Course Outline for Mathematics 253
Noncredit Applied Algebra and Data Analysis

Effective: Fall 2019
SLO Rev: 10/24/2018
Catalog Description:

MTH 253 - Noncredit Applied Algebra and Data Analysis

108.00 Hours

May be repeated 99 time(s)
This noncredit course is part of a noncredit certificate of competency in Preparation for College Mathematics for the Statistics and Liberal Arts pathway. This course is free and is intended to prepare students for the rigor of college-level mathematics coursework required in non-STEM fields. Students may repeat this course until mastery of the skills is met. This course covers the same content as MTH 53 Applied Algebra and Data Analysis. Students who are transitioning to college, who are unsure of their abilities, or who have been out of school for while may prefer to take the noncredit MTH 253 instead of MTH 53 since it is free and may be repeated. This course covers equations and formulas; linear, exponential, logarithmic functions; measurement and conversion of units; exponents and scientific notation; introduction to descriptive statistics including graphical methods; introduction to probability. This course is intended for students who are following the Statistics and Liberal Arts Mathematics pathway.
1701.00 - Mathematics, General
Letter Grade Only
Type Hours
Lecture 90.00
Laboratory 18.00
Total 108.00
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. use scientific notation to perform calculations and make comparisons;
  4. interpret and apply formulas involving several variables;
  5. solve linear equations involving fractions, decimals, and percents;
  6. solve exponential equations using logarithms;
  7. apply proportional reasoning appropriately in real-life situations;
  8. create, apply, and interpret graphs;
  9. interpret graphical displays of univariate quantitative and categorical data;
  10. create and interpret scatterplots of bivariate quantitative data;
  11. calculate and interpret the mean and median for a set of data;
  12. create and interpret frequency and relative frequency tables;
  13. apply and interpret the relative frequency definition of probability;
  14. interpret two-way tables for bivariate categorical data;
  15. analyze data and determine the appropriate model for the situation;
  16. create graphs and find equations of linear models;
  17. create graphs and find equations of exponential models;
  18. represent models using functional notation;
  19. apply the models to make estimations;
  20. calculate and interpret linear and exponential rates of growth;
  21. interpret absolute error and relative error in real life situations;
  22. model real growth and decay situations and data with exponential graphs and functions;
  23. apply and interpret linear and exponential models in context of the real data or situations;
  24. solve systems of equations using graphing and substitution methods;
  25. 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. Issues in measurement 
      1. Absolute and relative measurement error
      2. Accuracy and precision
      3. Scientific notation for very large and small numbers
  3. Rates and Ratio
    1. Simplify rates and ratios
    2. Unit conversion for rates
  4. Proportionality
    1. Solve proportions
    2. Applications of proportional reasoning
  5. Linear functions, graphs and models 
    1. Cartesian coordinate system
      1. Create scatterplots from ordered pairs and data
      2. Interpret scatterplots
    2. Rate of change
      1. Calculate rate of change from data
      2. Visualize rate of change from graph
      3. Interpret rate of change
    3. Linear Functions
      1. Relationship between equations and graphs
      2. Interpret slope and intercept
      3. Domain and range in applications
    4. Linear Models
      1. Use a scatterplot to draw a reasonable model
      2. Find the equation of a linear model
        1. By hand
        2. By using technology
      3. Interpret model
        1. Slope of model
        2. Intercepts of model
        3. Ordered pairs
      4. Use the model to make estimates for the independent and dependent variables
      5. Calculate and interpret estimation errors
  6. Data summary and interpretation
    1. Variables and data
      1. Categorical and quantitative variables
      2. Bivariate and univariate data
      3. Raw and summarized data
    2. Frequency and relative frequency tables
      1. Create from raw data
      2. Interpret
    3. Pie charts, bar graphs, and histograms
      1. Choose appropriate representation
      2. Interpret
    4. Two-way tables
      1. Interpret
      2. Calculate relative frequencies
    5. Mean and median
      1. Calculate from raw data
      2. Interpret
  7. Probability
    1. Basic probability
      1. Relative frequency definition
      2. Venn diagrams
  8. Exponents
    1. Laws of exponents
    2. Interpret exponents
    3. Negative exponents
    4. Rational exponents
    5. Scientific notation
  9. Exponential and Logarithmic Functions
    1. Equations of exponential functions
    2. Exponential models for real-world situations
    3. Graphs of exponential and logarithmic functions
    4. Interpret the coefficient and base of an exponential model
    5. Use logarithms to solve exponential equations
    6. Evaluate logarithms
    7. Applications involving logarithms
  10. Systems of Linear Equations
    1. Solve by graphing
    2. Solve by substitution
    3. Applications

Lab

  1. Basic use of a graphing calculator
    1. Function graphing
    2. Windows settings
    3. Choose appropriate scales for graphs
    4. Trace graphs
    5. Use tables
    6. Make scatterplots
    7. Graphical equation-solving
    8. Use intersect to solve linear equations
    9. Use intersect to solve systems of equations
    10. Find regression equations
  2. Calculator techniques for exponential and logarithmic functions
    1. Notation for large and small numbers
    2. Use logarithms to solve problems
    3. Other applications
Methods of Instruction:
  1. Lecture/Discussion
  2. Demonstration
  3. Class and group discussions
  4. Group Activities
  5. Problem Solving
  6. Presentation
Assignments and Methods of Evaluating Student Progress:
  1. 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 and to fit function to data. (b) Collaborative exercises using the graphing calculator to graph functions. (c) Collaborative exercises using computer applications to better understand the concept of mean vs. median. (d) Collaborative exercises using computer applications to learn various distribution shapes.
  1. Homework
  2. Quizzes
  3. Class Participation
  4. Lab Activities
  5. Exams/Tests
  6. 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. Bennet, J., W Briggs (2014). Using and Understanding Mathematics: A Quantitative Reasoning Appraoch (6th). Pearson.
  2. Lehmann, J. (2014). Elementary and Intermediate Algebra: Functions and Authentic Applications (2nd). Pearson.
  3. Lehmann, J. (2015). A Pathway to Introductory Statistics (1st). Pearson.
  4. Custom (2017). Combined custom text from above (3rd). Pearson.
  • A graphing calculator is required.
  • Access code to a required on-line homework system.
Abbreviated Class Schedule Description:
This noncredit course is part of a noncredit certificate of competency in Preparation for College Mathematics for the Statistics and Liberal Arts pathway. This course is free and is intended to prepare students for the rigor of college-level mathematics coursework required in non-STEM fields. Students may repeat this course until mastery of the skills is met. This course covers the same content as MTH 53 Applied Algebra and Data Analysis. Students who are transitioning to college, who are unsure of their abilities, or who have been out of school for while may prefer to take the noncredit MTH 253 instead of MTH 53 since it is free and may be repeated. This course covers equations and formulas; linear, exponential, logarithmic functions; measurement and conversion of units; exponents and scientific notation; introduction to descriptive statistics including graphical methods; introduction to probability. This course is intended for students who are following the Statistics and Liberal Arts Mathematics pathway.
Discipline:
Mathematics-Basic Skills: Noncredit, Mathematics*, or