MATH 199 QUANTITATIVE METHODS I 199 DLP... · 2009-07-09 · Trabajo Final: Ejercicio Cooperativo (Debate/Concurso) 25% Durante el quinto taller, se llevará a cabo un ejercicio cooperativo

Sistema Universitario Ana G. Méndez

School for Professional Studies

Florida Campuses

Universidad del Este, Universidad Metropolitana, Un iversidad del Turabo

MATH 199

QUANTITATIVE METHODS I

METODOS CUANTITATIVOS I

© Sistema Universitario Ana G. Méndez, 2006, 2008

Derechos Reservados.

© Ana G. Méndez University System, 2006, 2008. All rights reserved.

MATH 199 Quantitative Methods I 2

Prep. 2004. Sylvia Y. Cosme. Rev. 2004, 2008. Armando J. Sánchez, EPM, MS/EMS

TABLA DE CONTENIDO/TABLE OF CONTENTS

Página/Page

Prontuario ........................................................................................................................ 3

Study Guide .................................................................................................................. 12

Workshop One .............................................................................................................. 20

Taller Dos ...................................................................................................................... 25

Workshop Three ............................................................................................................ 29

Taller Cuatro ................................................................................................................. 33

Workshop Five/Taller Cinco .......................................................................................... 37

Anejo A/Appendix A ...................................................................................................... 43

Anejo B/Appendix B ...................................................................................................... 45

Anejo C/Appendix C ...................................................................................................... 50

Anejo D/Appendix D ...................................................................................................... 52

Anejo E/Appendix E ...................................................................................................... 53

Anejo F/Appendix F ....................................................................................................... 55

Anejo G/Appendix G...................................................................................................... 56

Anejo H/Appendix H ...................................................................................................... 57

Anejo I/Appendix I ......................................................................................................... 58

Anejo J/Appendix J........................................................................................................ 60

Anejo K/Appendix K ...................................................................................................... 61

Anejo L/Appendix L ....................................................................................................... 62

Anejo M/Appendix M ..................................................................................................... 63

Anejo N/Appendix N ...................................................................................................... 65



Prontuario

Título del Curso Métodos Cuantitativos I

Codificación MATEMATICA 199

Duración Cinco Semanas

Prerrequisito MATEMATICA 121 o aprobación de prueba diagnóstica de

álgebra

Descripción

Curso dirigido a estudiantes de la Escuela de Administración de Empresas con un

enfoque hacia aplicaciones en los conceptos presentados y que mayormente se utilizan

en el comercio. Se estudian las funciones, desigualdades, sistemas de ecuaciones

lineales y sucesiones matemáticas. Se discute la representación gráfica y aplicaciones

de las funciones lineales, cuadráticas, exponenciales y logarítmicas comúnmente

utilizadas. Se presenta el uso de las funciones en la administración de empresas a

través de los conceptos financieros de interés simple, interés compuesto, valor

presente y valor futuro.

Matemática 199 capacitará al estudiante para utilizar efectivamente los principios y

conceptos del álgebra y el pre-cálculo, que frecuentemente se utilizan en procesos

cuantificables que contribuyen al proceso decisional de las empresas.

Objetivos Generales

1. Determinar la solución de ecuaciones utilizando las propiedades de las

igualdades.

2. Solucionar desigualdades lineales en una variable.

3. Hallar las soluciones de ecuaciones cuadráticas a través de diferentes métodos.

4. Identificar relaciones que sean funciones.

5. Definir y resolver diferentes tipos de funciones.

6. Aplicar el conocimiento de las funciones a situaciones cotidianas.

7. Trabajar con aplicaciones de funciones utilizadas en áreas de la administración

de empresas.

8. Resolver sistemas de ecuaciones lineales a través de los métodos mayormente

utilizados.

9. Solucionar ejercicios de aplicación con sistemas de ecuaciones lineales.



Texto y Recursos

Barnett, Raymond A., Ziegler, Michael R., (1995). Essentials of College

Mathematics. (3rd .ed.) New Jersey: McMillan.

Referencias y material suplementario:

Barnett, R. A., Ziegler, M. R., Byleen, K. E. (2007). College

Mathematics. (11th. ed.). Prentice Hall.

Barnett, Raymond A., Ziegler, Michael R., (1994). Applied Mathematics.

McGraw Hill.

Arya, Jagdish C., Lardner, Robin W., (2002). Matemáticas Aplicadas a la

administración y a la economía. (4ta. ed.) México: Prentice Hall.

Evaluación

1. Trabajos para realizar de cada taller 15%

Antes de cada taller el/la estudiante deberá completar ciertas tareas asignadas que

le ayudarán a prepararse para las actividades que se realizarán en el taller. Estas

constarán de la búsqueda en la Internet sobre información básica conceptual

provista en el modulo que le ayudará en el proceso de comprensión de los temas

bajo estudio. En adicion, el/la estudiante deberá completar una variedad de

ejercicios y preguntas guías que le ayudarán en el proceso de comprensión de

conceptos que se desarrollan en la práctica de las actividades que se efectuaron en

el taller. Los mismos, constarán de una selección de ejercicios asignados por el

facilitador. El/La estudiante deberá incluir el procedimiento que utilizo para llegar a

los resultados de los ejercicios asignados. Si el procedimiento no es incluido, no se

le dara credito completo por el ejercicio aunque el resultado sea correcto. Estas

tareas deberán entregarse a partir de la primera reunión. Este es un trabajo

individual; no se aceptaran copias del Internet o de las direcciones electrónicas

utilizadas. (Ver Anejo A: Política de Honestidad Académica) . Cada trabajo tiene

un valor de 100 puntos para un total agregado de 500 puntos. La evaluación de

estas tareas estará dividida en 70% por contenido y 30% por objetivos de lenguaje.

(Ver Anejo B: Rúbrica para evaluar tareas previas a los talleres) . El/la



estudiante que entregue la tarea posterior al taller asignado tendrá un descuento de

20 puntos por cada reunión que pase posterior a la fecha de entrega.

2. Cuatro (4) trabajos cooperativos 15%

De la primera a la cuarta reuniión, el/la estudiante tendrá la oportunidad de trabajar

en grupo con diferentes compañeros matriculados en el curso MATH 199. El

facilitador estará a cargo de incorporar los grupos en cada uno de los talleres. Cada

grupo trabajará una situación asignada que se resolverá y presentará en la clase.

La solución del trabajo se entregará al finalizar el tiempo provisto por el facilitador

con el nombre de todos los participantes por grupo. Habrá cuatro (4) trabajos

cooperativos a partir del Taller Uno, cada uno de ellos con un valor de 100 puntos

para un total agregado de 400 puntos. En la quinta reunión no se realizará esta

actividad ya que habra un trabajo final cooperativo (debate/concurso). (Ver Anejo

C: Rúbrica para evaluar trabajo en grupo) .

3. Cuatro (4) pruebas para realizar en los talleres 20%

A partir de la segunda reunión y hasta el último taller, al principio de cada taller se

dará una prueba corta sobre el material discutido en el taller anterior. Luego de

haber asistido al taller anterior, haber completado la tarea asignadas y haber

participado en el trabajo cooperativo, el/la estudiante estará capacitado para

contestar esta prueba. La misma constará de una selección de ejercicios prácticos

que fortalecerán las destrezas y conceptos presentados. Estas pruebas tendrán un

valor de 100 puntos cada una para un total agregado de 400 puntos.

4. Trabajo Final: Ejercicio Cooperativo (Debate/Concu rso) 25%

Durante el quinto taller, se llevará a cabo un ejercicio cooperativo (debate-

concurso). Éste, será un trabajo en grupo. Sin embargo, la evaluación considerará

ambas variables de desempeño: individual y grupal. Dependiendo de la cantidad de

estudiantes matriculados en el curso, el facilitador seleccionará aleatoreamente

hasta un máximo de seis (6) grupos cuya composición no excederá cinco (5)

estudiantes por grupo. Cada uno de los grupos tendrá la oportunidad de contestar

ejercicios prácticos de los temas que se han facilitado en los talleres. Esta actividad

tiene un valor de 100 puntos. El facilitador informará la composición de los grupos al



comienzo del quinto taller. (Ver Anejo D: Rúbrica para la evaluación del trabajo

cooperativo final).

5. Portafolio 10%

En el quinto taller, los estudiantes entregarán un portafolio. (Ver Anejo E:

Portafolio). Este trabajo tiene un valor de 100 puntos y se realizará individualmente

(Ver Anejo F: Rúbrica para la evaluación del Portaf olio). El facilitador informara

durante el taller uno cuáles serán los trabajos asignados que se incluirán en el

portafolio. Las actividades efectuadas en cada uno de los talleres, brindarán las

destrezas necesarias para que el estudiante pueda desarrollar el portafolio.

6. Asistencia y participación 15%

La asistencia a todos los talleres es necesaria e indispensable, dos o más

ausencias equivalen a fracaso del curso. El/la estudiante deberá demostrar

responsabilidad por su proceso de aprendizaje y deberá siempre traer los

materiales asignados. En caso de ausencia, el/la estudiante debe realizar todas las

gestiones necesarias para comunicarse con el facilitador, de manera que pueda

prepararse adecuadamente para la próxima reunión. Todas las actividades

realizadas en el taller ausente, sujetas a evaluación, serán consideradas y

ponderadas de acuerdo con los parámetros específicos. Es decir, es vigente la

pérdida de puntuación por cada trabajo del cual no fue partícipe el/la estudiante por

causa de la ausencia. (Ver Anejo G: Parámetros Específicos para Evaluar

Asistencia y Participación).

7. Escala de evaluación:

La evaluación final se calculará a base de promedios ponderados, pero

considerando la escala estándar de porcientos.

Nota A B C D F

Porciento 100-90 89-80 70-79 60-69 59-0

NOTA:



El estudiante debe obtener una calculadora científica , ya que es una de las

herramientas principales para poder realizar eficientemente las tareas y actividades

provistas para cada taller.

Descripción de las normas del curso

1. Este curso sigue el programa “Discipline-Based Dual Language Immersion

Model®” del Sistema Universitario Ana G. Méndez, el mismo esta diseñado para

promover el desarrollo de cada estudiante como un profesional bilingüe. Cada

taller será facilitado en inglés y español, utilizando el modelo 50/50. Esto

significa que cada taller deberá ser conducido enteramente en el lenguaje

especificado. Los lenguajes serán alternados en cada taller para asegurar que

el curso se ofrece 50% en inglés y 50% en español. Para mantener un balance,

el módulo debe especificar que se utilizarán ambos idiomas en el quinto taller,

dividiendo el tiempo y las actividades equitativamente entre ambos idiomas. Si

un estudiante tiene dificultad en hacer una pregunta en el idioma especificado,

bien puede escoger el idioma de preferencia para hacer la pregunta. Sin

embargo, el facilitador deberá contestar la misma en el idioma designado para

ese taller. Esto deberá ser una excepción a las reglas pues es importante que

los estudiantes utilicen el idioma designado. Esto no aplica a los cursos de

lenguaje que deben ser desarrollados en el idioma propio todo en inglés o todo

en español según aplique.

