Chabot College
Fall 2013
Course Outline for Mathematics 53A
ELEMENTARY APPLIED ALGEBRA AND DATA ANALYSIS
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Catalog Description:
MTH 53A - ELEMENTARY APPLIED ALGEBRA AND DATA ANALYSIS
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Equations and formulas; linear functions; measurement and conversion of units; exponents and scientific
notation; proportional reasoning and problem solving. Intended for students who do not need calculus.
Prerequisite: MTH 104 (completed with a grade of "C" or higher) or an appropriate skill level demonstrated
through the Mathematics Assessment process.
Strongly Recommended: ENGL 102 or , ENGL 101B
Units
Contact Hours
Week
Term
3.00
Lecture
Laboratory
Clinical
Total
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3.00
3.00
1.00
0.00
4.00
52.50
17.50
0.00
70.00
Prerequisite Skills:
Before entry into this course, the student should be able to:
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apply the commutative, associative and distributive laws;
perform computations with signed numbers without a calculator;
apply order of operations in evaluating algebraic expressions;
simplify exponential expressions with whole number exponents;
create, interpret, and solve simple linear equations;
find area, circumference, diameter and radius of a circle;
solve a right triangle using Pythagorean Theorem;
simplify square roots of perfect squares;
solve problems using percents;
find the areas, perimeters, and volumes of geometric figures and objects;
translate between words and the mathematical symbols for variables and operations;
interpret operations and variables in algebraic expressions;
graph simple relationships between two variables;
solve word problems, including those using formulas and linear equations.
Expected Outcomes for Students:
Upon completion of this course, the student should be able to:
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use formulas and the metric system to find areas and volumes;
use dimensional analysis to perform multi-step unit conversions;
use scientific notation to perform calculations and make comparisons;
create and solve linear equations involving fractions, decimals, and percents;
interpret absolute value;
interpret and apply formulas involving several variables and parameters;
create, apply, and interpret graphs and equations of linear functions;
create, apply, and interpret graphs and equations of simple inverse variation functions;
apply proportional reasoning appropriately in real-life situations;
3.00 units
10. calculate, interpret, and apply constant rate of change;
11. create and interpret scatterplots of bivariate quantitative data;
12. use a graphing calculator as a tool in problem solving.
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Course Content:
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Variables, expressions, equations, and functions
A. Order of operations
B. Distance and absolute value
C. Linear equations and inequalities
a. Review of equation solving principles
b. Word problems with decimals, fractions, and percents
c. Solving inequalities
D. Formulas
a. Parameters and variables
b. Solving for one variable in terms of another
E. Laws of Exponents
a. Interpreting exponents
b. Negative exponents and reciprocals
F. Functions
a. Function notation
b. Evaluating for given values of the independent variable
c. Finding the value of independent variable for a given value of dependent variable
Geometry and measurement
A. Dimension
B. Common three-dimensional figures
C. Metric System
a. Powers of ten and metric prefixes
b. Relationship among meters, liters, and grams
c. Comparison with U.S. customary system
d. One-step unit conversion
e. Dimensional analysis and multi-step unit conversion
D. Issues in measurement
a. Absolute and relative measurement error
b. Accuracy and precision
c. Scientific notation for very large and small numbers
d. Order of magnitude
Proportional reasoning
A. Rates and Ratios
a. Difference between rates and ratios
b. Simplify rates and ratios
c. Unit conversion for rates
B. Proportionality
a. Solving proportions
b. Applications of proportional reasoning
Linear functions and graphs
A. Cartesian coordinate system
a. Creating scatterplots from ordered pairs and data
b. Interpreting scatterplots
B. Rate of change
a. Calculating rate of change from data
b. Visualizing rate of change from graph
c. Interpreting rate of change
C. Linear Functions
a. Relationship between equations and graphs
b. Domain and range in applications
c. Interpreting slope and intercept
d. Intersecting lines
e. Linear models for real situations
Direct and inverse variation
A. Comparing y =kx and y=k/x
B. Domain and range for visualizing graphs
C. Application
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Methods of Presentation
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Basic use of a graphing calculator (Laboratory)
A. Function graphing
B. Setting windows
C. Choosing appropriate scales for graphs
D. Tracing graphs
E. Using tables
F. Making scatterplots
G. Graphical equation-solving
H. Notation for large and small numbers
Lectures
Practice/Demonstration
Class and group discussions
Group Activities
Presentation
Assignments and Methods of Evaluating Student Progress
1. Typical Assignments
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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.)
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
Lab assignments: (a) Collaborative exercises using the graphing calculator to make
scatterplots; (b) Collaborative exercises using the graphing calculator to graph functions.
2. Methods of Evaluating Student Progress
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Textbooks (Typical):
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Homework
Quizzes
Class Participation
Class Work
Lab Activities
Midterm Examination
Final Examination
Bennett, J., W. Briggs (2011). Using and Understanding Mathematics: A Quantitative Reasoning
Approach (5th/e). Addison Wesley.
Lehmann, J (2011). Elementary and Intermediate Algebra: Functions and Authentic Applications
Prentice Hall.
Custom (2012). Combined text of the above Pearson Publishing.
Special Student Materials
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A graphing calculator is required.