Discipline: Mathematics
Originator: Kenneth Cramm

Riverside Community College District
Integrated Course Outline of Record

Mathematics 105
MAT-105 : Corequisite Support for Math 5
College:
Lecture Hours: 36.000
Outside-of-Class Hours: 72.000
Units: 2.00
Grading Methods: Pass/No Pass
Course Description
Prerequisite: Appropriate Placement
Corequisite: MAT-5
Course Credit Recommendation: Non-Degree Credit

A concurrent co-requisite course containing geometry and algebra concepts designed to support students in Calculus for Business and Life Science. Topics include a review of skills developed in geometry and intermediate algebra: area and volume, factoring, graphing, operations on rational and radical expressions, linear, exponential and logarithmic expressions and equations, functions including composition and inverses, and an in-depth focus on linear and quadratic functions. Topics are taught strategically throughout the semester to provide a "just in time" instruction of skills needed to master concepts in MAT 5 as they arise in that course. A diverse approach to problem solving processes and enhancement of study strategies will prepare the student for later university courses. 36 hours lecture. (Pass/No Pass.)
Short Description for Class Schedule
A concurrent co-requisite course containing geometry and algebra concepts designed to support students in Calculus for Business and Life Science.
Entrance Skills:
Before entering the course, students should be able to demonstrate the following skills:
  1. This corequisite skill will be completed using MAT 105: Determine the limit of a function.
    • MAT-5 - Determine the limit of a function.
Course Objectives:
Upon successful completion of the course, students should be able to demonstrate the following activities:
  1. Analyze the uses of geometric area and volume formulas.
  2. Simplify and factor expressions.
  3. Create equations from application problems and solve.
  4. Determine and use all components of lines.
  5. Find the sum, difference, product, quotient, and composition of two functions.
  6. Analyze a given graph to determine whether the graph represents a function or a 1-1 function, evaluate the function, and determine the domain and range of the function.
  7. Find and use the intercepts, the increasing/decreasing nature, and end behavior of an equation to produce its graph.
  8. Apply theories of affective domain
  9. Solve equations to include polynomial, rational, radical, exponential, and logarithmic.
  10. Solve linear and nonlinear inequalities.
Student Learning Outcomes:
Upon successful completion of the course, students should be able to demonstrate the following skills:
  1. Demonstrate the use of quantitative reasoning by developing a problem-solving strategy, performing appropriate analysis and computation, and critically assessing the meaning of the conclusion or outcome.
    • Critical Thinking: Students will be able to demonstrate higher-order thinking skills about issues, problems, and explanations for which multiple solutions are possible. Students will be able to explore problems and, where possible, solve them. Students will be able to develop, test, and evaluate rival hypotheses. Students will be able to construct sound arguments and evaluate the arguments of others.
    • Information Competency & Technology Literacy: Students will be able to use technology to locate, organize, and evaluate information. They will be able to locate relevant information, judge the reliability of sources, and evaluate the evidence contained in those sources as they construct arguments, make decisions, and solve problems.
Course Content:

Enhanced experience in MAT 5 course topics are found in these MAT 105 course topics:

  1. Affective Domain
    1. Growth mindset
    2. Grit/Perseverance
    3. Motivation and inspiration
    4. Confidence
    5. Productive struggle
    6. Responsibility 
  2. Graphs and Functions
    1. Definition of a function and a 1-1 function
    2. Graphs of functions to include linear, quadratic, rational, radical, exponential, logarithmic and piece-wise
    3. Graphs of non-functions
  3. Algebraic expressions and equations
    1. Simplification of expressions
    2. Basic rules of exponents and logarithms
    3. Factoring expressions
    4. Solve equations to include linear, quadratic, rational, radical, exponential, and logarithmic
  4. Applications
    1. Increasing and decreasing functions
    2. Maximize area
    3. Exponential growth and decay
    4. Compound interest
  5. Advanced Techniques
    1. Using substitution to solve equations
    2. Summation notation
    3. Technology and calculator uses for business and life science
    4. Affective domain lessons

Methods of Instruction:
Methods of instruction used to achieve student learning outcomes may include, but are not limited to, the following activities:
  • Ice breakers, team building activities, and collaborative learning to increase understanding and application of theories of the affective domain, which may include but is not limited to growth mindset, college fear factor, perseverance, and motivation;
  • Lectures/presentations/ demonstrations with question and answer periods that both disseminate information and pose problems in geometry and intermediate algebra.
  • Showing films or videos, distributing handouts, using calculators and manipulatives, using computers, and/or using electronic or computer-based media in order to reinforce understanding of concepts related to graphing a function, simplifying algebraic expressions, and mastering writing mathematics.
  • Cooperative/collaborative learning tasks and activities designed to assist students in mastering the techniques of factoring expressions and solving equations.
  • One-to-one tutoring and guided practice in solving problems using geometric area and volume formulas.
  • Computer-assisted, graphics calculators and/or web-enhanced instruction for finding line equations, vertex of a parabola, and the equation of a circle.
Methods of Evaluation:
Students will be evaluated for progress in and/or mastery of student learning outcomes using methods of evaluation which may include, but are not limited to, the following activities:
  • Individual and group assignments including problem sets, essays, reports, projects, and calculator/computer assignments designed to demonstrate successful understanding and application of basic concepts and definitions in geometry and intermediate algebra.
  • Low stakes quizzes designed to assess students’ ability to recall, critically analyze, and apply information to determine the equation of a line.
  • Participation in class discussions to ensure progress in mastering graphing functions using intercepts and end behavior.
  • Participation in collaborative learning projects and problem sets to demonstrate mastery of area and volume formulas used in geometry and intermediate algebra.
  • Low stakes final examination designed to assess students’ mastery and ability to demonstrate quantitative reasoning by developing a problem-solving strategy, performing appropriate analysis and computation, and critically assessing the meaning of the conclusion or outcome.
Sample Assignments:
Outside-of-Class Reading Assignments
Read and analyze textbook, detailed examples, and review class notes covering all topics to include using substitution to solve quadratic equations.
Outside-of-Class Writing Assignments
Use the language and symbols of geometry and algebra to solve problems sets on all topics to include solving exponential and logarithmic equations
Other Outside-of-Class Assignments
Practice graphing skills for all functions and non-functions to be able to sketch any function with precision.
Course Materials:
All materials used in this course will be periodically reviewed to ensure that they are appropriate for college level instruction. Possible texts include the following:
  • Barnett, Ziegler, Byleen. Applied Calculus for Business, Economics, Life Sciences and Social Sciences. 13th Pearson, 2015.
  • Hughes-Hallett. Applied Calculus. 6th Wiley, 2018.
  • Tan. Applied Calculus For the Managerial, Life, and Social Sciences. 10th Cengage, 2015.
  • Graphics calculators such as the Texas Instruments TI-84
  • Software appropriate for Business/Life Science calculus
Codes/Dates:
Board of Trustees Approval Date: 12/11/2018
COR Rev Date: 12/11/2018