Download For assessment purposes, these are linked to #7. Recommended

Maui Community College
Course Outline
1. Course Title:
MATH 23
Number of credits:
3
Abbreviated Course Title:
Practical Algebra
Date of Outline:
March 25, 2004
2. Course Description:
Prepares student for math courses that are noncalculus based. Reviews basic algebraic skills,
estimation, the use of a calculator and basic
geometry. Teaches simplifying algebraic
expressions, basic descriptive statistics, solving
simple rational equations, graphing linear
equations and inequalities in two variables,
solving systems of equations in two variables,
using the calculator to simplify radicals, using
the quadratic formula to solve quadratic
equations, and graphing quadratic equations.
Uses mathematical skills to solve application
problems.
3. Credits/ Contact Hours:
3 hours / lecture-individualized study
4. Prerequisites:
MATH 22 with at least a C or placement at
MATH 23 and ENG 19 with at least a C or
registration in ENG 22/55, or consent.
Co-requisites:
Recommended Preparation:
At least 10th grade reading skills
Approved by______________________________Date_______________
5. General Course Objectives:
Prepares student for math courses which are noncalculus based. Reviews basic algebraic skills, estimation, the use of a calculator
and geometry. Teaches simplifying algebraic expressions, basic descriptive
statistics, solving simple rational equations, graphing linear equations and
inequalities in two variables, solving systems of equations in two variables, using
the calculator to simplify radicals, using the quadratic formula to solve quadratic
equations, and graphing quadratic equations. Uses mathematical skills to solve
application problems.
6. Specific Course Competencies:
For assessment purposes, these are linked to #7. Recommended Course Content.
On successful completion of this course, students will be able to:
a.
round rational numbers and estimate sums, differences, products
and quotients
b. perform operations with real numbers including rational numbers
c. simplify expressions using the rules for order of operations
d. simplify expressions with variables and several parentheses
e. solve equations in one variable, including equations with several
parentheses
f.
solve application problems including equations with several
parentheses
g. solve inequalities in one variable, including inequalities with
several parentheses
h. solve application problems using inequalities in one variable
i.
solve formulas for one of the variables
j.
convert from one measurement into another in both the Metric and
the American Systems, including converting linear measures,
measures for capacity, and measures for mass (Converting within
each system is covered, but conversions from one system to
another is not covered)
k. find the perimeters and areas of rectangles, squares, triangles,
parallelograms and trapezoids
l.
find the circumference and area of a circle
m. find the perimeter and area of figures that are a combination of parts of
rectangles, squares, triangles, parallelograms, trapezoids, and circles
n. find the volume of rectangular solids, cubes, right circular cylinders,
right circular cones, and spheres
o. compute mean, median, and mode of a list of numbers
p. draw bar and line graphs
q. interpret information from bar, line, and circle graphs
r. identify the quadrants of a Cartesian coordinate system
s. graph points on a Cartesian coordinate system
t.
graph linear equations, including horizontal and vertical lines and applications
u. graph a line using its intercepts
v. define exponents
w. simplify expressions with exponents, using the product, quotient and
power rules
x. convert decimal notation to scientific notation and vice versa
y. compute problems using scientific notation, including application problems
z. evaluate polynomials, including polynomials in several variables
aa. collect like terms in a polynomial
bb.
cc.
dd.
ee.
ff.
organize a polynomial in ascending or descending order
identify the degree of a term and the degree of a polynomial
classify polynomials as monomials, binomials, or trinomials
add, subtract, and multiply polynomials, including polynomials in several variables
solve simple rational equations, where the denominators donot involve any factoring
of polynomials
gg. find the slope and intercepts of a linear equation from an equation of the line
hh. find the slope of a line when given two points on the line
ii. find the equation of a line when given two points on the line
jj. write the equation of a line in slope/y-intercept form
kk. determine if two lines are parallel, perpendicular, or neither parallel nor
perpendicular, given the equations of the lines
ll. graph inequalities in two variables
mm.solve problems involving direct variation
nn. solve systems of equations in two variables by graphing, elimination, and substitution
methods
oo. solve application problems involving age, numbers, mixture, coin, perimeter,
complementary and supplementary angles, and motion problems using systems of
equations in two variables
pp. definition of square root, the use of a calculator to determine an
approximation of a square root
qq. use a calculator to add, subtract, multiply, and divide radicals
and determining an approximate answer (to the nearest
thousandths), where none of the radicands have variables in them
rr. solve simple radical equations (none that result in quadratic equations)
ss. use the Pythagorean Theorem to solve application problems
tt. identify quadratic equations and write in standard form, solve quadratic
equations using only the quadratic formula
uu. use quadratic equations to solve application problems
vv. graph quadratic equations
7. Recommended Course Content and Approximate Time Spent
Linked to #6. Student Learning Outcomes.