2. El curso es conducido en formato acelerado, eso requiere que los estudiantes se

preparen antes de cada taller de acuerdo al módulo. Cada taller requiere un

promedio de diez (10) horas de preparación y en ocasiones requiere más.

3. La asistencia a todos los talleres es obligatoria. El estudiante que se ausente al

taller deberá presentar una excusa razonable al facilitador. El facilitador

evaluará si la ausencia es justificada y decidirá como el estudiante repondrá el

trabajo perdido, de ser necesario. El facilitador decidirá uno de los siguientes:

permitirle al estudiante reponer el trabajo o asignarle trabajo adicional en

adición al trabajo a ser repuesto.



Toda tarea a ser completada antes del taller deberá ser entregada en la fecha

asignada. El facilitador ajustará la nota de las tareas repuestas.

4. Si un estudiante se ausenta a más de un taller el facilitador tendrá las siguientes

opciones:

a. Si es a dos talleres, el facilitador reducirá una nota por debajo basado en

la nota existente.

b. Si el estudiante se ausenta a tres talleres, el facilitador reducirá la nota a

dos por debajo de la nota existente.

5. La asistencia y participación en clase de actividades y presentaciones orales es

extremadamente importante pues no se pueden reponer. Si el estudiante provee

una excusa válida y verificable, el facilitador determinará una actividad

equivalente a evaluar que sustituya la misma. Esta actividad deberá incluir el

mismo contenido y componentes del lenguaje como la presentación oral o

actividad a ser repuesta.

6. En actividades de grupo el grupo será evaluado por su trabajo final. Sin

embargo, cada miembro de grupo deberá participar y cooperar para lograr un

trabajo de excelencia, pero recibirán una calificación individual.

7. Se espera que todo trabajo escrito sea de la autoría de cada estudiante y no

plagiado. Se debe entender que todo trabajo sometido esta citado

apropiadamente o parafraseado y citado dando atención al autor. Todo

estudiante debe ser el autor de su propio trabajo. Todo trabajo que sea plagiado,

copiado o presente trazos de otro será calificado con cero (vea la política de

honestidad académica).

8. Si el facilitador hace cambios al módulo o guía de estudio, deberá discutirlos y

entregar copia a los estudiantes por escrito al principio del primer taller.

9. El facilitador establecerá los medios para contactar a los estudiantes proveyendo

su correo electrónico, teléfonos, y el horario disponibles.

10. EL uso de celulares esta prohibido durante las sesiones de clase; de haber una

necesidad, deberá permanecer en vibración o en silencio.

11. La visita de niños y familiares no registrados en el curso no está permitida en el

salón de clases.



12. Todo estudiante esta sujeto a las políticas y normas de conducta y

comportamiento que rigen al SUAGM y el curso.

Nota: Si por alguna razón no puede acceder las dire cciones electrónicas

ofrecidas en el módulo, no se limite a ellas. Exis ten otros “web sites” que podrá

utilizar para la búsqueda de la información deseada . Entre ellas están:

• www.google.com

• www.altavista.com

• www.ask.com

• www.excite.com

• www.pregunta.com

• www.findarticles.com

• www.telemundo.yahoo.com

• www.bibliotecavirtualut.suagm.edu

• www.eric.ed.gov/

• www.flelibrary.org/

El facilitador puede realizar cambios a las direcci ones electrónicas y/o añadir

algunas de ser necesario.



Filosofía y Metodología Educativa

Este curso está basado en la teoría educativa del Constructivismo.

Constructivismo es una filosofía de aprendizaje fundamentada en la premisa, de que,

reflexionando a través de nuestras experiencias, podemos construir nuestro propio

conocimiento sobre el mundo en el que vivimos.

Cada uno de nosotros genera nuestras propias “reglas “y “métodos mentales”

que utilizamos para darle sentido a nuestras experiencias. Aprender, por lo tanto, es

simplemente el proceso de ajustar nuestros modelos mentales para poder acomodar

nuevas experiencias. Como facilitadores, nuestro enfoque es el mantener una

conexión entre los hechos y fomentar un nuevo entendimiento en los estudiantes.

También, intentamos adaptar nuestras estrategias de enseñanza a las respuestas de

nuestros estudiantes y motivar a los mismos a analizar, interpretar y predecir

información. Existen varios principios para el constructivismo, entre los cuales están:

1. El aprendizaje es una búsqueda de significados. Por lo tanto, el aprendizaje debe

comenzar con situaciones en las cuales los estudiantes estén buscando

activamente construir un significado.

2. Significado requiere comprender todas las partes. Y, las partes deben entenderse

en el contexto del todo. Por lo tanto, el proceso de aprendizaje se enfoca en los

conceptos primarios, no en hechos aislados.

3. Para enseñar bien, debemos entender los modelos mentales que los estudiantes

utilizan para percibir el mundo y las presunciones que ellos hacen para apoyar

dichos modelos.

4. El propósito del aprendizaje, es para un individuo, el construir su propio significado,

no sólo memorizar las contestaciones “correctas” y repetir el significado de otra

persona. Como la educación es intrínsicamente interdisciplinaria, la única forma

válida para asegurar el aprendizaje es hacer del avalúo parte esencial de dicho

proceso, asegurando que el mismo provea a los estudiantes con la información

sobre la calidad de su aprendizaje.

5. La evaluación debe servir como una herramienta de auto-análisis.

6. Proveer herramientas y ambientes que ayuden a los estudiantes a interpretar las

múltiples perspectivas que existen en el mundo.



7. El aprendizaje debe ser controlado internamente y analizado por el estudiante.



Study Guide

Course Title Quantitative Methods I

Code : MATH 199

Time Length Five Weeks

Prerequisite MATH 121 or diagnostic test in algebra.

Description

Course for students of Business Administration with emphasis in applications of

concepts primarily used in the commercial workplace. Studies functions, inequalities,

systems of linear equations, and mathematical series. Graphical representation and

applications of most frequently used functions in business such as: lineal, quadratic,

exponential and logarithmic functions. Applications to finance presented through the

concepts of simple interest, compound interest, future value, and present value.

MATH 199 will enable and qualify the student to effectively use principles and

concepts of algebra and pre-calculus mostly used in quantitative thinking contributing to

the decisional processes given in areas of business administration.

General Objectives

1. Determine the solution of an equation in one variable using the properties of

equations.

2. Solve linear inequalities in one variable.

3. Find solutions to quadratic equations through different methods.

4. Identify relations that are functions.

5. Define and solve different functions.

6. Solve applied exercises involving functions.

7. Solve systems of linear equations through commonly used methods.

8. Solve applied exercises with systems of linear equations.

Texts and Resources

Barnett, Raymond A., Ziegler, Michael R. (1995). Essentials of College Mathematics.

(3rd .ed.) New Jersey: MacMillan.

References and Supplementary Materials:

Barnett, R. A., Ziegler, M. R., Byleen, K. E. (2007). College

Mathematics. (11th. ed.). Prentice Hall.



Bittinger, Marvin L. (2000). Intermediate Algebra, Alternative Version.

(8th .ed.). Addison Wesley.

Arya, Jagdish C., Lardner, Robin W. (2002). Matemáticas Aplicadas a la

administración y a la economía. (4ta. ed.) México: Prentice Hall.

Evaluation

1. Assignment to do previous to each workshop 15%

Previous to each workshop students must finish certain assignments that will help

them to prepare for the activities in the workshop. The assignments will consist of

Internet sites research related of basic conceptual information provided in the

module that will help the learning of the workshop objectives. Additionally, the

student will complete the assigned exercises that will help him/her in the learning

process to understand and apply specific concepts that will be developed in the

activities at each workshop. These exercises are a selection of problems selected by

the facilitator. The student must include the procedures utilized to obtain the results

of the assigned problems. If the procedure is not included, there will be no full credit

to the assigned problem even if the result is correct. The assignments must be

submitted starting at the first meeting. This must be an individual work; copies from

the internet or from the URLs used will not be accepted. (See Appendix A:

Academic Honesty Policy) . Each assignment will be worth one hundred (100)

points for an accumulated score of five hundred (500) points. The evaluation of

these assignments will be 70% for content and 30% for language objectives. (See

Appendix B: Rubrics to evaluate assignments prior t o the workshops) . The

students that turn in the assignments after the corresponding workshop will have a

deduction of 20 points per each workshop that passes before the assignment is

turned in.

2. Collaborative Exercises (4) 15%

Collaborative exercises will be given from workshop one until workshop four. The

student will have the opportunity to work with other students registered in the course

MATH 199. The facilitator will select randomly the students to form each group.

Each group will work a situation that will be discussed and presented in the



workshop. The solution to this exercise will be handled out to the facilitator at the

end of the activity with all the names of the members of the team. Each of these

assignments will be worth one hundred (100) points for an accumulated score of four

hundred (400) points. This activity will not be done in workshop five since the

students will do a final collaborative exercise (debate/contest). (See Appendix C:

Rubric to evaluate group work).

3. Workshop tests (4) 20%

From Workshop 2 until Workshop 5, at the beginning of each workshop a short test

will be given about the material covered in the previous workshop. After attending

the previous workshop, completing the assignments and participating in the

collaborative exercise, the student will be able to answer this test. It will include a

selection of practical exercises to reinforce the analyzed skills and concepts already

studied. Each test will be worth one hundred (100) points for an accumulated score

of four hundred (400) points.

4. Final Exercise: Collaborative Exercise (Debate/Con test) 25%

During workshop 5, a collaborative exercise (Debate-Contest) will be held. It will

require team work. However, the assessment will consider both, individual and

group performance appraisal. Based upon the number of students registered in this

course, the facilitator will select at random a maximum of six (6) groups with no more

of five (5) students in each group. Each team will have the opportunity to answer

applications and practical exercises related to concepts that were presented in

previous workshops. The activity will have a value of 100 point. The facilitator will

inform the student his/her group assignment at the beginning of Workshop 5. (See

Appendix D: Rubric for evaluation of the final coll aborative work).

5. Portfolio 10%

I workshop five, the students will turn in a portfolio. (See Appendix E: Portfolio) .

This activity will be done individually and will be worth one hundred (100) points

(See Appendix F: Rubric for Portfolio evaluation). During workshop one the

facilitator will inform the students the assigned work to be included in the portfolio.

