MOHAWK VALLEY COMMUNITY COLLEGE
ROME AND UTICA, NEW YORK
COURSE OUTLINE
MA108
CONCEPTS IN MATHEMATICS
PREPARED BY JIM BURNS - 6/90
Reviewed and Found Acceptable by Nancy Call, 6/91 and 6/92
Reviewed, Revised as Needed, and/or Found Acceptable by Jim Burns, 6/93
- 6/95
Reviewed and Found Acceptable by Gabriel Melendez, 5/96
Reviewed, Revised as Needed, and/or Found Acceptable by Guy Snedeker,
5/97 – 5/07
Reviewed, Revised as Needed, and/or Found Acceptable by Mary Hartz,
12/07 - 5/12
Reviewed and Found Acceptable by Anna Radlowski, 5/13
Reviewed and Revised as Needed by Anna Radlowski, 5/14
COURSE OUTLINE
TITLE:
Concepts in Mathematics
CATALOG NO.:
MA108
CREDIT HOURS:
3
LAB HOURS:
0
PREREQUISITES:
An appropriate placement test result or
MA090 Essential Math Skills or MA091
Introductory Algebra.
CATALOG DESCRIPTION:
This course is a survey of mathematics for students in those programs
that do not require a mathematics sequence. It provides an
appreciation of mathematical ideas in historical and modern settings.
Topics include problem solving, logic, geometry, statistics, and
consumer mathematics.
STUDENT OUTCOMES:
At a level appropriate for students whose mathematical background
includes the ability to perform arithmetic operations on signed
numbers, fractions, decimals, and percents, and to solve linear
equations in a single variable, students successfully completing the
course will be able to:
1. Analyze arguments and construct valid arguments after a study of
propositional logic including connectives, truth tables, quantifiers,
Euler diagrams, and argument forms
2. Demonstrate an understanding of the definition and classification
of geometrical objects including lines, angles, and polygons
3. Solve problems involving measurement of angles, lengths, areas, and
volumes using appropriate properties, formulas, and theorems of
geometry
4. Use statistical tools, including distribution tables, histograms,
measures of central tendency, measures of variation, normal
distributions, and z-scores to summarize and analyze sets of data
5. Perform calculations involving: present and future values for both
simple and compound interest on loans and deposits; finance charges
on credit arrangements; true annual percentage rate on loans; and
regular monthly payments and repayment schedules on home mortgages
6. Demonstrate an understanding of methods of reasoning and problems
solving as applied to particular topics in the course
7. Demonstrate awareness of the nature and history of mathematical
thought
SUNY Learning Outcomes
1. The student will develop well-reasoned arguments.
2. The student will identify, analyze, and evaluate arguments as they
occur in their own and other’s work.
3. The student will demonstrate the ability to interpret and draw
inferences from mathematical models such as formulas, graphs,
tables, and schematics.
4. The student will demonstrate the ability to represent mathematical
information symbolically, visually, numerically, and verbally.
5. The student will demonstrate the ability to employ quantitative
methods such as arithmetic, algebra, geometry, or statistics to
solve problems.
6. The student will demonstrate the ability to estimate and check
mathematical results for reasonableness.
MAJOR TOPICS:
1. PROBLEM SOLVING
Inductive reasoning; pattern recognition; estimation; using charts,
tables, sketches, and graphs; “guess, test, and revise” strategy.
Student Outcomes:
1.1
1.2
1.3
1.4
1.5
1.6
1.7
Identify and extend patterns in sequences of numbers or figures
Estimate results of calculations.
Obtain information from graphs and charts.
Solve applied problems.
Determine probable next values in a number sequence using the
method of successive differences.
Find sums of series of consecutive integers or of consecutive odd
integers using summation formulas.
Identify contributions and achievements of various
mathematicians.
2. LOGIC
Statements; connectives and quantifiers; truth tables; conditionals;
equivalent statements; negations of statements; valid and invalid
argument forms; Euler diagrams.
Student Outcomes:
2.1
2.2
2.3
2.4
2.5
2.6
Write negations of quantified statements.
Translate compound statements from English into symbolic form.
Write English versions of statements given in symbolic form.
Make truth tables for statements involving two or three
variables.
Determine equivalence of statements using truth tables.
Write negations of compound statements using DeMorgan's laws and
other logical equivalences.
2.7
Determine validity of arguments containing
using Euler diagrams.
2.8 Determine validity of arguments containing
using truth tables.
2.9 Recognize valid argument forms and invalid
2.10 Identify contributions and achievements of
mathematicians.
quantified statements,
compound statements,
argument forms.
various
3. CONSUMER MATHEMATICS
Simple and compound interest; installment loans, credit arrangements,
and finance charges; annual percentage rates; mortgage payments and
repayment schedules.
Student Outcomes:
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
Solve applied problems involving percent increase and decrease.
