen apellido mapuche con aquellos de apellido tradicional en el Colegio Gabriela Mistral podemos decir que la razón que representa dicha comparación es:[[1]](escribir razón de la forma a/b).

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$\\color{naranja}{\\mbox{ ACTIVIDAD 2}}$

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La empresa contratada para realizar el viaje de ida y vuelta, informa que el servicio no cubre el gasto de petróleo e informa que el rendimiento de este autobús es de $\\var{rendimiento}$ kilómetros por litro. Si sabemos que tenemos 3 rutas posibles, A, B, C y que el valor del litro de petróleo está actualmente a \\$ $\\var{precio}$ pesos.

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Considerando está información,

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a) complete la siguiente tabla (considere aproximar con dos decimales):

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RutaKilómetroslitros de petróleo
A200 kilómetros[[0]]
B225 kilómetros[[1]]
C240 kilómetros[[2]]
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b) Por lo tanto, a partir de la información de la tabla la opción más conveniente tendrá un gasto a relizar en petróleo de \\$[[3]](ingresa valor aproximado sin decimales).

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$\\color{naranja}{\\mbox{ ACTIVIDAD 3}}$

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Otra visita importante que realizarán los estudiantes, es un cementerio mapuche donde existen dos Totem (Chemamull) muy antiguos ubicados uno al lado del otro. Según las indicaciones de un historiador de la zona, se destacan estas figuras de madera que están construidas en razón de $\\var{r1}$  : $\\var{r2}$ .

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Si sabemos que la figura mayor tiene una altura de $\\var{alturache}$  metros:

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La longitud de la figura menor será de:[[0]] (Considere hasta dos decimales)

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$\\color{naranja}{\\mbox{ ACTIVIDAD 4}}$

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A partir de la visita al museo, la profesora decide realizar una actividad con sus estudiantes, que consistirá en la construcción de tres piezas de Totem, a partir de una pieza de madera que tiene una longitud de $\\var{largopieza}$ centímetros  .

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a) ¿Cuál será la longitud de las tres piezas a construir si deberán estar en razón de $\\var{a}$  : $\\var{b}$  : $\\var{c}$  ?

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PiezaLargo (en centímetros)
Mayor[[2]]
mediano[[1]]
Menor[[0]]
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$\\color{orange}{\\mbox{ ACTIVIDAD 5}}$

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Como primera actividad de la jornada los organizadores de la visita llevarán un gru-po de estudiantes a conocer la araucaria y recolectar piñones, uno de los principales alimentos frutos de los pueblos originarios. En esta actividad participaron $\\var{alumno1}$ alumnos durante 20 minutos, logrando recoletar $\\var{pinones1}$ piñones.

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a) Si hubieran participado $\\var{alumno1 + 5}$ alumnos ¿Cuántos piñones hubieran recolectado en el mismo tiempo? 

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[[0]] (considerar dos decimales)

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b) ¿Cuántos alumnos se necesitarían si quisiéramos recolectar $\\var{pinones1 - 50}$ piñones?

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[[1]] (considerar dos decimales)

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c) ¿Cuánto tardaríamos en recolectar $\\var{pinones1}$ si la cantidada de estudiantes fuera $\\var{alumno1 - 10}$

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[[2]] (considerar dos decimales)

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$\\color{naranja}{\\mbox{ ACTIVIDAD 6}}$

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Junto a la ruca principal que los estudiantes han visitado durante esta gira, se encuentran $\\var{trabajadores}$ personas trabajando en la construcción de una nueva ruca gracias al beneficio de un proyecto de cultura. Los trabajadores se han tomado $\\var{diastrabajo}$ días en construir el nuevo espacio trabajando 5 horas diarias sin descanso. Ante las preguntas de los estudiantes sobre la baja cantidad de personas trabajando, el maestro principal les comenta que hay 3 maestros con problemas de salud, por lo que no han podido participar de la construcción.

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a) ¿Qué hubiera pasado con los días de trabajo si aumentamos la cantidad de maestros?

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[[0]]

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b) ¿Cuánto hubieran tardado en construir la ruca si lo hubieran realizado los ocho maestros, bajo las mismas cinco horas diarias de trabajo?

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[[1]] (considere dos decimales)

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