The activities conducted in each workshop will provide the students the skill and

knowledge necessary to do the portfolio.



6. Attendance and Participation 15%

Attendance to workshops is mandatory; with two or more absences the students will

fail the class. The student should show responsibility for the learning process and

must complete all assigned work. In case of absence, the student must

communicate with the facilitator, in order to be ready for the next workshop. All

classroom activities done in his/her absence will be subject to an evaluation based

upon specific parameters. In other words, absenteeism will produce loss of points.

(See Appendix G: Specific parameters to evaluate at tendance and

participation).

7. Scale:

Final grade to be calculated based on percentages.

Grade A B C D F

Percentage 100-90 89-80 70-79 60-69 59-0

NOTE:

A scientific calculator is recommended, since it is an essential tool to better and

efficiently perform assignments and activities to be presented and discussed in each

workshop.



Description of course policies

1. This course follows the Sistema Universitario Ana G. Méndez Discipline-Based Dual

Language Immersion Model® designed to promote each student’s development as a

Dual Language Professional. Workshops will be facilitated in English and Spanish,

strictly using the 50/50 model. This means that each workshop will be conducted

entirely in the language specified. The language used in the workshops will

alternate to insure that 50% of the course will be conducted in English and 50% in

Spanish. To maintain this balance, the course module may specify that both

languages will be used during the fifth workshop, dividing that workshop’s time and

activities between the two languages. If students have difficulty with asking a

question in the target language in which the activity is being conducted, students

may choose to use their preferred language for that particular question. However,

the facilitator must answer in the language assigned for that particular day. This

should only be an exception as it is important for students to use the assigned

language. The 50/50 model does not apply to language courses where the delivery

of instruction must be conducted in the language taught (Spanish or English only).

2. The course is conducted in an accelerated format and requires that students prepare

in advance for each workshop according to the course module. Each workshop

requires an average ten hours of preparation but could require more.

3. Attendance at all class sessions is mandatory. A student that is absent to a

workshop must present the facilitator a reasonable excuse. The facilitator will

evaluate if the absence is justified and decide how the student will make up the

missing work, if applicable. The facilitator will decide on the following: allow the

student to make up the work, or allow the student to make up the work and assign

extra work to compensate for the missing class time.

Assignments required prior to the workshop must be completed and turned in on the

assigned date. The facilitator may decide to adjust the grade given for late

assignments and make-up work.

4. If a student is absent to more than one workshop the facilitator will have the

following options:



a. If a student misses two workshops, the facilitator may lower one grade based

on the students existing grade.

b. If the student misses three workshops, the facilitator may lower two grades

based on the students existing grade.

5. Student attendance and participation in oral presentations and special class

activities are extremely important as it is not possible to assure that they can be

made up. If the student provides a valid and verifiable excuse, the facilitator may

determine a substitute evaluation activity if he/she understands that an equivalent

activity is possible. This activity must include the same content and language

components as the oral presentation or special activity that was missed.

6. In cooperative activities the group will be assessed for their final work. However,

each member will have to collaborate to assure the success of the group and the

assessment will be done collectively as well as individually.

7. It is expected that all written work will be solely that of the student and should not be

plagiarized. That is, the student must be the author of all work submitted. All quoted

or paraphrased material must be properly cited, with credit given to its author or

publisher. It should be noted that plagiarized writings are easily detectable and

students should not risk losing credit for material that is clearly not their own (see

Academic Honesty Policy).

8. If the Facilitator makes changes to the study guide, such changes should be

discussed with and given to students in writing at the beginning of the first workshop.

9. The facilitator will establish a means of contacting students by providing an email

address, phone number, hours to be contacted and days.

10. The use of cellular phones is prohibited during sessions; if there is a need to have

one, it must be on vibrate or silent mode during class session.

11. Children or family members that are not registered in the course are not allowed to

the classrooms.

12. All students are subject to the policies regarding behavior in the university

community established by the institution and in this course.



Note: If for any reason you cannot access the URL’s presented in the module, do

not stop your investigation. There are many search engines and other links you

can use to search for information. These are some examples:

• www.google.com

• www.altavista.com

• www.ask.com

• www.excite.com

• www.pregunta.com

• www.findarticles.com

• www.telemundo.yahoo.com

• www.bibliotecavirtualut.suagm.edu

• www.eric.ed.gov/

• www.flelibrary.org/

The facilitator may make changes and add additional web resources if deemed

necessary.



Teaching Philosophy and Methodology

This course is grounded in the learning theory of Constructivism. Constructivism

is a philosophy of learning founded on the premise that, by reflecting on our

experiences, we construct our own understanding of the world in which we live.

Each of us generates our own “rules” and “mental models,” which we use to make

sense of our experiences. Learning, therefore, is simply the process of adjusting our

mental models to accommodate new experiences. As teachers, our focus is on making

connections between facts and fostering new understanding in students. We will also

attempt to tailor our teaching strategies to student responses and encourage students to

analyze, interpret and predict information.

There are several guiding principles of constructivism:

1. Learning is a search for meaning. Therefore, learning must start with the issues

around which students are actively trying to construct meaning.

2. Meaning requires understanding wholes as well as parts. And parts must be

understood in the context of wholes. Therefore, the learning process focuses on

primary concepts, not isolated facts.

3. In order to teach well, we must understand the mental models that students use to

perceive the world and the assumptions they make to support those models.

4. The purpose of learning is for an individual to construct his or her own meaning, not

just memorize the "right" answers and regurgitate someone else's meaning. Since

education is inherently interdisciplinary, the only valuable way to measure learning is

to make the assessment part of the learning process, ensuring it provides students

with information on the quality of their learning.

5. Evaluation should serve as a self-analysis tool.

6. Provide tools and environments that help learners interpret the multiple perspectives

of the world.

7. Learning should be internally controlled and mediated by the learner.



Workshop One

Specific Objectives

At the end of this workshop, the student:

1. Solve linear equations in one variable using the addition and multiplication

properties.

2. Solve application problems by translating a verbal situation into a linear equation

in one variable.

3. Solve linear inequalities in one variable using the addition and multiplication

properties.

4. Express in interval notation the solution set for a linear inequality.

5. Solve application problems in the area of business administration by translating a

verbal situation into a linear inequality in one variable.

6. Solve quadratic equations using the following methods; square root, factorization

and quadratic formula.

7. Solve application problems in the area of finance and economy using quadratic

equations.

8. Create the graph for a linear equation in two variables.

9. Determine the slope of a line.

10. Determine the intercept of a linear equation in two variables.

11. Write the equation of a line if the slope and the Y-intercept are known.

12. Determine the equation of a line if the slope and one point in the line are known.

13. Determine the equation of a line if two points in the line are known.

14. Define a Function and identify if a line in a graph is for a function.

15. Utilize the function notation to solve problems.

16. Define and identify the domain and range of a function.

17. Draw the graphs for linear and quadratic functions.

18. Solve application problems in the area of business administration with linear and

quadratic functions.

Language Objectives

1. Demonstrate a command of standard English (vocabulary used, syntax and flow

of ideas)



2. Uses grammar appropriately and correctly.

3. Manages and uses verbs appropriately and correctly.

URLs

These sites offer examples and information about linear equations in one and two

variables, inequalities, quadratic equations, equation of a line, slope and functions.

http://www.analyzemath.com/

http://archives.math.utk.edu/topics/algebra.html

http://www.phschool.com/math/awsm/algebra/index.html

http://www.math.armstrong.edu/MathTutorial/index.html

http://math.rice.edu/~lanius/Algebra/hottub.html

http://www.purplemath.com/modules/ineqsolv.htm

http://www.math.com/school/subject2/lessons/S2U3L4GL.html

http://www.sosmath.com/algebra/quadraticeq/bdef/bdef.html

http://www.themathpage.com/alg/quadratic-equations.htm

http://www.mathsisfun.com/equation_of_line.html

http://www.math.com/school/subject2/lessons/S2U4L2GL.html

http://www.purplemath.com/modules/fcnnot.htm

Assignments before Workshop One

1. The students will search information and examples about the objectives for

workshop one on the recommended textbooks and/or on the Internet, or any other

bibliographic textbooks.

2. After reading about the objectives in workshop one, the students will define the

following terms and will provide examples. This must be an individual work; copies

from the internet or from the URLs used will not be accepted. (See Appendix A:


a. Linear equation

b. Linear Inequality

c. Quadratic equation

d. Graphs

e. Cartesian system and its relation with linear and quadratic equations

f. Slope of a line



g. Linear and Quadratic Functions

3. After searching the terms in part two above, the students will answer the following

questions as part of the assignment. Again, this must be an individual work; copies

from the internet or from the URLs used will not be accepted. (See Appendix A:


A. Consider the following equations:

a. 3 + 4 = 7

b. 5 – 1 = 2

c. 21 + 2 = 24

d. x – 5 = 12

e. 9 – x = x

f. 13 + 2 = 15

Which equatioons are true?

Which equations are false?

Which equations are neither true nor false?

B. Explain what is established by the addition and multiplication properties when

solving linear equations?

C. Explain why do we need to invert the inequality sign every time we divide or

multiply both sides of the inequality by a negative number?

D. Explain what does the slope describe in a line?

E. How can you determine if a graph is a function?

F. What is the relationship between functions and equations?

G. What are the general steps to construct a graph for an equation or a function?

4. This assignment shall be turn in to the facilitator and shall be properly identified with

the student name, date and workshop. This assignment is worth 100 points; the

evaluation of this assignment will be 70% for content and 30% for language

objectives. (See Appendix B: Rubrics to evaluate assignments p rior to the

workshops).

Activities



1. The facilitator will present and explain the objectives, the teaching methodology, and

the evaluation criteria for MATH 199. During this process, the facilitator will verify

that every student in the class has been registered in order to take this course.

Furthermore, the facilitator will review that every student has the module and the

textbook. Also, the facilitator will provide his/her contact information in case of

students need to contact him/her. The facilitator will establish the schedule and days

of contact.

2. The facilitator may conduct an ice breaking exercise to have the students introduce

them self. After all the students have been presented, a Student Representative will

be selected. Also, the facilitator will inform about other issues or announcements

such as new coming courses, holidays, and dates of the Student Representative

meeting.

3. The facilitator will discuss what should be included in a portfolio and what should be

included in it. The facilitator will provide specific information about the work to be

included in the portfolio and the rubrics for the portfolio evaluation. The facilitator will

answer any questions the students may have related to the portfolio.

4. Assignment to be completed before workshop one: The student will submit the

assignment to the facilitator. The facilitator will clarify any doubts and will answer any

questions the student’s may have regarding the assignment.