Calculate simple interest and maturity values for a loan.
Determine final amounts on deposit and interest earned on
accounts involving compound interest.
Determine present value of investments involving compound
interest.
Determine annual percentage rate on a loan.
Calculate interest on credit cards using: unpaid balance method;
previous balance method; average daily balance method.
Calculate monthly mortgage payments for a home loan, and use this
information to determine total cost of interest for the loan.
Prepare a loan amortization schedule.
4. GEOMETRY
Lines, angles, and polygons; computation of lengths, areas, and volumes;
Pythagorean Theorem; similar triangles.
Student Outcomes:
4.1
4.2
4.3
4.4
4.5
Classify angles as acute, right, obtuse, or straight.
Classify triangles as equilateral, isosceles, or scalene.
Classify quadrilaterals by type.
Classify polygons by number of sides.
Solve problems involving angle measurement using angle
relationships and angle sum formulas.
4.6 Find lengths of missing sides in similar triangles, using
proportions.
4.7 Find lengths of missing sides in right triangles, using the
Pythagorean Theorem.
4.8 Find perimeters and areas of two-dimensional figures, including
compound figures.
4.9 Find volumes of three-dimensional figures.
4.10 Solve applied problems using perimeter, area, and volume.
4.11 Identify contributions and achievements of various
mathematicians.
5. STATISTICS
Tables and graphs; measures of central tendency; measures of variation;
percentiles; z-scores; normal distribution.
Student Outcomes:
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
Construct a frequency distribution for a set of data.
Draw the histogram representing a distribution.
Draw the frequency polygon representing a distribution.
Draw a stem-and-leaf plot for a set of data.
Identify deceptions in visual displays of data.
Calculate mean, median, mode, and midrange for a set of raw data.
Calculate mean and median for data in a frequency table.
Calculate range and standard deviation for a set of raw data.
Compare data from two different scales by converting the data
values to z-scores.
5.10 Find percentages of normally distributed data falling in various
ranges using the 68-95 Rule and the Normal Table.
TEACHING GUIDE
TITLE:
Concepts in Mathematics
CATALOG NUMBER:
MA108
CREDIT HOURS:
3
LAB HOURS:
0
PREREQUISITES:
An appropriate placement test result or
MA090 Essential Math Skills or MA091
Introductory Algebra.
CATALOG DESCRIPTION:
This course is a survey of mathematics for
students in those programs that do not
require a mathematics sequence. It provides
an appreciation of mathematical ideas in
historical and modern settings. Topics
include problem solving, logic, geometry,
statistics, and consumer mathematics.
TEXT:
Thinking Mathematically, Blitzer, Robert, Prentice-Hall, Fourth
Custom Edition, 2014
CALCULATOR USAGE:
The student is required to have and use a scientific calculator with an
exponent key.
Chapter 1
1.1
1.1A
1.2
1.3
5 hours
Inductive and Deductive Reasoning
Exploring Number Patterns
Estimation, Graphs and Mathematical Models
Problem Solving
Chapter 3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
Problem Solving and Critical Thinking
Logic
8 hours
Statements, Negations, and Quantified Statements
Compound Statements and Connectives
Truth Tables for Negation, Conjunction, and Disjunction
Truth Tables for the Conditional and the Biconditional
Equivalent Statements and Variations of Conditional Statements
Negations of Conditional Statements and DeMorgan’s Laws
Arguments and Truth Tables
Arguments and Euler Diagrams
Chapter 8 Consumer Mathematics and Financial Management
8.1
8.2
8.3
8.4
8.5
8.6
7 hours
Percent
Simple Interest
Omit: example 4 (Determining a Simple Interest Rate) and
example 6 (A Discounted Loan)
Compound Interest
Optional: Continuous Compounding
Installment Buying
Omit: Unearned Interest, the Actuarial Method, the Rule of 78,
and Early Loan Payoff
The Cost of Home Ownership
Omit: Computing Monthly Mortgage Payments Using a Formula
(omit)
Chapter 10 Geometry
8-9 hours
10.1 Points, Lines, Planes, and Angles
10.2 Triangles
10.3 Polygons, Perimeter, and Tessellations
Optional: Tessellations
10.4 Area and Circumference
10.5 Volume and Surface Area
Omit: Surface Area
10.6 (omit)
10.7 (omit)
Chapter 12 Statistics
8-9 hours
12.1
12.2
12.3
12.4
Sampling, Frequency Distributions, and Graphs
Measures of Central Tendency
Measures of Dispersion
The Normal Distribution
Omit: all content in this section after example 5 (this includes
Percentiles and Quartiles, Polls and Margins of Error, and Other
Kinds of Distributions)
12.5 Problem Solving with the Normal Distribution
12.6 (omit)
This teaching guide allows 4 hours for the in-class assessment of
student learning. A two-hour comprehensive final examination will
also be given.