COURSE DESCRIPTION: (for catalog)
This is a technical mathematics course for students in selected professional
technical programs. Topics
covered include graphs and equations of lines, applications of linear models and
solving literal equations ,
extensive geometry including angle relationships, surface area and volume of
three-dimensional figures,
right triangle trigonometry, and basic statistics. Emphasis is placed on
modeling problem situations
numerically, visually, graphically and/or algebraically. In-depth problems from
various fields are a core
part of the curriculum. A graphing calculator is required and integrated
throughout.
PREREQUISITE:
Math 60 with a C or better, or suitable performance on the mathematics placement
exam.
INSTRUCTIONAL MATERIALS REQUIRED OF STUDENT: (text, supplies, etc.)
Text, TI-83 or TI-83+ Graphing Calculator, Engineering Paper, Protractor, 15-cm.
ruler.
STUDENT LEARNING OUTCOMES:
Upon successful completion of this course, the student will be able to:
1. Overarching Objectives
Goal: Create capable problem solvers and creative
learners able to deal with real-world mathematics and
communicate at this level.
a) Communicate effectively (orally and in writing) a
problem solving process, results, and conclusions using
mathematical terminology and correct mathematical syntax appropriate to the
level of study.
b) Apply mathematical reasoning and modeling to solve
problems arising from the real world .
c) Model problem situations using mathematics verbally,
numerically, visually, graphically, and/or
algebraically, and make connections among the four models as appropriate at this
level.
d) Determine if a solution is reasonable and verify
results.
e) Use skills from previous courses in problem solving and
application situations (especially area, Cartesian
coordinates, ratios, Proportions , formulas, and unit conversions).
2. Equations
Goal: Develop fluency in algebraic processes at this
level
a) Distinguish between expressions and equations , between
simplifying and solving.
Factoring
a) Factor out common factors in a multi-term algebraic expression.
Solving Literal Equations
a) Solve literal equations and formulas for a first- degree variable . The
solving process should include monic
factoring.
Verify literal solutions using numerical substitution .
3. Linear Relationships
Goal: Engage students in problem solving that
incorporates their past geometrical knowledge as well as threedimensional
geometry and coordinate geometry.
Three-Demensional Figures
a) Calculate lateral area, surface area and volume of
prisms, cubes , cylinders, cones, pyramids, spheres and
combined solids in applications.
Coordinate Geometry
a) Define and apply latitude and longitude to identify a
point on a map.
b) Locate a point in the plane using polar coordinates.
c) Convert between polar and rectangular coordinate representations.
4. Trigonometry
Goal: Develop fluency in solving problems involving
angles and right triangle trigonometry.
Angles
a) Measure angles using a protractor and estimate the
measurement of angles.
b) Identify and define straight, right, acute, obtuse, and co terminal angles.
c) Convert between decimal degrees and degrees, minutes, seconds.
d) Construct geometric figures with specific length and angle measurements using
a protractor and a ruler .
e) Create scale drawings and report and scale of the drawing.
f) Use the properties of similar triangles to solve application problems.
g) Determine unknown angles in geometric figures using the principles of
complementary, supplementary, adjacent,
opposite, alternate interior, and corresponding angles; and parallel and
perpendicular lines.
h) Solve triangles using properties of equilateral, right and isosceles
triangles.
i) Determine missing angles in polygons given sufficient information.
j) Distinguish between an angle in “standard position” and a bearing angle.
Right Triangle Trigonometry
a) Define radians and use radians to solve applications
involving arc length, sector area, and angular velocity.
b) Convert between radians and degrees.
c) Define all six trigonometric relationships based on a right triangle.
d) Evaluate sine, cosine and tangent ratios for interior angles of a right
triangle given sufficient information.
e) Solve for any part of a right triangle given sufficient information.
f) Model real-world problems using the right triangle trigonometric definitions.
Include problems involving percent
slope .
5. Statistics
Goal: Foster familiarity with the mean and measurements
of variation in context.
a) Define and compute the mean of a set of data. Explain
the meaning of the mean in the context of a data set.
b) Define and compute the standard deviation, the coefficient of variation , and
the standard error of a data set.
Explain the meaning of each measurement of variation in the context of a data
set.
c) Explain how two sets of data ( one with large standard deviation and one with
small standard deviation) can have
the same mean.
d) Use the mean, standard deviation, coefficient of variation, and standard
error to describe data from a real-world
situation.
e) Given the mean, standard deviation, coefficient of variation, and standard
error from a real-world situation,
explain what these statistics mean.
GENERAL INSTRUCTIONAL METHODS:
Passing this course with a C or better serves as a prerequisite for Math 95.
Ensure that your grading plan will mean that
students satisfying this requirement are prepared for Math 95. This requires
attention to the amount of verifiable individual
work completed by the student. You must give a cumulative in-class final exam to
help ensure that students are truly prepared
for the next course.
EVALUATION PROCESS:
Grades should be based on a balanced variety of grading opportunities spread
throughout the term. Although you may not
choose to use every method below, a variety of methods is expected. Student
evaluation must include problems or activities
that incorporate and integrate several outcomes, and closely resemble situations
that exist in the real world.
• Worksheets
• Projects
• In-class In dividual Exams
• In-class Team Exams
• Take-Home Individual Exams
• Take-Home Team Exams
• Writing Assignments
• Daily Homework
• Attendance
• Teamwork/Participation