5. The facilitator will discuss the material related to the objectives in workshop one and

may provide and discuss some practice problems during the workshop. The

facilitator will discuss the terms and provide examples that will help the learning

process and the application of these terms.

6. The facilitator will provide additional problems for the students to practice the

procedures associated with the solution of application problems. These problems will

allow the students to clarify any questions and to improve their skills and knowledge

in the workshop material.

7. Collaborative Exercise: After completion of the previous activities the facilitator will

divide the class in groups of three to five students. Each group will work the

collaborative exercise (see Appendix N ). A speaker will be selected in each group.

The facilitator will let the students know how much time they have to solve the



problem. The solution will be turn in to the facilitator on a piece of paper with the

name of all the members of the group. (See Appendix C: Rubric to evaluate

group work)

8. The facilitator will select one group and asked them to solve and present results of

the collaborative exercise. Each group will have the opportunity to discuss their

solution if different from the solution presented by the first group.

9. The facilitator will discuss the assignment to be completed before workshop two.

Also, the facilitator will provide a list of problems to be included as part of the

assignment before workshop two.

Assessment

Rubric to evaluate group work.

Short Test: There will not be a short test in Workshop One. The test for the material

discussed in Workshop 1 will be administered at the beginning of Workshop Two.



Taller Dos

Objetivos Específicos

Al finalizar el Taller, el estudiante:

1. Definir e indenticar una función exponencial.

2. Hacer la gráfica de ecuaciones y funciones exponenciales.

3. Aplicar las propiedades de las funciones exponenciales.

4. Definir y aplicar funciones exponenciales con base ℮.

5. Resolver ecuaciones exponenciales.

6. Convertir de notación exponencial a notacion logarítmica y viceversa.

7. Definir e identificar funciones logarítmicas.

8. Identificar y aplicar las propiedades de las funciones logarítmicas.

9. Resolver ecuaciones logarítmicas.

10. Evaluar exponentes y logaritmos utilizando la calculadora.

Objetivos de Lenguaje

1. Demostrar dominio del idioma Español (vocabulario, sintaxis, presentación de

ideas).

2. Utilización apropiada y correcta de gramática.

3. Aplicación y utilización correcta y apropiada de los verbos.

Direcciones Electrónicas

En estos sitios los estudiantes podrán encontrar información sobre funciones

exponenciales y logarítmicas.

http://www.ping.be/~ping1339/exp.htm

http://www.geocities.com/CapeCanaveral/Launchpad/2426/

http://www.analyzemath.com/

http://archives.math.utk.edu/topics/algebra.html

http://www.phschool.com/math/awsm/algebra/index.html

http://w3.cnice.mec.es/Descartes/Bach_CNST_1/Funcion_exponencial/Func-exp.htm

http://huitoto.udea.edu.co/Matematicas/2.1.html

http://netlizama.usach.cl/avcapituloVI.pdf

http://personal5.iddeo.es/ztt/Tem/T3_Funcion_Logaritmica.htm

http://w3.cnice.mec.es/Descartes/Bach_CNST_1/Funcion_logaritmica/Func-log.htm



Tareas a realizar antes del Taller Dos

1. El/la estudiante leerá y buscará información relacionadas a los objetivos del taller

dos en los libros de texto recomendados o en direcciones electrónicas o cualquier

otra referencia bibliográfica.

2. Una vez realice la lectura, los estudiantes contestarán las siguientes preguntas.

Este es un trabajo individual; no se aceptarán copias del Internet o de las

direcciones electrónicas utilizadas. (Ver Anejo A: Honestidad Académica).

• Definir exponentes, dar ejemplos

• Definir funcion exponencial y listar las propiedades de exponentes

• Definir que es una función exponencial con base e

• Definir función logarítmicas y listar las propiedades de logaritmos

• Dar tres (3) ejemplos de funciones exponenciales utilizadas en

administración de empresas.

3. El facilitador asignará problemas adicionales del libro de texto como parte de esta

tarea para entregar. Estos problemas ayudarán a los estudiantes a entender los

objetivos del taller. Este es un trabajo individual; no se aceptarán copias del Internet

o de las direcciones electrónicas utilizadas. (Ver Anejo A: Honestidad

Académica).

4. Esta tarea deberá entregarla al facilitador debidamente identificada con su nombre,

fecha y taller. La misma tiene un valor de 100 puntos. La evaluación de esta tarea

estará dividida en 70% por contenido y 30% por objetivos de lenguaje. (Ver anejo

B: Matriz valorativa para tareas previas a los tall eres).

Actividades

1. El facilitador devolverá los trabajos completados por los estudiantes durante el taller

uno (Tarea y Trabajo Cooperativo). Estos trabajos estarán evaluados de acuerdo

con las matrices incluidas en el módulo. El facilitador discutirá la puntuación

obtenida con los estudiantes según sea necesario. El facilitador contestará cualquier

pregunta que los estudiantes tengan en relación a los trabajos del taller uno. Estos

trabajos serán incluidos en el Portafolio el cual sera entregado en el taller cinco.



2. Trabajo para realizar previo al Taller Dos : El/la estudiante entregará la tarea

asignada. El facilitador contestará preguntas relacionadas a la tarea y aclarará

todas las dudas que los estudiantes tengan.

3. Prueba corta: Al comienzo del taller los estudiantes tomarán una prueba corta

sobre el material discutido en el taller anterior. Luego de haber asistido al taller

anterior, participar en las actividades del taller y haber hecho la tarea a entregar, los

estudiantes estarán capacitados para contestar esta prueba.

4. El facilitador discutirá en la clase el material relacionado a los objetivos del taller y

podrá asignar o hacer algunos problemas de práctica durante el taller. Estos

problemas ayudarán a los estudiantes a aclarar dudas y contestar cualquier

pregunta que tengan lo cual los ayudará a mejorar su conocimiento y destrezas

referentes al material de la clase.

5. El facilitador dará problemas adicionales para que los estudiantes los resuelvan en

clase para practicar los procedimientos associados con la solución de los mismos.

Estos problemas ayudarán a los estudiantes a clarificar cualquier duda o pregunta

que tengan, tambien los ayudara a mejorar el conocimiento sobre el material

discutido en el taller.

6. Trabajo cooperativo : Luego de termian las actividades anteriores, el facilitador

dividirá la clase en grupos de tres a cinco estudiantes dependiendo del tamano de la

clase. Cada grupo trabajará el siguiente ejercicio. El facilitador les dirá a los

estudiantes cuanto tiempo tienen para resolver el problema. La solución será

entregada en una hoja de papel con los nombres de los miembros del grupo. (Ver

Anejo N para ejercicio y Anejo C: Matriz valorativa para trabajo en grupo).

(Nota : El facilitador puede asignar otro trabajo cooperativo diferente al que está en el

módulo. Si el trabajo cooperativo es cambiado, el facilitador debe notificar al los

estudiantes del cambio en el taller anterior)

7. El facilitador discutirá la tarea que los estudiantes deben completer antes del

próximo taller. En adición, el facilitador proveerá una lista de los problemas a

resolver como parte de la tarea a entregar en el taller tres.



Avalúo

Prueba corta : Los estudiantes tomarán una prueba corta al inicio del taller sobre el

material del taller anterior.

Matriz valorativa para trabajo en grupo .



Workshop Three

Specific Objectives


1. Define and understand the following terms:

a. Simple interest

b. Compound interest

c. Principal

d. Annual Interest Rate

e. Payment period

f. Annuity

g. Ordinary Annuity

h. Amortization

i. Future Value of an Annuity

j. Present Value of an Annuity

2. Recognize and use the formulas and equations for simple interest, compound

interest, future value and present value of an annuity.

3. Calculate the effective interest rate using a scientific or accounting calculator.

4. Obtain the future value or present value of an annuity using a scientific or

accounting calculator

5. Create an amortization table to amortize a loan and determine the amount of

interests paid and the final loan amount paid.

Language Objectives

1. Demonstrate a command of standard English (vocabulary used, syntax and flow of

ideas)



Electronic Links (URLs)

These sites offer examples and information about Financial Mathematics.

http://www.cs.utah.edu/~zachary/isp/applets/Interest/Interest.html

http://www.getobjects.com/Components/Finance/TVM/iy.html

http://banking.about.com/od/loans/a/simpleinterest.htm



http://math.about.com/library/weekly/aa042002a.htm

http://math2.org/math/general/interest.htm

http://www.investopedia.com/terms/a/annuity.asp

http://www.investorwords.com/200/amortization.html

http://banking.about.com/od/loans/g/amortization.htm

http://www.getobjects.com/Components/Finance/TVM/fva.html

http://www.getobjects.com/Components/Finance/TVM/pva.html

Assignments before Workshop Three

1. The students will search information and examples about the objectives for

workshop three on the recommended textbooks and/or on the Internet, or any other

bibliographic textbooks.

2. After reading about the objectives in workshop three, the students will define and

provide examples about the following terms. Defining these terms will help the

students understand the objectives of the workshop. This must be an individual

work; copies from the internet or from the URLs used will not be accepted (see

Appendix A: Academic Honesty).

a. Simple interest

b. Compound interest

c. Loan Principal

d. Annual Interest Rate

e. Annuity

f. Ordinary Annuity

g. Amortization

h. Future Value of an Annuity

i. Present Value of an Annuity

3. The facilitator will assign additional problems from the textbook as part of this

assignment. These problems will help the students understand the terms and

objectives of this workshop. This must be an individual work; copies from the internet

or from the URLs used will not be accepted (See Appendix A: Academic

Honesty).






objectives. (See Appendix B: Rubrics to evaluate assignments pr ior to the

workshops).

5. In addition, the students will search in the newspaper and/or magazine for an article

about compound interests or any other term/concept to be discussed in workshop

three. The students must be prepared to discuss their article in class.

Activities

1. The facilitator will return the work completed by the students during workshop two

(Assignment, Short Test and Collaborative Exercise). The work completed would be

assessed based on the rubrics included in the module. The facilitator will discuss the

points obtained with the students as necessary. The facilitator will answer any

questions the students may have related to the workshop one completed work. The

assessed work from workshop one will be included in the Portfolio that will be turn in

during workshop five.

2. Assignment to be completed before workshop three : The students will submit

the assignment to the facilitator. The facilitator will clarify any doubts and will answer

any questions the student’s may have regarding the assignment.

3. Short Test: At the beginning of the workshop the students will answer the short test

about the material discussed in the previous workshop. After attending the previous

workshop, participated in the workshop activities and completed the assignment

prior to the workshop, the students will be able to answer the short test.

4. The facilitator will asked some of the students to discuss the article that they

research in the newspaper or magazine. The students must highlight the areas of

the article that provide information about the objectives to be discussed in this

workshop.

