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Introduction
What is the 'Fundamental Theorem
of Algebra', whom did it come from, and what is it good for?
Subject:Mathematics
Topic: Fundamental Theorem of Algebra
Grade Level:10-12
Student Lesson
 Standards Addressed
10th-12th Grade Mathematical
Analysis:
Fundamental Theorem of Algebra
4.0 Students
know the statement of, and can apply, the fundamental theorem of algebra.
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Instructional Objectives
- After exploring available resources related to
the topic, the student will be able to identify the Fundamental Theorem
of Algebra.
- The student, after studying and practicing
proper application of the Fundamental Theorem of Algebra will be able to
give examples demonstrating comprehension of the Fundamental Theorem of
Algebra.
- Students will be able to determine whether or
not a given algebraic expression is completely factored by applying the
Fundamental Theorem of Algebra to a variety of polynomial expressions.
- The student will be able to break down a given
polynomial into its component parts (factors) and be able to
differentiate linear from irreducible quadratic factors.
- The student will be able to synthesize
knowledge of previously learned topics to the Fundamental Theorem of
Algebra when faced with applicable problems. Students will be able
to express and validate the irreducibility of quadratic factors and
multiciplicity of factors by the application of graphical analysis or
through analysis of the discriminant.
- The student will be able to evaluate a given
polynomial function in such a way that he/she can justify and support
statements of complete factorization, real and imaginary roots, and
graphical expression of the function.
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Student Activities
Pre-Test
Post-Test
Introductory
Activity
The students will explore a web-based equation solver, factoring, and
graphing programs. They will be given appropriate problems to solve,
factor, and graph.
Math.com's
equation solver & factoring page
Enabling Activities
The students will find, read and explore internet sites related to the
Fundamental Theorem of Algebra. Using resources of their choice, they
will apply the FTA to given polynomial equations verifying their conclusions
using multiple approaches.
SOS
Math 's Fundamental Theorem of Algebra
FTA
(mathworld)
www.und.nodak.edu/dept/math/history/fundalg.htm
www-groups.dcs.st-and.ac.uk/~history/HistTopics/Fund_theorem_of_algebra.html
Interactive
Learning Network (FTA & Descartes Rule of Signs)
Culminating Activity
The students will (in teams) present their findings on the 'who,when,where,
what, and why' of the Fundamental Theorem of Algebra. This will include
the presentation of computer generated graphs relating to equations chosen by
the students to demonstrate the application of the FTA. The students
will also take a post test.
Pre-Test (word 2000 doc
windows)
Pre-Test (web page)
Post-Test (word 2000 doc windows)
Post-Test
(web page)
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Assessment
The grading rubric for the student team presentation is as follows:
For each of the criteria listed, students will receive
a score from 1-4:
(1=needs improvement, 2=basic,
3=proficient, 4=exemplary)
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The student team demonstrates:
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1
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2
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3
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4
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Definition of the FTA,
(who, when, what, where)
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Appropriate examples
demonstrating the FTA
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Usefulness of the FTA
(why)
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Impromptu demonstration
of FTA to teacher given problem
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Synthesis -- Relates FTA
to other/previous topics
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The post-test will be graded on a straight raw score and compared to the
pre-test to determine improvemnt toward achieving the standard.
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Results
After implementing your lesson (sometime
between January & March), insert a chart of your pre-test, post-test, and
culminating assessment data.
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Web Resources & Supplementary Materials
Pre-Test
Post-Test
Math.com's
equation solver & factoring page
SOS
Math 's Fundamental Theorem of Algebra
FTA
(mathworld) very technical
www.und.nodak.edu/dept/math/history/fundalg.htm
www-groups.dcs.st-and.ac.uk/~history/HistTopics/Fund_theorem_of_algebra.html
Interactive
Learning Network (FTA & Descartes Rule of Signs)
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Red Bluff Joint Union High School
Red Bluff, California
Kevin Penner
Last Revised: 07/20/2000
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