ALGEBRA II
COURSE DESCRIPTION: This
course will help students to view algebra as a language of modeling the real
world through problem solving and using the language of manipulation symbols.
Students will make connections by integrating algebra, geometry, data analysis,
and other curricular areas. Student reasoning will involve linear equations and
inequalities; systems of linear equations and matrices; quadratic equations,
polynomial functions, rational expressions and functions; trigonometry; and
sequences and series.
COURSE
GOALS/OBJECTIVES/STANDARDS: The
standards for this course engage students in advanced algebraic concepts through
the study of functions, polynomials, complex matrices, and sequences and
series. The standards help students to view algebra as a language of modeling
the real world through problem solving and engaging authentic applications.
Graphing utilities should be used as tools to assist in problem solving and
verifying or developing solutions to equations. Students should be encouraged
to talk and write about mathematics, to use the language and symbols of algebra
to communicate, and to discuss problems and methods of problem solving. The
student produces evidence that demonstrates understanding of the following
standards:
a.
Uses numerical
operations, exponentiation and root extraction in forming and working with
algebraic expressions.
b.
Uses matrices to solve
systems of equations.
c.
Understands and uses
operations such as opposite, reciprocal, raising to a power, taking a root and
taking a logarithm.
d.
Understands and uses
number systems; natural, rational, irrational, imaginary, real and complex.
e.
Compares numbers using
order relations, differences, ratios, proportions, percents, proportional
change.
f.
Carries out counting
procedures such as those involving sets (unions and intersections) and
arrangements (permutations and combinations).
g.
Uses appropriate
technology effectively and efficiently in carrying out complex calculations.
M2: Geometry and
Measurement Concepts
a.
Models situations
geometrically to formulate and solve problems
b.
Compares slope (rise
over run) and angle of elevation as measures of steepness
c.
Investigates geometric
patterns, including sequences of growing shapes
d.
Represents geometric
curves and graphs of functions in standard coordinate systems
M3: Functions and
Algebra Concepts
a.
Models given situations
with formulas and functions, and interprets given formula and functions in
terms of situations
b.
Describes, generalizes,
and uses basic types of functions: linear, exponential, power, rational, square
and square root, cube and cube root
c.
Utilizes the concept of
slope, evaluation and inverse in working with functions
d.
With with rates of many
kinds expressed numerically, symbolically and graphically
e.
Uses arithmetic and
geometric sequences and their sums, and
sees these as the discrete forms of linear and exponential functions
f.
Defines, uses and
manipulates expressions involving variables, parameters, constants, and unknown
in work with fomula, functions, equations, and inequalities
g.
Represents functional
relationships in formulas, table, and graphs and translates between pairs of these
h.
Solves equations
symbolically, graphically, and numerically and knows how to use the quadratic
formula for solving quadratic equations
i.
Makes predictions by
interpolating or extrapolating from given data or a given graph
j.
Understands the basic
algebraic structure of number systems
k.
Uses equations to
represent curves such as lines, circles and parabolas
l.
Uses technology to
represent and analyze functions and their graphs
m.
Uses functions to
analyze patterns and represent their structure
n. Identifies conic sections and their properties to include parabolas, ellipses, and hyperbolas
M4: Statistics and Probability Concepts
a.
Organizes, analyzes, and
displays single-variable data choosing appropriate frequency distribution,
circle graphs, line plots, histograms, and summary statistics
b.
Organizes, analyzes, and
displays two-variable data using
scatter plots, estimated regressions lines, and computer-generated regression
lines and correlation coefficients
c.
Uses sampling techniques
to draw inferences about large populations
d.
Understands that making
an inference about a population from a sample always involves uncertainty and
that the role of statistics is to estimate the size of that uncertainty
e.
Interprets
representations of data, compares distribution of data, and critiques
conclusions and DoDea Curriculum Standards: 2000 Final Draft Mathematics uses
of statistics, both in school materials and public documents
f.
Explores questions of
experimental design, use of control groups, and reliablity
g.
Creates and uses models
of probabilistic situations and understands the role of assumptions in this
process
h.
Uses concepts such as
equally likely, sample space, outcome, and event in principles for
probabilities
i.
Constructs appropriate
sample spaces, and applies the addition and multiplication principles for
probabilities
j.
Chooses an appropriate
probability model and uses it to arrive at a theoretical probability for a
chance event
k.
Uses relative
frequencies based on empirical data to arrive at an experimental probability for a chance event
l.
Designs simulations to
estimate probabilities
m. Works with the normal distribution in some of its basic applications
M6: Mathematical
Skills and Tools
a.
Carries out numerical
calculations and symbol manipulations effectively, using mental computations,
pencil and paper, or other technological aids
b.