5. The facilitator will discuss the material related to the objectives in workshop three

and may provide and discuss some practice problems during the workshop. These

problems will allow the students to clarify any questions and to improve their skills

and knowledge in the workshop material.



6. Collaborative Exercise: After completion of the previous activities the facilitator will

divide the class in groups of three to five students. Each group will work the following

collaborative exercise. A speaker will be selected in each group. The facilitator will

let the students know how much time they have to solve the problem. The solution

will be turn in to the facilitator on a piece of paper with the name of all the members

of the group. (See Appendix N for exercise and Appendix C for Rub ric to

evaluate group work). (Note : The facilitator can assign another collaborative

exercise different from the one in the module. If the collaborative exercise is

changed, the facilitator should notify the students about the change in the previous

workshop).

7. The facilitator will select one group and asked them to solve and present results of

the collaborative exercise. Each group will have the opportunity to discuss their

solution if different from the solution presented by the first group.

8. The facilitator will discuss the assignment to be completed before workshop four.

Also, the facilitator will provide a list of problems to be included as part of the

assignment before workshop four.

Assessment

Short Test: The students will answer a short test at the beginning of the workshop

about the material discussed in the previous workshop.

Group activity rubric



Taller Cuatro

Objetivos Específicos

Al finalizar el Taller, el estudiante:

1. Resolver un sistema de ecuaciones lineales graficamente.

2. Determinar si un system de ecuaciones es consistente, inconsistente, dependiente o

independiente.

3. Resolver un sistema de ecuaciones lineales utilizando el metodo de substitucion.

4. Resolver un sistema de ecuaciones lineales utilizando el metodo de eliminacion.

5. Resolver problemas aplicados a finanzas y economia utilizando un sistema de dos

ecuaciones lineales.

6. Definir una Matriz y determinar la dimension de las matrices..

7. Sumar y restar matrices.

8. Obtener el producto de una matriz con un valor constante.

9. Multiplicar matrices.

10. Resolver problemas utilizando matrices.

Objetivos de Lenguaje

1. Demostrar dominio del idioma Español (vocabulario, sintaxis, presentación de

ideas).

2. Utilización apropiada y correcta de gramática.

3. Aplicación y utilización correcta y apropiada de los verbos.

Direcciones Electrónicas

En estos sitios los estudiantes podrán encontrar información sobre sistemas de

ecuaciones lineales y matrices.

http://www.sosmath.com/soe/SE2001/SE2001.html

http://www.sparknotes.com/math/algebra1/systemsofequations/

http://www.mathmax.com/introalg/chapter/bk3c8.html

http://www.mathnotes.com/Intro/aw_introchap7.html

http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/tutorialsf1/unit3_1.html

http://www.colorado.edu/engineering/CAS/courses.d/IFEM.d/IFEM.AppB.d/IFEM.AppB.

pdf

http://www.maths.surrey.ac.uk/explore/emmaspages/option1.html



http://www.intmath.com/Matrices-determinants/4_Multiplying-matrices.php

http://www.sosmath.com/matrix/matrix1/matrix1.html

http://www.sectormatematica.cl/contenidos/matriz.htm

Tareas a realizar antes del Taller Cuatro

1. El/la estudiante leerá y buscará información relacionada a los objetivos del taller

cuatro en los libros de texto recomendados o en direcciones electrónicas o cualquier

otra referencia bibliográfica.

2. Una vez realice la lectura, los estudiantes definirán y buscarán ejemplos de los

siguientes términos. es un trabajo individual; no se aceptarán copias de la Internet o

de las direcciones electrónicas utilizadas. (Ver Anejo A: Honestidad Académica).

• Sistema de ecuaciones lineales

• Sistema de ecuaciones lineales Consistentes

• Sistema de ecuaciones lineales Independientes

• Sistema de ecuaciones lineales Inconsistentes

• Sistema de ecuaciones lineales Dependientes

• Mencione tres métodos utilizados para resolver un sistema de ecuaciones

lineales

• Matrices

• Regla para sumar o restar matrices

• Regla para multiplicar dos matrices

3. El facilitador asignará problemas adicionales del libro de texto como parte de esta

tarea para entregar. Estos problemas ayudarán a los estudiantes a entender los

objetivos del taller. Este es un trabajo individual; no se aceptarán copias del Internet

o de las direcciones electrónicas utilizadas. (Ver Anejo A: Honestidad

Académica).

4. Esta tarea deberá entregarla al facilitador debidamente identificada con su nombre,

fecha y taller. La misma tiene un valor de 100 puntos. La evaluación de esta tarea

estará dividida en 70% por contenido y 30% por objetivos de lenguaje. (Ver anejo

B: Matriz valorativa para tareas previas a los tall eres).



Actividades

1. El facilitador devolverá los trabajos completados por los estudiantes durante el taller

tres (Tarea, Prueba Corta y Trabajo Cooperativo). Estos trabajos estarán evaluados

de acuerdo con las matrices incluidas en el módulo. El facilitador discutirá la

puntuación obtenida con los estudiantes según sea necesario. El facilitador

contestará cualquier pregunta que los estudiantes tengan en relación a los trabajos

del taller uno. Estos trabajos serán incluidos en el Portafolio el cual sera entregado

en el taller cinco.

2. Trabajo para realizar previo al Taller Cuatro : El/la estudiante entregará la tarea

asignada. El facilitador contestará preguntas relacionadas a la tarea y aclarará

todas las dudas que los estudiantes tengan.

3. Prueba corta: Al comienzo del taller los estudiantes tomarán una prueba corta

sobre el material discutido en el taller anterior. Luego de haber asistido al taller

anterior, participar en las actividades del taller y haber hecho la tarea a entregar, los

estudiantes estarán capacitados para contestar esta prueba.

4. El facilitador discutirá en la clase el material relacionado a los objetivos del taller y

podrá asignar o hacer algunos problemas de práctica durante el taller. Estos

problemas ayudarán a los estudiantes a aclarar dudas y contestar cualquier

pregunta que tengan lo cual los ayudará a mejorar su conocimiento y destrezas

referentes al material de la clase.

5. El facilitador dará problemas adicionales para que los estudiantes los resuelvan en

clase para practicar los procedimientos associados con la solución de los mismos.

Estos problemas ayudarán a los estudiantes a clarificar cualquier duda o pregunta

que tengan, tambien los ayudara a mejorar el conocimiento sobre el material

discutido en el taller.

6. Trabajo cooperativo : Luego de terminar las actividades anteriores, el facilitador

dividirá la clase en grupos de tres a cinco estudiantes dependiendo del tamaño de la

clase. Cada grupo trabajará el siguiente ejercicio. El facilitador les dirá a los

estudiantes cuanto tiempo tienen para resolver el problema. La solución será

entregada en una hoja de papel con los nombres de los miembros del grupo. (Ver



anejos N para ejercicio y C para Matriz para evalua r trabajo en grupo). (Nota :

El facilitador puede asignar otro trabajo cooperativo diferente al que esta en el

módulo. Si el trabajo cooperativo es cambiado, el facilitador debe notificar al los

estudiantes del cambio en el taller anterior)

7. El facilitador discutirá la tarea que los estudiantes deben completer antes del

próximo taller. En adición, el facilitador proveerá una lista de los problemas a

resolver como parte de la tarea a entregar en el taller cinco.

Evaluación

Prueba corta: Los estudiantes tomarán una prueba corta al inicio del taller sobre el

material del taller anterior.

Matriz valorativa para trabajo en grupo.



Workshop Five/Taller Cinco

NOTA: Este taller es bilingüe. Tanto,

el Facilitador como los estudiantes,

deberán utilizar el idioma asignado

para cada tarea y actividad.

NOTE: This is a bilingual workshop.

Both the facilitator and student

should use the language assigned

for each homework and activity.

Specific Objectives


1. Apply the knowledge gained during the course MATH 199 and actively participate in

the final collaborative exercise (debate-contest).

2. As part of the final collaborative exercise (debate-contest) , solve application

problems that will cover all the objectives learned during the class.

Language Objectives

1. Demonstrate a command of standard English (vocabulary used, syntax and flow of

ideas)



Electronic Links (URLs)

For this workshop, the students should use all the URLs included in the previous

workshops to review the objectives learned in class.

http://www.cs.utah.edu/~zachary/isp/applets/Interest/Interest.html

http://www.getobjects.com/Components/Finance/TVM/iy.html

http://banking.about.com/od/loans/a/simpleinterest.htm

http://math.about.com/library/weekly/aa042002a.htm

http://math2.org/math/general/interest.htm

http://www.investopedia.com/terms/a/annuity.asp

http://www.investorwords.com/200/amortization.html

http://banking.about.com/od/loans/g/amortization.htm

http://www.getobjects.com/Components/Finance/TVM/fva.html

http://www.getobjects.com/Components/Finance/TVM/pva.html



http://www.sosmath.com/soe/SE2001/SE2001.html

http://www.sparknotes.com/math/algebra1/systemsofequations/

http://www.mathmax.com/introalg/chapter/bk3c8.html

http://www.mathnotes.com/Intro/aw_introchap7.html

http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/tutorialsf1/unit3_1.html

http://www.colorado.edu/engineering/CAS/courses.d/IFEM.d/IFEM.AppB.d/IFEM.AppB.

pdf

http://www.maths.surrey.ac.uk/explore/emmaspages/option1.html

http://www.intmath.com/Matrices-determinants/4_Multiplying-matrices.php

http://www.sosmath.com/matrix/matrix1/matrix1.html

http://www.sectormatematica.cl/contenidos/matriz.htm

Assignments before Workshop Five

1. As a final review, the students will search information and examples about the

objectives learned in class during all the previous workshops on the recommended

textbooks and/or on the Internet, or any other bibliographic textbooks.

2. The facilitator will assign additional problems from the textbook as part of this

assignment. These problems will help the students understand the terms and

objectives of the workshop. This must be an individual work; copies from the internet

or from the URLs used will not be accepted. (See Appendix A: Academic

Honesty).




objectives. (See Appendix B: Rubrics to evaluate assignments pr ior to the

workshops).

4. The students will review and study ALL the material presented in the previous

workshops. It is very important to review the collaborative exercises solved already

in the other workshops. In addition the students should review the practice problems

and the exercises included in the assignments. This will help them get prepared to

participate and solve the problems to be included in the final collaborative exercise

(debate-contest).



Activities

1. The facilitator will start the class with a short review.

2. The facilitator will return the work completed by the students during workshop four

(Assignment, Short Test and Collaborative Exercise). The work completed would be

assessed based on the rubrics included in the module. The facilitator will discuss the

points obtained with the students as necessary. The facilitator will answer any

questions the students may have related to the workshop one completed work. The

assessed work from workshop one will be included in the Portfolio that will be turn in

during workshop five

3. Assignment to be completed before workshop five: The students will include the

assignment in the Portfolio. The facilitator will clarify any doubts and will answer any

questions the student’s may have regarding the assignment.