A. Review of Pre-algebra (1 week)
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
l)
m)
n)
o)
Rounding and estimating (a)
Performing operations with real numbers including rational numbers
by using the rules for order of operations (b, c)
Simplifying expressions with variables (d)
Solving equations and using them in applications, (including
equations with parentheses) (e, f)
Solving inequalities and using them in applications (g, h)
Solving formulas for one of the variables (i)
Measurement - American and Metric; measures for linear, capacity,
weight, and mass (Conversions within each system are covered, but
conversions from one system to another are not covered) (j)
Geometry - areas and perimeters of rectangles, squares, triangles,
parallelograms, and trapezoids, circumference and area of circles,
and volumes of rectangular solids, cubes, right circular cylinders, right
circular cones, and spheres (k, l, m, n)
B. Descriptive statistics and graphing (2 weeks)
a) Averages, Medians and Modes (o)
b)
c)
d)
e)
f)
g)
h)
i)
Bar and Line Graphs (p)
Circle Graphs (q)
Applications with circle, bar, and line graphs (q)
Graphing points, identifying quadrants, and finding coordinates of points (r, s)
Graphing linear equations and identifying the y-intercept (t)
Applications of linear equations (t)
Graphing using the x and y-intercepts (u)
Graphing horizontal and vertical lines (t)
C. Simplifying algebraic expressions and solving simple rational
equations (2 weeks)
a) Review of the definition of exponents and the product, quotient, and power rules
(v, w)
b) Scientific Notation and its applications (x, y)
c) Evaluating polynomials, collecting like terms, descending and ascending order,
degree of and classifying polynomials (z, aa, bb, cc, dd)
d) Adding, subtracting, and multiplying polynomials (ee)
e) Evaluating, adding, subtracting and multiplying polynomials in several variables
(ee)
f) Solving simple rational equations where the denominators do not involve
factoring a polynomial (ff)
D. Graphs, slopes and applications (3 weeks)
a) Equations of lines – finding the slope and y-intercept of a line given the equation
and vice versa, finding an equation of a line when the slope and a point are
given, finding the slope of a line given two points, finding the equation of a line
given two points (gg, hh, ii, jj)
b) Parallel and perpendicular lines (kk)
c) Graphing inequalities in two variables (ll)
d) Direct variation and its applications (mm)
E. Systems of Equations (2 weeks)
a)
b)
c)
d)
Solving systems of equations by graphing (nn)
Solving systems of equations by substitution (nn)
Solving systems of equations by elimination (nn)
Solving application problems involving age, numbers, mixture, coin, perimeter,
complementary and supplementary angles, and motion problems using systems
of equations (oo)
F. Radical Equations and Quadratic Equations (5 weeks)
a)
b)
c)
d)
Definition of square roots, radical, and radicand (pp)
Using a calculator to determine an approximation of a square root (pp)
Applications of square root (pp)
Using a calculator to add, subtract, multiply, and divide radicals (with no variables
in them) and getting an approximate answer (to the nearest thousandths) (qq)
e) Solving simple radical equations (none that result in a quadratic) (rr)
f) Pythagorean theorem and its applications (ss)
g) Identifying a quadratic equation and writing it in standard form (tt)
h) Solving quadratic equations by using the quadratic formula (noother methods of
solving are taught) (tt)
i) Using quadratic equations to solve application problems (uu)
j) Graphing quadratic equations (vv)
8. Recommended Course Requirements:
Recommended course requirements include regularly assigned homework problems for
practice, along with regular quizzes, unit tests, and a final exam.
9. Text and Materials:
An appropriate text(s) and materials will be chosen at the time the course is to be offered
from those currently available in the field. Examples include:
Developmental Mathematics, Fifth Edition, Marvin Bittinger and Judith
Beecher, Addison-Wesley Publishing Company, 2000
Supplementary handouts on using a calculator to determine the square root
of a number and on graphing quadratic equations may be included, if necessary
Optional textbook: Student Solutions Manual for the above textbook
10. Evaluation and Grading:
A student's grade in the course is determined by computing an average of the semester's
course work which would include the quizzes (5% - 15%), the unit tests (55% - 65%), and the
final exam (25% - 35%). It is not appropriate to evaluate student competency in a
mathematics course by using only a midterm and final exam. The homework may be included
in the final grade (0% - 5%).
In the math department, grades are usually assigned according to the
following scale:
90% - 100% = A
80% - 89% = B
70% - 79% = C
60% - 69% = D
0% - 59% = F or N
The student may select to receive a "credit/no credit" for the course instead
of a letter grade. If he/she wishes to select this option, he/she must inform
the instructor.
Some flexibility is given to instructors in these matters. Each instructor will
clearly inform students on his/her syllabus what the forthcoming course
work will entail and how it will be weighted and graded respectively.
11. Methods of Instruction:
This course may be taken as a lecture class or in an individualized study math lab. In the
lecture class, use is made of cooperative learning, lecture sessions involving much student
participation and feedback, self-checking homework assignments, frequent quizzes and tests
to inform students of their progress and a final exam at the end of the.
In the individualized study lab class, similar methods of instruction are used, but in place of
the lecture sessions, the students work for short periods of time one-on-one with an
instructor or tutor. The student would be expected to learn more on his/her own by reading
the textbook and watching videotapes of the lessons.