Syllabus
Platte
Canyon High School: Algebra 3
Instructor:
Debbi Marks
Fall,
2001
General Information
This
class meets every school day for 90 minutes from 7:25 to 9:05.
Instructor Information
Debbi
Marks
Platte
Canyon High School, Room 215
303-838-4642
Ext 219
email:
debbimarks@uswest.net
I
am available before school, after school and during 3rd period.
You may drop in or make an appointment to see me if you need extra help
or for any other reason.
Course Prerequisites
Algebra
2 with a grade of “C” or better.
Textbook
Advanced
Algebra Through Data Exploration
by Jerald Murdock, Ellen and Eric Kamischke.
Objectives
This course is an academically challenging program that
has been designed with the following objectives:
•
To be able to work with mathematics that may be represented graphically,
numerically, analytically or verbally and understand the connections among these
representations.
•
To be able to model problem situations with functions.
•
To read, analyze, and solve challenging problems.
•
To work and communicate effectively in groups.
•
To prepare for various standardized tests such as ACT, SAT and CSAP.
Classroom
Procedures and Grades
Instruction in the Algebra 3 will include a variety of
activities. Lecture and discussion,
calculator explorations, lab activities, and guided practice will all be used
regularly. Students are expected to
actively participate in all of these activities. Class discussion is important to assist understanding and to
build on the ideas of classmates.
Frequent tests and quizzes will be used to monitor the
progress of students. “Pop”
quizzes will be given regularly to ensure that students keep up with their work
and understanding. Most tests will
contain two section, one non-calculator and the other will be calculator active.
Grades will be based on the accumulation of points.
Homework will be worth 5 – 10 points for each assignment.
Quizzes range from 10 – 40 points.
Tests range from
60 – 145 points. Other
activities and assessments will be given points as well.
No late work will be accepted.
Materials
pencils, red grading pen, TI-83 or TI-83 Plus graphing
calculator, loose-leaf binder, notebook paper, graph paper
Calculators
A graphing calculator is essential for this class.
Each student may borrow a calculator each day that must be returned at
the end of the period. If students need to borrow a calculator overnight, checkout
can be arranged. We will be using
TI-83+ calculators throughout the course. If
you wish to purchase a calculator, one option is Wholesale Electronics
(1-800-880-9400). This company has them for sale for $95.00 and $6.00 for
shipping as of August 25, 2001. They
accept MC and VISA. Best Buy in
Denver has them for $84.00 plus tax as advertised in the paper recently.
Expectations
•
You
are expected to assume responsibility for your own learning.
You are expected to ask questions to clarify your understanding and to
enhance your learning experience.
•
You are expected to attend class and be on time.
•
All assignments must be turned in. All
homework is due the next day. Late
assignments will not receive credit but must be turned in.
•
Homework and tests must be done
in pencil. You will grade
your
homework with a different color pen.
•
You are expected to actively participate in classroom discussion and
activities.
•
Each student must bring their materials (paper, pencils, red pen, book,
calculator) to class each day to be prepared.
•
Each student is expected to keep and organized notebook with all of their
materials. This should be brought to class every day.
•
Any test grade of lower than a C must schedule a conference within the
next 24 hours to correct mistakes and relearn the material.
Course Objectives
I.
Patterns and Recursion
A.
Recognize and visualize mathematical patterns.
B.
Use and write recursive definitions for arithmetic geometric and other
sequences.
C.
Write and use recursive routines to model real-world sequences.
D.
Experiment with the concept of a limit of a sequence.
E.
Predict and identify limits of real-world sequences.
F.
Display, organize and visualize sequences with graphs.
G.
Represent graphs of sequences as discrete graphs.
H.
Identify similarities and differences between sequences and series.
I.
Find the sum of recursively defined sequences.
J.
Recognize and use different representations of sequences and series.
II.
Sequences, Series and Explicit Formulas
A.
Find an use explicit formulas to describe arithmetic sequences.
B.
Explore, compare and contrast arithmetic recursive definitions, explicit
formulas and linear graphs and equations.
C.
Recognize the difference between arithmetic sequences and series.
D.
Find and use explicit formulas for arithmetic series.
E.
Find and use explicit formulas to describe geometric sequences.
F.
Explore, compare and contrast geometric recursive definitions, explicit
and related graphs.
G.
Recognize the difference between geometric sequences and series.
H.
Find the sums of infinite series.
I.
Find limits of infinite sequences.
J.
Investigate and create fractal patterns.
III.
Rational Functions
A.
Use real world examples and patterns to identify rational
functions.
B.
Graphs, Tables, and Equations
1.
Graph rational functions by paper-and-pencil,
calculator, and/or computer.
2.
Solve problems involving rational situations.
3.
Experiments (problem solving)
a.
Design and conduct an experiment.
b.
Collect and analyze the data.
c.
Graph the data and find the curve of best fit.
4.
Discuss exponent rules, complex fractions and
clearing fractions.