Uses a variety of
methods to estimate the values, in appropriate units, of quantities met in
applications and rounds numbers used in applications to an appropriate degree
of accuracy
c.
Evaluates and analyzes
formulas and functions of many kinds, using both pencil and paper and more
advanced technology
d.
Makes and uses rough
sketches, schematic diagrams, or precise scale diagrams to enhance a solution
e.
Uses the number line and
Cartesian coordinates in the plane and in space
f.
Creates and interprets
graphs of many kinds, such as function graphs, circle graphs, scatter plots,
regression lines, and histograms
g.
Sets up and solves
equations symbolically (when possible) and graphically
h.
Knows how to use
algorithms in mathematics
i.
Uses technology to
create graphs or spreadsheets that contribute to the understanding of a problem
j.
Knows standard methods
to solve basic problems and uses these methods in approaching more complex
problems
k.
Uses matrix theory with
graphics calculators to solve systems of equations, transformations, and finite
functions
SCOPE AND SEQUENCE: Fall
Semester
Review
of Algebra 4 classes
Chapter 2 Linear Equations and Functions 7 classes
Chapter 3 Systems of Linear Equations and
Inequalities 7 classes
Chapter 4 Matrices and Determinants 7
classes
Chapter 5 Quadratic Functions
7 classes
Chapter 6 Polynomial and Polynomial
Functions 6 classes
Spring Semester
Chapter 8 Exponential and Logarithmic
Functions 8 classes
Chapter 9 Rational Equations and
Functions 8
classes
Chapter 11 Sequences and Series
8 classes
Chapter 13 Trigonometric Ratios and
Functions 6
classes
Chapter 14 Trigonometric Graphs, Identities, and
Equations 6 classes
CONTINOUS SCHOOL
IMPROVEMENT:
“All students will improve their written communication skills across the curriculum.” The 6 + 1 Traits is the model selected to improve school-wide writing in all subject areas. The 6 + 1 Trait writing framework is a powerful way to learn and use a common language to refer to characteristics of writing as well as establish a common vision of what strong writing looks like. Teachers and students will use the 6 + 1 Trait model to identify areas of strength and weakness as they continue to strive towards continued writing improvement. Success of all students requires that the 6 + 1 trait become a consistent and integral component of each course taught at AFNORTH International High School.
All tests (4 to 5 per
semester) will contain at least one problem in which the student will be
required to write a paragraph detailing how they would solve and check that
problem. Those problems will be scored based on a rubric involving content,
student understanding and use of one of the 6 + 1 traits. Students will receive
in class training and practice in writing the above paragraphs.
COURSE GRADING AND ASSESSMENT:
Your marks are cumulative for the semester. Chapter Tests are weighted 40%, quizzes 30%, homework, homework checks and classwork are 10% and the Final Exam is 20%.
Class work involves taking notes during the lecture, copying the sample problems, and working productively on the homework assignment for the rest of the period. It also requires bringing a calculator, paper and a writing instrument to every class. Positive participation, attitude, and being on task throughout the class.
CLASSROOM
EXPECTATIONS:
It is expected that all students come to class with a willingness to learn. Classroom time is to be used for learning. Behavior should never interfere with learning. No gum chewing is allowed. No Walkmans, earphones, computer games or gameboys are allowed. No hats or headgear of any kind including bandanas are allowed. Students needing to use the restroom and get a drink of water should do so during the very generous 10-minute passing period. Seating assignments are made by the teacher and may change from time to time. Text, calculator and homework are to be brought to all classes.
TEXTBOOK: Larson, Boswell, Kanold, and Stiff, Algebra 2 – Equations, Graphs, Applications McDougal Littell, Illinois, 2004.
SUPPLIES:
A calculator is required for every class. I recommend the TI-83 plus with the graphing screen. A TI-30 is a great $10 calculator and will be sufficient for many problems. Binder paper, graph paper and a writing instrument are required. One section in the student’s binder for Algebra II is sufficient. A separate binder for Algebra II is discouraged. Spiral notebook paper is also not recommended.
HOMEWORK POLICY:
Assignments are essential and will be given virtually every day. The assignment will be started during class but will take about 40 minutes outside of class every other day on average. Since students have been given the semester’s homework assignments in advance, there is no excuse for not being aware of the assignment. Homework needs to be completed and accurate because students transcribe selected problems onto their homework checks which determine their homework grade for the course. Come in during seminar if you have difficulty with your homework. I am also available by appointment after school.
MAKE-UP WORK
POLICY:
Students are expected to get assignments prior to planned absences. Homework assignments are given a semester in advance. If you are going to miss 2 or more classes make an appointment and get help before you leave. Quizzes and tests can be made up during Seminar.