Discipline: Mathematics
Originator: Robert Prior

Riverside Community College District
Integrated Course Outline of Record

Mathematics 136
MAT-136 : Corequisite Support for MAT-36
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-36
Course Credit Recommendation: Non-Degree Credit

A concurrent corequisite course containing algebra concepts designed to support students in Trigonometry. Topics include a review of skills developed in intermediate algebra: factoring, graphing linear and quadratic functions, operations on rational and radical expressions, linear and quadratic expressions and equations, and an in-depth focus on operations on functions, including composition and inverses. Topics are taught strategically throughout the semester to provide a "just in time" instruction of skills needed to master concepts in MAT-36 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 corequisite course containing algebra concepts designed to support students in Trigonometry.
Entrance Skills:
Before entering the course, students should be able to demonstrate the following skills:
  1. This corequisite skill will be completed using MAT 136: Solve trigonometric equations.
    • MAT-36 - Solve trigonometric equations, triangles, and applications.
Course Objectives:
Upon successful completion of the course, students should be able to demonstrate the following activities:
  1. Simplify and factor polynomial expressions.
  2. Simplify radical expressions, including rationalizing the denominator.
  3. Solve linear, quadratic, rational, and radical equations.
  4. From a graph, determine whether a relation is a function and whether a function is one-to-one.
  5. Evaluate a function; determine the domain and range of a function.
  6. Find the sum, difference, product, quotient, and composition of two functions.
  7. Given a one-to-one function, identify and graph its inverse.
  8. Find and use the intercepts, the increasing/decreasing nature, and end behavior of a function to produce its graph.
  9. Apply theories of affective domain.
Student Learning Outcomes:
Upon successful completion of the course, students should be able to demonstrate the following skills:
  1. Analyze a function to determine its defining elements (including domain and range), its graph, and its inverse, if one exists.
    • 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.
Course Content:
  1. Affective Domain
    1. Productive Struggle.
    2. Growth mindset.
    3. Grit/Perseverance.
    4. Motivation and inspiration.
    5. Confidence.
    6. Responsibility.
  2. Algebraic expressions and equations
    1. Apply basic operations on, and simplification of, radical expressions.
    2. Apply basic operations on, and simplification of, polynomial expressions.
    3. Factor polynomial expressions.
    4. Develop and use the Pythagorean Theorem.
    5. Solve linear, quadratic, rational, and radical equations.
  3. Functions
    1. Identify domain and range of a function.
    2. Evaluate a function for a given argument (both numerical and non-numerical).
    3. Identify the inverse of a one-to-one function.
  4. Graphs
    1. Demonstrate familiarity with the features of the Cartesian Coordinate System.
    2. Demonstrate familiarity with the features of a function such as intercepts, intervals of increase/decrease, and maxima/minima.
    3. Graph linear and quadratic functions.
    4. Graph circles.
    5. Graph inverse functions.
  5. Additional Topics
    1. Using substitution to solve equations.
    2. Calculator use for evaluating numerical expressions.
    3. Technology for identifying features of the graph of a function.
    4. Any algebraic skills or concepts related to the preparation for MAT-36 content.
    5. 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 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 the Pythagorean Theorem.
  • 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 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 generating the graphs of inverse functions.
  • 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 ancillary 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 algebra to solve problems sets on all topics.

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:
  • Blitzer, Charles F.. Trigonometry. 2nd Pearson, 2017.
  • McKeague. Trigonometry. 8th Thompason Brooks/Cole, 2016.
  • Prior. Essential Algebra for Trigonometry. Priority Educational Products, 2018.
  • Prior. Trigonometry. 4th Priority Educational Products, 2018.
Board of Trustees Approval Date: 12/11/2018
COR Rev Date: 12/11/2018