C.
“A”, Intercepts, Asymptotes, and Symmetry
1.
Discuss “a” and rate of change for rational functions.
2.
Using graphs and tables, find the intercepts of
rational
functions.
3.
Discuss symmetry for rational functions.
4.
Discuss asymptotes and limits and their impact on domain and range.
D.
Rational Equations and Functions
1.
Derive rational functions from graphs, tables, and
situations.
2.
Analyze rational functions from equations, graphs,
tables, and situations.
3.
Find the zeros graphically and the roots algebraically.
4.
Identify rational equations as inverse variations.
5.
Recognize the different forms (proper and improper) of
rational
equations and convert (long divide or
multiply) between them.
E.
Analyze and explain the behaviors, transformations, and
general properties of rational functions from algebraic,
graphic, and tabular approach.
F.
Systems of equations
1.
Linear and Rational
a.
Solve systems of linear and rational equations
graphically.
b.
Solve systems of linear and rational equations algebraically.
2.
Quadratic and Rational
a.
Solve systems of quadratic and rational equations graphically.
b.
Solve systems of quadratic and rational equations algebraically.
G.
Compare and contrast rational functions with previously learned
functions.
IV.
Exponential and Logarithmic Functions
A.
Use real world examples, patterns, and finite differences (tables) to
identify exponential and logarithmic functions.
B.
Graphs, Tables, and Equations
1.
Graph exponential and logarithmic functions by paper-and-pencil,
calculator, and/or computer.
2.
Solve problems involving exponential and logarithmic situations.
3.
Experiments (problem solving)
a.
Design and conduct an experiment.
b.
Collect and analyze the data.
c.
Graph the data and find the curve of best fit.
4.
Develop tables for exponential functions and discuss the meaning of
negative exponents and exponent rules for operations.
5.
Investigate the rules for logarithms.
C.
“A”, Intercepts and Symmetry
1.
Discuss “a” and rate of change for exponential and logarithmic
functions.
2.
Using graphs and tables, find the intercepts of exponential and
logarithmic functions.
4.
Discuss symmetry around the line y = x for inverse functions.
(i.e. for exponential and logarithmic functions)
5.
Discuss asymptotes and limits.
D.
Exponential and Logarithmic Equations
1.
Derive exponential and logarithmic equations from graphs, tables, and
situations.
2.
Analyze exponential and logarithmic functions from equations, graphs,
tables, and situations.
3.
Find the zeros graphically.
E.
Analyze and explain the behaviors, transformations, and general
properties of exponential and logarithmic functions from a symbolic, graphic,
and tabular approach.
F.
Systems of equations
G.
Compare and contrast exponential and rational functions with
previously
learned functions.
H.
Apply the properties of exponents.
V.
Triangle Trigonometry and Parametric Equations
A.
Use degrees to measure angles.
B.
Define trigonometric functions of acute and general angles.
C.
Use trigonometric tables to find values of trigonometric functions.
D.
Find the sides and angles of a right triangle.
E.
Use the law of cosines to find sides and angles of triangles.
F.
Use the law of sines to find sides and angles of triangles.
G.
Solve any given triangle.
H.
Apply triangle area formulas.
I.
Simulate objects in motion by writing appropriate parametric equations
and setting conditions that allow control of the movement of a point across the
calculator screen.
J.
Algebraically manipulate equations to convert between parametric and
Cartesian form.
K.
Find different parametric equations and the nonparametric equation that
correctly represent a graph.
VI.
Analytic Geometry
A.
Find the distance between any two points and the midpoint of the line
segment joining them.
B.
Learn the relationship between the center and radius of a circle and
the equation
of the circle.
C.
Learn the relationship between the focus, directrix, vertex and axis of
a
parabola and the equation of the parabola.
D.
Learn the relationship between the center, foci and intercepts of an
ellipse and the equation of the ellipse.
E.
Learn the relationship between the foci, intercepts and asymptotes of
a
hyperbola and the equation of the hyperbola.
F.
Use graphs to determine the number of real solutions of a quadratic
system and estimate the solution.
G.
Use algebraic methods to find exact solutions of quadratic systems.
Solve
systems of linear equations in three variables.
VII.
Discrete Math and Probability
A.
Explore the meaning of randomness.
B.
Use simulations and experimental evidence to develop initial probability
concepts.
C.
Understand and use geometric probability as a model for solving
probability problems.
D.
Develop strategies for counting and calculating random selection
outcomes.
E.
Examine the differences between experimental and theoretical probability.
F.
Use tree diagrams and the counting principle as organizational strategies
for counting
G.
Apply strategies involving permutations.
H.
Recognize counting strategies that involve combinations.
I.
Calculate
and
and understand the relationship
between each.
J.
Calculate standard deviation from a set of data.
Web Site
I
have created a web site that has an Algebra 3 section and links to useful sites.
The web site is located at
https://plattecanyonms.tripod.com/
and the algebra section can be found under my name.