Download NONCREDIT COURSE OUTLINE: HSMTH 42 Last Revised and Approved: 11/06/2009

NONCREDIT COURSE OUTLINE: HSMTH 42
Last Revised and Approved: 11/06/2009
HSMTH 42 - CONTEMPORARY MATHEMATICS 2
Total Hrs Lecture
50.00
0.00
Total Hrs Lab
Total Course Hrs
Total Student Hrs
High School Credits
COURSE DESCRIPTION
This course gives students the opportunity to examine the many different ways mathematics is used in the “real” world. This course
requires logic, creative thinking, and problem-solving techniques as well as some basic algebra and geometry skills. Students
investigate sophisticated mathematical applications in life science, social science, business, management, and economics. Topics
include symmetry and growth in nature, probability, and statistics. (May be repeated once.)
ENROLLMENT RESTRICTIONS
PREREQUISITES
COREQUISITES
ADVISORIES
OUTLINE OF COURSE CONTENT
The course will address the following topics:
I. Growth and symmetry
A. Spiral growth in nature
1. Fibonacci numbers
2. Quadratic formula
3. Equivalent equations
4. Golden ratio
5. Similarity.
B. Symmetry
1. Reflections
2. Rotations
3. Translations and glide reflections.
C. Fractal geometry
1. Koch Snowflake
2. Sierpinski Gasket
3. Recursive replacement
4. Boundary and area.
II. Statistics
A. Collecting statistical data
1. Population
2. Samples
3. Surveys
4. Bias
5. Public opinion polls
6. Clinical studies.
B. Descriptive statistics
1. Graphical descriptions of data
2. Data points
3. Variables
4. Numerical summaries of data
5. Measures of spread
6. Standard deviation.
C. Chances, probabilities, and odds
1. Random experiments and sample spaces
2. Counting: multiplication rule
MIRACOSTA COLLEGE
HSMTH 42 COURSE OUTLINE
--FOR COMPLETE OUTLINE OF RECORD SEE MCC WEBCMS DATABASE-Page 1 of 3
50.00
99.50
5.00
NONCREDIT COURSE OUTLINE: HSMTH 42
Last Revised and Approved: 11/06/2009
3. Permutations and combinations
4. Probability assignment
5. Impossible vs. certain events
6. Independent events.
PERFORMANCE OBJECTIVES
Upon successful completion of this course, students will be able to do the following:
Growth and symmetry
1). Use recursion algorithms to define the Fibonacci sequence
2). Calculate Fibonacci numbers
3). Apply the Quadratic Formula
4). Solve the equation x^2 = x + 1 and define the Golden Ratio
5). Calculate the area and perimeter of similar shapes
6). Explain what is meant by a gnomon
7). Calculate the necessary lengths needed to create a gnomon
8). Determine whether or not rectangles and triangles are “golden”
9). Determine what type(s) of symmetry a two-dimensional object may have
10). Find the image of an object after applying any of the four basic rigid motions in the plane.
Fractal geometry
1). Use recursive replacement rules to approximate simple fractals
2). Identify self-similarity in a fractal
3). Calculate the boundary and area of the Koch Snowflake and Sierpinski Gasket.
Statistics
1). Differentiate between a population and a sample
2). Calculate sample and response rates
3). Analyze a sampling example to detect sources of bias
4). Analyze a clinical study to determine the type (e.g., controlled, randomized, blind, double-blind)
5). Describe the placebo effect
6). Calculate the median, mean, and first and third quartiles of a data set
7). Calculate the range and interquartile range of a given data set
8). List the five-number summary for a given data set and construct a box plot
9). Find the standard deviation for a small data set
10). Differentiate between a measure of spread and a measure of location.
Probability
1). Describe the sample space for a given event
2). Explain what is meant by the probability of an outcome
3). Apply the multiplication rule
4). Apply the laws of probability to determine the validity of a probability space
5). Compute the probability of an event when the probability space of the experiment is given
6). Identify the different situations in which permutations or combinations are used.
ASSIGNMENTS
Assignments will be consistent with, but not limited by, the following types and examples:
1). Practice using recursion algorithms to define the Fibonacci sequence
2). Determine whether or not rectangles and triangles are “golden”
3). Practice calculating the median, mean, and first and third quartiles of a data set of data
4). Practice computing the probability of an event when the probability space of the experiment is given.
Outside-of-class assignments are required and may include, but will not be limited to, the following:
1). Complete homework assignments from the textbook and teacher-generated worksheets
2). Write solutions to take-home test problems using logical, well-organized steps.
MIRACOSTA COLLEGE
HSMTH 42 COURSE OUTLINE
--FOR COMPLETE OUTLINE OF RECORD SEE MCC WEBCMS DATABASE-Page 2 of 3
NONCREDIT COURSE OUTLINE: HSMTH 42
Last Revised and Approved: 11/06/2009
STUDENT LEARNING OUTCOMES
Learning Outcome
Mode of Assessment
1. Identify relationships between the Fibonacci sequence and
the golden ratio.
1. A written performance task e.g., word problem, will be
assessed utilizing a departmental rubric.
2. Describe the process by which a fractal is constructed.
2. A written performance task e.g., word problem, will be
assessed utilizing a departmental rubric.
3. Predict outcomes based on probabilistic models.
3. A written performance task e.g., word problem, will be
assessed utilizing a departmental rubric.
METHODS OF INSTRUCTION
Instructional methodologies will be consistent with, but not limited by, the following types or examples:
1). Direct instruction
2). Investigation
3). Classroom discussion and drill
4). Small groups
5). Individualized formats
6). Hands-on material.
METHODS OF EVALUATION
Evaluation methodologies will be consistent with, but not limited by, the following types or examples:
1). Homework and quizzes
2). Unit tests
3). Participation and contributions to class activities.
REQUIRED TEXTBOOKS
Examples of typical textbooks for this course include the following:
1). Tannenbaum, Peter. Excursions in Modern Mathematics. 5th ed., Prentice Hall, 2004. ISBN: 0131001914
OTHER REQUIRED INSTRUCTIONAL MATERIALS
1). Scientific calculator
2). Graph paper
3). Colored pencils.
COURSE REPEATABILITY
Total Completions Allowed:
In Combination With:
2
MIRACOSTA COLLEGE
HSMTH 42 COURSE OUTLINE
--FOR COMPLETE OUTLINE OF RECORD SEE MCC WEBCMS DATABASE-Page 3 of 3