Santa Barbara City College Course Outline

MATH 041 - Fundamentals in Mathematics and Pre-Algebra

MATH 041
Fundamentals in Mathematics and Pre-Algebra
Disciplines
Mathematics - Basic Skills: noncredit
5.000
0 - May not be repeated
Foundational course, including language development and place value; definitions, concepts and operations on whole numbers, fractions, decimals, ratios, proportions, percentage and signed numbers; U.S. and metric measurement systems; introduction to algebra, rules of exponents, roots, evaluation and simplification of algebraic expressions; solving linear equations and introduction to graphing. Application/word problems throughout the course.
80.000-90.000 Total Hours
0.000 Total Hours
160.000-180.000 Total Hours
80.000-90.000 Total Hours
Prerequisite: None
Prerequisite or Corequisite: None
Concurrent Corequisite: None
Course Advisories: None
Limitation on Enrollment: None
Course Objectives:
Demonstrate skills in addition, subtraction, multiplication, and division of whole numbers.
Demonstrate skills in addition, subtraction, multiplication, and division of fractions and decimals.
Illustrate a conceptual understanding of place value in whole numbers and decimals.
Illustrate a conceptual understanding of signed numbers.
Demonstrate skills in addition, subtraction, multiplication and division of signed numbers.
Solve basic ratio and proportion problems, limiting the scope to linear expressions and equations.
Solve basic percent problems, limiting the scope to linear equations.
Solve linear equations.
Solve simple geometric problems involving perimeters, areas, and volumes, limiting the objects to rectangles, triangles, circles, and rectangular prisms (or any such combinations.)
Solve application problems involving the preceding areas.
Convert different units of measurement using the English and metric systems.
Demonstrate skills in rules of exponents.
Student Learning Outcomes
Demonstrate skills in adding, subtracting, multiplying and dividing whole numbers, fractions, decimals, and signed numbers.
Evaluate simple algebraic expressions or formulas, including geometric formulas, given certain values.
Use inverse operations to solve simple linear equations.
Translate basic phrases or word problems into algebraic expressions or equation.
Solve basic geometric problems involving perimeters, areas, or volumes, limiting the scope to linear equations.
Solve basic ratio, proportion, and percent problems, limiting the scope to linear equations.
Use various U.S. and metric systems of measurement.
Graph simple linear equations.


COURSE CONTENT FOR MATH 41:

  1. Whole Numbers
    1. Reading and writing whole numbers.
    2. Place value of whole numbers
    3. Addition of whole numbers
    4. Subtraction of whole numbers
    5. Multiplication of whole numbers
    6. Division of whole numbers including long division
    7. Rounding whole number
    8. Roots of whole numbers
    9. Factors, multiples, and prime factorization of whole numbers.
    10. Least common multiple and greatest common factor of whole numbers.
    11. Properties of Whole numbers
    12. Introduction of exponents
    13. Order of operations
    14. Solving word problems involving whole numbers
  2. Fractions
    1. Basic concepts of fractions
    2. Mixed numbers
    3. Writing a fraction in lowest terms
    4. Multiplication of fractions
    5. Applications of Multiplication
    6. Dividing fractions
    7. Multiplication and Division of Mixed Numbers
    8. Adding and subtracting like fractions
    9. Least common denominators
    10. Adding and subtracting unlike fractions
    11. Adding and subtracting mixed numbers
    12. Order relations and the order of operations
  3. Decimals
    1. Reading and writing decimals
    2. Place value of decimals
    3. Rounding decimals
    4. Addition of decimals
    5. Subtraction of decimals
    6. Multiplication of decimals
    7. Division of decimals
    8. Translating fractions to decimals and decimals to fractions.
  4. Ratio and Proportion
    1. Ratios
    2. Rates
    3. Proportions
    4. Solving proportions (limiting the scope to linear equations)
    5. Applications of proportions (limiting the scope to linear equations)
  5. Percent
    1. Basic concepts of percent
    2. Translating percents to and from fractions.
    3. Translating percents to and from decimals.
    4. Using proportions to solve percent problems (limiting the scope to linear equations)
    5. General applications of percent
    6. Simple interest
    7. Sales Tax, Commissions, and Discounts.
    8. Percent Increase and Decrease
  6. Measurement
    1. The English system (length, volume, and weight)
    2. Denominate numbers
    3. The metric system (length, volume, and weight)
    4. Metric to English and English to Metric conversions
  7. Geometry
    1. Rectangles and squares
    2. Triangles
    3. Circles
    4. Volume of rectangular prisms
    5. Pythagorean Theorem.
    6. Similar triangles (in the context of proportions)
  8. The Real Number System
    1. Definitions of Natural, Whole, Integer, Rational, Irrational numbers, and Real numbers
    2. Addition of Real Numbers
    3. Subtraction of Real Numbers
    4. Multiplication of Real Numbers
    5. Division of Real Numbers
    6. Roots of Real Numbers
    7. Signed Numbers and Order
    8. Addition of Signed numbers
    9. Subtraction of Signed numbers,
    10. Multiplication of Signed numbers
    11. Division of signed numbers
  9. Pre Algebra
    1. Introduction to Variables
    2. Evaluate expressions with one or more variables
    3. Properties of Exponents
    4. Simplifying Algebraic Expressions
    5. Addition, Subtraction and Multiplication of Monomials
    6. Distributive Property with algebraic expressions
    7. The Addition and Multiplication Properties of Equality
    8. Linear Equations in one variable
    9. Applications/Word Problems
  10. Graphing
    1. x and y axes
    2. Quadrants
    3. Point plotting
    4. Using two variable equations to plot points


Methods of Instruction
Directed Study
Discussion
Individualized Instruction
Lab
Lecture
Projects
Lectures, collaborative activities, discussion, tutorial software (such as ALEKS), supplemental handouts or videos. Students are expected to work inside and/or outside of class on assigned projects, supplementary reading and/or videos, tutorial software (such as ALEKS) and/or specified textbook and corresponding exercises.
List all the of the factors of 12. 1) [For courses utilizing ALEKS] Complete Intermediate Objective number 1, from ALEKS, focusing on whole numbers and place value. 2) [For courses utilizing the traditional textbook] Do all the odds at the end of a particular section.
Complete all intermediate objectives assigned through ALEKS OR complete all daily homework assignments.
A student's grade will be based on multiple measures of performance. Such measures will include at least three exams and a comprehensive final examination requiring demonstrations of problem-solving skills. In addition, instructors will make use of quizzes, and written homework assignments to judge a student's mathematical skills and familiarity with mathematical vocabulary. Instructors are required to provide students, in writing, with a course syllabus in accordance with district policy, which will include the specific procedures by which students will be evaluated. These procedures must be consistent with the objectives and course content stated above.
  • Pre-Algebra Miller, O'Neill, Hyde, McGraw Hill, 2014.
  • ALEKS Web-based homework tool., McGraw Hill, 2016.
11/02/2016
Board of Trustees: 04/27/2017
CAC Approval: 03/06/2017