4. Short Test: At the beginning of the workshop the students will answer the short test

about the material discussed in the previous workshop. After attending the previous

workshop, participated in the workshop activities and completed the assignment

prior to the workshop, the students will be able to answer the short test.

5. Portfolio: The students will finalize the Portfolio in accordance with the guidance

previously provided by the facilitator. They will ensure that all the work is included

and everything is in order. The students then will turn in the Portfolio to the facilitator.

6. Final Collaborative Exercise (Debate-Contest): During this workshop the students

will participate in a final collaborative exercise (Debate-Contest). This will be a team

work, however, the assessment will consider both, individual and group performance

appraisal. Based upon the number of students registered in this course, the

facilitator will select at random a maximum of six (6) groups with no more of five (5)

students in each group. Each group will have the opportunity to answer applications

and practical exercises related to the concepts that were presented in ALL the

previous workshops. (See Appendix D: Rubric for evaluation of the final

collaborative work). The rules for this final collaborative exercise are as follows:



a. The collaborative exercise will consist of five (5) application problems that will

cover the objectives learned in the course workshops. Half of these exercises will

be in English and the other half will be in Spanish.

b. The application problems will cover the objectives, concepts and procedures

learned in class. Each problem will have a time limit of no more than 30 minutes

to be solved by each group.

c. After the facilitator divide the class in groups, the member of each group will seat

together in order to discuss and solve the problems.

d. The facilitator will provide the final instructions and rules to complete the

collaborative exercise. Any questions regarding the exercise or the rules will be

answer by the facilitator.

e. The applications problems will be solve one at a time; each group will work the

same exercise at the same time in the time allowed by the facilitator. The

facilitator has the option to let the students use the book and class notes as

reference.

f. The facilitator will give a copy of the first problem to each group; at that time the

facilitator will tell the students the amount of time the have to solve the problem

and then they will start. The solution of the problems will be in the language the

problem was written.

g. The groups will work quietly and without interruptions. If a student do not follow

the rules and disrupt the other groups, his/her group will have a penalty

(deduction) of five (5) points from that problem.

h. The first group to finish the problem before the time allowed, will obtained a

bonus of five (5) points and will present their solution in front of the class.

i. If none of the groups finish the problem before the time allowed, the facilitator will

provide an additional five (5) minutes to finish the problem and there won’t be a

bonus of five (5) points.

j. When the time allowed is finished, the facilitator will collect the solution from all

the groups. Then the facilitator will select a person from one of the groups to

present their solution in front of the class.



k. After one of the groups present their solution in front of the class, the other

groups will have the opportunity to agree or disagree with the solution presented.

In case of a disagreement a group can challenge the first group, the second

group will present their solution in front of the class. If the second group is

correct, they will receive a bonus of five (5) points. In case that none of the

groups obtained the correct answer, the facilitator will provide and discuss the

correct solution.

l. If the solution from a group is incorrect but the procedure used is correct, the

group will get partial credit for the problem.

m. After completing the discussion on the first problem, the facilitator will provide a

copy of the next problem to each group. The process will be repeated until all the

problems in the collaborative exercise are completed and their solution has been

presented.

n. All the students should have an active participation in the discussion and solution

of the problems to earn individual points. The individual points will be between 5

and 10 points per problem depending on the type of exercise.

o. The facilitator can grant additional points to a group depending on the number of

correct solutions and the participation of the group members.

7. After completion of the final collaborative exercise, the students will write two or

three paragraphs were they will provide feedback to the facilitator about the course

and his/her teaching techniques. The students should include if their expectations

about the course were met.

8. The students will complete the class evaluation. The student representative will

return the course evaluation to the front office.

9. Closing activity – to be determined by the facilitator.

Assessment

Short Test: The students will answer a short test at the beginning of the workshop

about the material discussed in the previous workshop.

Group work rubric



Anejos/Appendixes



Anejo A/Appendix A

Academic Honesty - Plagiarism

Dear Student:

The internet, although a very resourceful tool in today’s world has become a tool where

students and other professionals can find what others have done in seconds; thus

promoting or developing the temptation to use what others have done without giving

them the appropriate credit for their work. In an article published by Indiana University, it

was stated that using the ideas of others without giving proper credit to the source of

that information is considered plagiarism .

Whenever we use information from other sources it is extremely important that you:

1. Give credit to the person’s ideas, theories or opinions.

2. Give credit to a person if we use a chart, graph, drawing or any other type of

knowledge needed to support a paper.

3. Give credit to a person or source if we use a quotation or paraphrase ideas that

belong to them.

For more information go to http://www.indiana.edu/~wts/pamphlets/plagiarism.shtml

or simply search for the topic of plagiarism under: www.plagiarism.org.

Important Note: Plagiarism is a serious issue and i t is considered an offense that has

serious consequences; which in turn may affect your academic success and

professional career. There are workshops offered to help you when writing papers to

avoid falling into this serious matter. You can che ck for time and dates of these

workshops in the Learning Resources Center. Our fa cilitators can also provide you with

help when writing papers and/or assignments.

Sincerely, Ricardo Ortolaza, Ed.D. Chief Learning Officer



Honestidad Académica - Plagio

Apreciado (a) Estudiante:

La red cibernética (Internet) se considera una herramienta efectiva en el mundo actual. La

misma se ha convertido en un recurso donde los estudiantes y los profesionales pueden

encontrar, rápidamente información e investigaciones que otros han realizado. Esto puede

propiciar la tentación de utilizar lo que otros han hecho o investigado sin darles el debido

crédito por su trabajo. En un artículo publicado por la Universidad de Indiana, se indica que

utilizar ideas de otras personas sin darle crédito al recurso que lo produjo se considera plagio.

Siempre que se utilice información de otras fuentes o recursos, es de suma importancia:

1. Dar crédito a las ideas, teorías y opiniones de otras personas o recursos.

2. Dar crédito a la persona o recurso de donde obtuvo tablas, gráficas, dibujos u otro tipo

de información o conocimiento para apoyar las ideas que expone en su trabajo.

3. Dar crédito si utiliza citas o parafrasea ideas que pertenecen a otras personas o

recursos.

Para más información visite la página:

http://www.indiana.edu/~wts/pamphlets/plagiarism.shtml

o simplemente busque información sobre plagio en: www.plagiarism.org.

Nota Importante: El plagio es un asunto serio y se considera una ofensa que tiene

consecuencias serias; que a su vez puede afectar su éxito académico y carrera

profesional. Existen talleres que le pueden ayudar a la creación de documentos y evitar

cometer plagio. Puede obtener información de las fe chas y horas de dichos talleres en el

Centro de Recursos Educativos. Nuestros facilitador es también le pueden proveer

información sobre cómo hacer sus trabajos evitando el plagio.

Sinceramente, Ricardo Ortolaza, Ed.D. Chief Learning Officer



Anejo B/Appendix B

Matriz Valorativa para Tareas Previas al Taller

Assignment before Workshop One

Student Name: ______________________ Date: _______________

Criteria Value Points Student Score

Content Part 2 – The definitions are complete, clear and well stated. The proper information and examples are provided for each term. The sentences are cohesive and have a proper flow.

20

Part 3 (a) – The answer is correct for each of the equations. 5

Part 3 (b) – The answer is clear and well stated. The addition and multiplication properties are clearly explained. The sentences are cohesive and have a proper flow.

10

Part 3 (c) – The answer is clear and well stated. The explanation is complete and provides enough information. The sentences are cohesive and have a proper flow.

10

Part 3 (d) – The answer is clear and well stated. It provides the necessary details to explain what a slope is. The sentences are cohesive and have a proper flow.

5

Part 3 (e) – The answer is clear and well stated. It provides the necessary details to explain how to determine if a graph is a function. The sentences are cohesive and have a proper flow.

5

Part 3 (f) – The answer is clear and well stated. The explanation provides enough information to establish the relationship between functions and equations. The sentences are cohesive and have a proper flow.

5

Part 3 (g) – The answer is clear and well stated. The general steps are provided and clearly explained. The sentences are cohesive and have a proper flow.

10

Language Demonstrate a command of standard English (vocabulary used, syntax and flow of ideas)

10

Uses grammar appropriately and correctly 10 Manages and uses verbs appropriately and correctly 10

Total Points 100 (70% content and

30% language )

Student’s total Score:

_______

Facilitador’s Signature: _________________________

Student’s Signature: __________________________



Tarea Previa al Taller Dos

Nombre Estudiante: ______________________ Fecha: _______________

Criteria Puntuación Puntuación Estudiante Cont enido

Parte 2 – Las definiciones están completas, son claras y bien establecidas. Se provee información correcta y se dan ejemplos según necesario. La respuesta se provee en oraciones claras y concisas.

20

Parte 3 – Se contestan todos los problemas, las contestaciones son correctas y se provee el procedimiento por el cual se obtuvo la respuesta (según sea necesario). El procedimiento y las formulas utilizadas son correctas. Los problemas se resuelven y se entrega en forma organizada y limpia.

50

Languaje Demostrar dominio del idioma Español (vocabulario, syntax, presentación de ideas)

10

Utilización apropiada y correcta de gramática 10 Aplicación y utilización correcta y apropiada de los verbos

10

Total de Puntos 100 (70% contenido y

30% languaje)

Puntuación total Estudiante: _______

Firma de Facilitador: _________________________

Firma de Estudiante: __________________________



Assignment before Workshop Three

Student Name: ______________________ Date: _______________

Criteria Value Points Student Score Content

Part 2 – The definitions are complete, clear and well stated. The proper information is provided and examples are provided for each term. The sentences are cohesive and have a proper flow.

20

Part 3 – All the problems are solved, the answers are correct and the procedure used to find the solution is provided (as necessary). The procedure and formulas used are correct. The assignment is clean and the problems are solved in an organized way.

45

Part 5 – The student searched and brought to class an article related to the class objectives. The student is ready to discuss the article in class.

5

Language Demonstrate a command of standard English (vocabulary used, syntax and flow of ideas)

10

Uses grammar appropriately and correctly 10 Manages and uses verbs appropriately and correctly

10

Total Points 100 (70% content and 30% language)

Student’s total Score: _______

Facilitator’s Signature: _________________________

Student’s Signature: __________________________



Tarea Previa al Taller Cuatro


Criteria Puntuación Puntuación Estudiante

Cont enido Parte 2 – Las definiciones están completas, son claras y bien establecidas. Se provee información correcta y se dan ejemplos según necesario. La respuesta se provee en oraciones claras y concisas.

