Course Outline for Mathematics 53A
Elementary Applied Algebra and Data Analysis

Effective: Spring 2018
SLO Rev: 03/14/2017
Catalog Description:

MTH 53A - Elementary Applied Algebra and Data Analysis

3.00 Units

Equations and formulas; linear functions; scatterplots and linear models; measurement and conversion of units; proportional reasoning and problem solving. Intended for students who do not need calculus.
Prerequisite: MTH 104 or an appropriate skill level demonstrated through the Mathematics Assessment process., Strongly Recommended: ENGL 102 or ENGL 101B.
1701.00 - Mathematics, General
Optional
Type Units Inside of Class Hours Outside of Class Hours Total Student Learning Hours
Lecture 3.00 54.00 108.00 162.00
Laboratory 0.00 18.00 0.00 18.00
Total 3.00 72.00 108.00 180.00
Measurable Objectives:
Upon completion of this course, the student should be able to:
  1. use formulas and the metric system to find areas and volumes;
  2. use dimensional analysis to perform multi-step unit conversions;
  3. solve linear equations involving fractions, decimals, and percents;
  4. interpret and apply formulas involving several variables and parameters;
  5. create and interpret scatterplots of bivariate quantitative data;
  6. apply and interpret linear models in context of the real data or situations;
  7. create graphs and find equations of linear functions;
  8. calculate and interpret linear rates of change;
  9. represent models using functional notation;
  10. use a graphing calculator as a tool in problem solving.
Course Content:

Lecture

  1. Variables, expressions, equations, and functions
    1. Order of operations
    2. Distance and absolute value
    3. Linear equations and inequalities
      1. Review of equation solving principles
      2. Word problems with decimals, fractions, and percents
      3. Solve inequalities
    4. Formulas
      1. Geometric formulas and literal equations
      2. Solve for one variable in terms of another
    5. Functions
      1. Function notation
      2. Evaluate for given values of the independent variable
      3. Find the value of independent variable for a given value of  dependent variable
  2. Geometry and measurement
    1. Dimension
    2. Metric System
      1. Powers of ten and metric prefixes
      2. Relationship among meters, liters, and grams
      3. Comparison with U.S. customary system
      4. One-step unit conversion
      5. Dimensional analysis and multi-step unit conversion
  3. Rates and Ratios
    1. Simplify rates and ratios
    2. Unit conversion for rates
  4. Cartesian coordinate system
      1. Create scatterplots from ordered pairs and data
      2. Interpret scatterplots
    1. Rate of change
      1. Calculate rate of change from data
      2. Visualize rate of change from graph
      3. Interpret rate of change
    2. Linear Functions
      1. Relationship between equations and graphs
      2. Domain and range in applications
      3. Interpret slope and intercept
    3. Linear Models
      1. Use a scatterplot to draw a reasonable model
      2. Find the equation of the model
        1. By hand
        2. By using technology
      3. Interpret the model
        1. Slope of the model
        2. Intercepts of the model
        3. Ordered pairs
      4. Use model to make estimates for independent and dependent variables
      5. Calculate and interpret estimation error

Lab

  1. Basic use of a graphing calculator
    1. Function graphing
    2. Window settings
    3. Choosing appropriate scales for graphs
    4. Trace graphs
    5. Use tables
    6. Make scatterplots
    7. Graphical equation-solving
    8. Find linear regression equations
    9. Use intersect to solve linear equations
Methods of Instruction:
  1. Lectures
  2. Practice/Demonstration
  3. Class and group discussions
  4. Group Activities
  5. Presentation
Assignments and Methods of Evaluating Student Progress:
  1. Exercises from the textbook: You are riding an exercise bicycle at a fitness center. The readout states that you are using 500 Calories per hour. Are you generating enough power to light a 100-watt bulb? (Note that 1 Calorie = 4184 joules and 1 watt = 1 joule per second.)
  2. Group collaborative: Use your graphing calculator or statistical software, make a scatterplot of the bivariate data given in the table. Identify the two variables, give their units, and explain how you chose the independent and dependent variables. With your group, write at least three sentences describing any trends, patterns, or striking features of the data that are visible from the scatterplot
  3. Lab assignments: (a) Collaborative exercises using the graphing calculator to make scatterplots; (b) Collaborative exercises using the graphing calculator to graph functions.
  1. Homework
  2. Quizzes
  3. Class Participation
  4. Class Work
  5. Lab Activities
  6. Midterm Examination
  7. Final Examination
Upon the completion of this course, the student should be able to:
  1. Critically analyze mathematical problems using a logical methodology.
  2. Communicate mathematical ideas, understand definitions, and interpret concepts.
  3. Increase confidence in understanding mathematical concepts, communicating ideas and thinking analytically.
Textbooks (Typical):
  1. Bennett, J., W. Briggs (2011). Using and Understanding Mathematics: A Quantitative Reasoning Approach (5th). Addison Wesley.
  2. Lehmann, J (2011). Elementary and Intermediate Algebra: Functions and Authentic Applications Prentice Hall.
  3. Custom (2016). Applied Algebra and Data Analysis (3rd). Pearson Publishing.
  • A graphing calculator is required.
  • Access code to a required on-line homework system.
Abbreviated Class Schedule Description:
Equations and formulas; linear functions; scatterplots and linear models; measurement and conversion of units; proportional reasoning and problem solving. Intended for students who do not need calculus.
Prerequisite: MTH 104 or an appropriate skill level demonstrated through the Mathematics Assessment process., Strongly Recommended: ENGL 102 or ENGL 101B.
Discipline:
Mathematics*