20

Parte 3 – Se contestan todos los problemas, las contestaciones son correctas y se provee el procedimiento por el cual se obtuvo la respuesta (según sea necesario). El procedimiento y las formulas utilizadas son correctas. Los problemas se resuelven y se entrega en forma organizada y limpia.

50


10

Utilización apropiada y correcta de gramática 10 Aplicación y utilización correcta y apropiada de los verbos

10

Total de Puntos 100 (70% contenido y 30%

languaje)

Puntuación total

Estudiante: _______

Firma de Facilitador: _________________________

Firma de Estudiante: __________________________



Tarea Previa al Taller Cinco


Criteria Puntuación Puntuación Estudiante

Contenido Part 2 – All the problems are solved, the answers are correct and the procedure used to find the solution is provided (as necessary). The procedure and formulas used are correct. The assignment is clean and the problems are solved in an organized way.

70


10

Utilización apropiada y correcta de gramática 10 Aplicación y utilización correcta y apropiada de los verbos 10

Total de Puntos 100 (70% contenido y 30%

languaje)

Puntuación total Estudiante:

_______



Anejo C/Appendix C

RUBRIC FOR COLLABORATIVE EXERCISE EVALUATION

Workshop One & Three NAME: _____________________________ Date: ______________

CRITERIA Value Points Workshop 1 Student Score

Workshop 3 Student Score

1. Frequently contribute to group discussions

10

2. Show interest in group discussions

10

3. Answer questions from other students and from the facilitator

5

4. Make questions related to the collaborative exercise

5

5. Present arguments based on the readings and class work

10

6. Show attention and is opened to the arguments from other students

10

7. Answer to the exercise is correct 25 8. Procedures and formulas are

included and correct. 20

9. Work is organized 5 TOTAL Points 100 Student’s

Score WS1:

Student’s Score WS3:

Comments; ___________________________________________________________________________



RÚBRICA PARA EVALUAR LA PARTICIPACIÓN EN EL TRABAJO EN GRUPO

Taller Dos & Cuatro NOMBRE: _____________________________ Fecha: ______________

CRITERIA Puntuación Taller 2 Puntos Est.

Taller 4 Puntos Est.

1. Contribuye frecuentemente a las discusiones en el grupo

10

2. Demuestra interés en las discusiones en grupo

10

3. Contesta preguntas del facilitador y sus compañeros

5

4. Formula preguntas pertinentes al ejercicio cooperativo

5

5. Presenta argumentos fundamentados en las lecturas y trabajos de la clase

10

6. Demuestra atención y apertura a los argumentos de sus compañeros

10

7. La respuesta del ejercicio es correcta

25

8. El procedimiento y las formulas estan incluidas y son correctas

20

9. El trabajo es organizado 5 TOTAL Puntos 100 Total Puntos

WS2:

Total Puntos WS4:

Comentarios; ___________________________________________________________________



Anejo D/Appendix D

RUBRIC FOR EVALUATION OF THE FINAL COLLABORATIVE EX ERCISE

NAME: _____________________________ Date: ______________

CRITERIA Value Points Student Score 1. Frequently contribute to group discussions 5 2. Show interest in group discussions 5 3. Present arguments based on the readings and

class work 5

4. Make questions related to the collaborative exercise

5

5. Show attention and is opened to the arguments from other students

5

6. Answer to exercise number one is correct, the procedure and formulas used are correct and the work is organized.

15

7. Answer to exercise number two is correct, the procedure and formulas used are correct and the work is organized.

15

8. Answer to exercise number three is correct, the procedure and formulas used are correct and the work is organized.

15

9. Answer to exercise number four is correct, the procedure and formulas used are correct and the work is organized.

15

10. Answer to exercise number five is correct, the procedure and formulas used are correct and the work is organized.

15

TOTAL Points 100 Student’s Score:

Comments;

___________________________________________________________________



Anejo E/Appendix E

PORTFOLIO

Guidelines to prepare the portfolio

1. Determination of sources of content

2. The following, but not limited to, documentation will be included:

a. Projects, surveys, and reports.

b. Oral presentations

c. Essays: dated writing samples to show progress

d. Research papers: dated unedited and edited first drafts to show progress

e. Written pieces that illustrate critical thinking about readings: response or

reaction papers.

f. Class notes, interesting thoughts to remember, etc.

g. Learning journals, reflexive diaries.

h. Self assessments, peer assessments, facilitator assessments.

i. Notes from student-facilitator conferences.

3. Organization of documentation

Documentation will be organized by workshop, and by type of assignment within

workshops. Workshops will be separated from one another using construction paper

or paper of different colors, with tabs indicating the workshop number.

4. Presentation of the portfolio

• Documentation will be posted in a binder or in a digital version (e-portfolio).

• The cover page will follow exactly APA guidelines applied to a cover page of

research papers submitted at Metro Orlando Campus. This cover page will be

placed at the beginning of the portfolio.

• The entire portfolio will follow APA style: Courier or Times New Roman font,

size 12, double space, and 1-inch margins. See a “Publication Manual of the

APA, Fifth Edition”

• A log of entries that can be expanded with each new entry properly

numbered. The table, which should be located at the beginning, should

include a brief description, date produced, date submitted, and date evaluated

(Appendix G ).



• Introduction and conclusion of the income and outcome of the portfolio.

• A list of references and appendixes of all assignments included will be added

to the end of the portfolio.

• The Portfolio Informational Sheet will be placed in the transparent front pocket

of the binder for identification purposes (Appendix F ).

5. Student-Facilitator Feedback Template: Progression follow-up

The final step in implementing portfolios, before returning them to the student or

school life, is sharing feedback with each student to review the contents, student

reflections, and your evaluations of individual items and all of the work together as

related to learning targets (Banks, 2005).

Facilitators will e-mail a feedback template to all students. This template will contain

information pertaining to weaknesses and strengths found in students’ portfolios

(Appendix J ). Facilitators will focus their attention on showing students what is

possible and their progress rather than what is wrong; however, this does not mean

that facilitators will not cover weaknesses and areas for improvement during the

conference. Facilitators will send this feedback template upon completion of

workshop one.

Students will also have the opportunity to respond to the facilitator’s feedback and

write their own comments and/or ideas of how to improve the quality of their

portfolios, and how to become better metacognitive learners on the feedback

template. Students will e-mail the template with their comments back to the facilitator

after every workshop.

6. Portfolio storage:

• Portfolio samples will be safely stored for a six-month term on campus.

• Students will sign an official document empowering Ana G. Mendez

University System with rights to use their portfolios with educational or

accreditation purposes during this term (Appendix K ).

• After this term, and if their authors authorize Ana G. Mendez University

System to discard their portfolios by signing an official document, portfolio

samples will be destroyed; otherwise, they will be returned to their original

authors (Appendix L ).



Anejo F/Appendix F

PORTFOLIO INFORMATIONAL SHEET

Sistema Universitario Ana G. Méndez Metro Orlando Campus

Universidad del Este, Universidad Metropolitana, Un iversidad del Turabo Check one: � Universidad del Este � Universidad Metropolitana � Universidad del Turabo Check one: � Undergraduate

� Graduate

Concentration

Student’s Name

Facilitator’s Name

Course:

Portfolio rated as

Reason of this rate



Anejo G/Appendix G

Log of Entries

Entry Description

Date of Entry

Date

Submitted

Date

Evaluated

Page #

1

2

3

4

5

6

7

8

9

10



Anejo H/Appendix H

Checklist for Portfolio Assessment

Has the student set academic goals?

Does the portfolio include enough entries in each area to make

valid judgments?

Does the portfolio include evidence of complex learning in realistic

setting?

Does the portfolio provide evidence of various types of student

learning?

Does the portfolio include students’ self-evaluations and

reflections on what was learned?

Does the portfolio enable one to determine learning progress and

current level of learning?

Does the portfolio provide clear evidence of learning to users of

the portfolio?

Does the portfolio provide for student participation and

responsibility?

Does the portfolio present entries in a well-organized and useful

manner?

Does the portfolio include assessments based on clearly stated

criteria of successful performance?

Does the portfolio provide for greater interaction between

instruction and assessment?

Adapted from: Gronlund, N. E. (2003). Assessment of student achievement. 7th ed. Boston: Pearson

Education, Inc.



Anejo I/Appendix I

Portfolio Rubric

4 3 2 1

PORTFOLIO APPEARANCE

� Readable: Are entries typed in an appropriate font and size? Are

entries free of errors? Do ideas expressed in entries follow a logical sequence with appropriate transitions among paragraphs and topics?

� Professionalism: Is the appearance of the portfolio

professional? Are graphics, colors and portfolio language consistent with professional workplace expectations? Is the portfolio presented in a neat and orderly manner?

� Organization: Is the portfolio organized in a manner that makes

it easy to follow and easy to quickly locate information?

PORTFOLIO CONTENT AND FUNCTION

� Content: Are all required entries included in the portfolio? Are

entries relevant to the content of the portfolio? Do all entries contain the student’s reaction or reflection on the selected topics? Do entries provide thorough understanding of content? Resume, Activities List, Varied Samples of Written Work, Evidence of Problem Solving, and Evidence of Decision Making.

� Authenticity: Are the samples and illustrations a true reflection

of the student’s efforts and abilities?

� Growth/Development: Do samples provide thorough

understanding of growth and development related to their field of concentration? Do items show what the student has learned?

� Collaboration: Do items show examples of both individual and

group work? Does the student provide clear understanding of collaboration, and use collaboration to support his/her learning?



� Reflection and Personal growth: Do items show exceptional

understanding of how to be a reflective thinker and how to seek opportunities for professional growth? Does the student include self-reflective comments? Does the student reflect enthusiasm for learning?

� Professional Conduct: Do items show clear understanding of

ethical behavior and professional conduct? Do items display the pride the student has in his or her work?

Overall Portfolio Impact

� Is this portfolio an asset in demonstrating the student’s value

(skills, abilities, knowledge) to a potential employer or college representative?

Rating Scale 4 = Outstanding 3 = Very good 2 = Good 1 = Needs improvement Source: Retrieved from www.lcusd.net/lchs/portfolio/rubric.htm on February 10th, 2007. Adapted 02/10/2007 by Fidel R. Távara, M.Ed. Coordinator of Assessment and Placement – Metro Orlando Campus



Anejo J/Appendix J

Portfolio Assessment Feedback Template Strengths Weaknesses Improvement Ideas Facilitato r’s comments

Student’s response and comments



Anejo K/Appendix K

Use and Return of Portfolio

Sistema Universitario Ana G. Méndez Universidad del Este, Universidad Metropolitana, Un iversidad del Turabo

I, ____________________________________, grant permission to the office of

Assessment and Placement of the Ana G. Méndez University System, to keep in

their records a copy of my portfolio. I understand that the portfolio is going to be

used for accreditation or educational purposes only, and that is not going to be

disclosed without my consent.

By signing this document I authorize the office of Assessment and Placement to

keep a copy of my portfolio for six months and return it to me at the end of this

period of time.

_______________________________ ___________

Student’s Name (print) Date

_______________________________ ___________

Student’s Signature Date



Anejo L/Appendix L

Use and Discard of Portfolio

Sistema Universitario Ana G. Méndez Universidad del Este, Universidad Metropolitana, Un iversidad del Turabo

I, ____________________________________, grant permission to the office of

Assessment and Placement of the Ana G. Méndez University System to keep in

their records a copy of my portfolio. I understand that the portfolio is going to be

used for accreditation or educational purposes only, and that is not going to be

disclosed without my consent.

By signing this document I authorize the Office of Placement and Assessment to

keep a copy of my portfolio for six months and discard it at the end of this period of

time.

_______________________________ ___________

Student’s Name (print) Date

_______________________________ ___________

Student’s Signature Date



Anejo M/Appendix M

PARÁMETROS ESPECÍFICOS PARA EVALUAR ASISTENCIA Y

PARTICIPACIÓN

La evaluación de asistencia y participación en los cinco talleres tiene un peso de

15% del total de la evaluación final del curso MATH 199. Es requisito insustituible la

asistencia a todas las cinco reuniones, dos o más ausencias equivalen a fracaso del

curso. Las actividades realizadas en el taller ausente, sujetas a evaluación, serán

consideradas y ponderadas de acuerdo con los parámetros específicos. Por lo

tanto, si el/la estudiante se ausenta y entrega los trabajos posteriormente, su

puntuación comenzará con descuento porcentual previamente establecido para

cada actividad realizada en la respectiva reunión; como se demuestra a

continuación:

Actividad Puntos Descontados

Trabajos a realizar previo a cada taller 20 puntos por cada taller que entregue tarde

Trabajo cooperativo Pierde todos los puntos

Prueba corta 20 puntos / Debe reponer antes del siguiente taller, de no ser así perderá todos los puntos.

Portafolio Pierde todos los puntos

Trabajo Final Cooperativo Pierde todos los puntos

Asistencia & Participación:

En un rango de 1 a 20 puntos, siendo 20 la puntuación mayor por cada taller, se

considerará que el/la estudiante haya efectuado aportaciones o preguntas efectivas

en la discusión de los conceptos, ejercicios y actividades del taller. Debe entenderse

por aportaciones efectivas todas aquellas preguntas, presentaciones o ayudas que

dirijan al grupo hacia un mejor entendimiento de los temas discutidos.



SPECIFIC PARAMETERS FOR THE ATTENDANCE AND PARTICIP ATION

EVALUATION

The evaluation for attendance and participation is worth 15% of the total final

evaluation of the class. Attendance to all five workshops is required and cannot be

replaced; students with two or more absences will fail the class. If the student is

absent, the student must contact the facilitator, in order to be ready for the next

workshop. The students will loose points accordingly based on the specific

parameters for all activities subject to evaluation during the workshop that the

student is absent, see table below:

Activity Discounted Points

Assignments prior to each workshop 20 points for each workshop that the work is late.

Collaborative Exercise Loose all the points

Quizzes 20 points / Must be taken prior to the next workshop otherwise will loose all the points.

Portfolio Loose all the points

Final Collaborative Exercise Loose all the points

Attendance & Participation:

In a range from 1 to 20 points, where 20 is the highest score the students can get in

each workshop, this will considered how effective were the students questions and

comments in relation to the discussion of the class topics, problems and workshop

activities. The affectivity of the student participation will be measured based on the

how the questions and comments helped to clarify the concepts and to make it more

understandable.



Anejo N/Appendix N

COLLABORATIVE EXERCISE

WORKSHOP 1

A company pays a monthly rent of $3,000 for the office space and it pays $1,000 to

each employee every month (there is a total of 12 employees). In addition each

employee gets a bonus of $10 for each unit that they complete during the month.

The company’s revenue is $18 for each unit completed by the employees. Answer

the following questions;

1. Write the equation for the monthly salary S(x) for EACH employee, where x

are the units completed by each employee during the month. Also, write the

equation for the monthly salary for ALL the employees, T(x).

2. If all the employees completed the same number of units (x) during the

month, write the equation for the company’s monthly revenue R(x) as a

function of x. Also, write the equation for the company’s profit, P(x).

3. Supposed that ONE employee completed 300 units in a month, calculate the

monthly salary for this employee. Additionally, supposed that EACH

employee completed 300 units in a month, calculate the company’s monthly

revenue.

4. Based on the company’s growth, they decided to change their location and

rent a bigger office that will cost $10,000 a month. They also decided to hire

50 employees in addition to the original 12 employees. The salary for the new

employees and the bonus will be the same as for the original employees

($1,000 a month plus $10 for each completed unit a month). The company’s

revenue remains the same at $18 for each unit completed in a month. What

will be the equation for the company’s profit P(x), taking into consideration the

new office and the new number of employees?

How many units (x) have to be completed by the employees in a month in

order for the company’s monthly revenue double the salary of all the

employees?



TRABAJO COOPERATIVO

TALLER DOS

Aplicación de Funciones Exponenciales

La cantidad de dinero en una cuenta de banco se puede calcular co la siguiente

formula, cuando sabemos la tasa de interés (i), el tiempo en anos (t) y la cantidad

con la cual se abrió la cuenta, principal (P);

A = P (1 + i)t

Por ejemplo: Una cuenta que se abre con $100 y gana el 5% de interés, cual es la

cantidad que Habrá en la cuenta en 7 anos?

A = 100 (1 + 0.05) 7 = 100 (1.05) 7 � A = 140.71

1. Resuelva la siguiente situación utilizando esta fórmula; George Washington

deposita $1.00 en el Banco Continental en 1776. El banco a pagado el 5% de

interés por todos estos años. ¿Cuánto dinero hay en la cuenta de banco hoy?

(Asumir que no se ha hecho ningún retiro de la cuenta)

Para calcular la cantidad de dinero (s) que habrá en una cuenta cuando se hace un

pago regular (r) durante un periodo de anos (t) se utiliza la siguiente fórmula si el

interés (i) es conocido;

s = r (1 + i)n – 1 (1 + i) i

Por ejemplo: Si se comienza una cuenta de IRA en 1980, en la cual se depositan

$2000 cada año y se gana el 8% de interés. Si la cuenta se tiene por 16 anos,

cuanto habrá en la cuenta?

s = 2000 (1 + .08)16 – 1 (1 + .08) = 2000 (1.08)16 – 1 (1.08) � s = 65500.5 0.08 0.08

2. Utilizando esta fórmula, resuelva la siguiente situación: Una pareja tienen un hijo

y quieren abrir una cuenta para cuando el niño empiece en la universidad. Ellos



quieren abrir una cuenta que les de el 8% de interés para que cuando el hijo tenga

18 anos la cuenta tenga $10,000. Para que esto ocurra, ¿cuánto tienen que

depositar cada año en cuenta?

3. Si una persona comienza un cuenta de IRA cuando cumple 21 anos, en la cual

deposita $2,000 cada año. Si el interés es del 8%, ¿cuánto dinero habrá en la

cuenta cuando esta persona se retire a los 65 años?

4. Asumiendo la misma situación del problema #3, pero ahora la persona quiere

tener $1,000,000 cuando se retire a los 65 años. ¿Cuánto esta persona tiene que

depositar cada año en la cuenta de IRA?



COLLABORATIVE EXERCISE

WORKSHOP 3

IRA Venture

Tim, Tom and Teresa are triplets.

- Tim started to invest in an IRA when he turned 30 years old. He deposited

$2,000 in the IRA every year for 10 consecutive years. Then he decided to

stop making any more deposits. He left the amount already deposited in the

account gaining interests until he turns 60 years old, at that time he will retire

and withdraw the money.

- Tom started to invest in an IRA when he turned 40 years old. He decided to

deposit $2,000 in the IRA every year until he turns 60 years old, at that time

he will retire and withdraw the money.

- Teresa started to invest in an IRA when she turned 30 years old. She decided

to deposit $2,000 in the IRA every year until she turns 60 years old, at that

time she will retire and withdraw the money.

As the financial analysts for Tim, Tom and Teresa, you need to determine how much

money each one will have in their IRA accounts when they decide to retire and

withdraw the money. To accomplish this task you should prepare a table showing

how much they are investing in their individual IRA accounts. The following table will

help you with the analysis; the table already has the calculations for each one during

the first fifteen years of their investment. You need to complete the table for the

remaining 15 years to show how much each one of them will have in their IRA when

they turn 60 years old.

Use the information provided in the table to determine how you will continue to

calculate the balance in each account.



Collaborative Exercise: IRA Venture

After completing the table, answer the following questions;

a. How much each one have at the time that they retire and withdraw the money

in the account?

b. In what year Tom and Tim will have in their accounts the same amount of

money?

c. In what year Teresa could have stop making payments to her IRA account

and still have more money than Tom at the time they retired?



TRABAJO COOPERATIVO

TALLER CUATRO

Balance de Costo y Ganancia

Toda compañía tiene unas ecuaciones de costo y ganancia con las cuales pueden

hacer una comparación para saber si la compañía esta produciendo lo suficiente

para tener una ganancia o si los costos son muy altos y no hay ganancias. Estas

ecuaciones son diferentes para cada compañía porque ellas dependen de los

costos fijos y variables de la compañía y del precio del producto que la compañía

produce.

Una compañía de lámparas de techo tiene un costo fijo de $800 mensuales por las

facilidades y otros gastos. El costo variable de la compañía es de $10 por cada

lámpara que se produce. Cada lámpara tiene un precio de $25 cada una. Las

ecuaciones de costo y ganancia que la compañía utiliza son las siguientes (donde x

son la cantidad de lámparas producidas en un mes):

Ecuación de costo; c = 10x + 800

Ecuación de ganancia; g = 25x

Utilizando esta información, conteste las siguientes preguntas;

- Cuantas lámparas la compañía tiene que producir y vender en un mes para que el

costo sea igual a la ganancia.

- Dibuje en una gráfica la línea para cada ecuación y encuentre el punto donde el

costo es igual a la ganancia.

Documents

MATH 199 QUANTITATIVE METHODS I 199 DLP... · 2009-07-09 · Trabajo Final: Ejercicio Cooperativo (Debate/Concurso) 25% Durante el quinto taller, se llevará a cabo un ejercicio cooperativo