High School Math Courses Quarter 2
9th Grade – Geometry
Geometry is one of the two essential math topics in high school and constitutes a major
component of the math content of college entrance examinations. The focus of geometry is to
move students from calculations and numeric problem solving to creating and analyzing visual
models of data and relationships through graphing. In addition, geometric shapes, their
characteristics and uses in the world around us are explored. Finally, concepts of logic and
mathematical proofs are introduced as the underpinnings for modern math structure and
teaching.
In the second quarter, the class studies parallel and perpendicular lines, angle
relationships generated by transversals and how to prove lines are parallel given angle
relationships. The class will learn to solve two common geometric challenges – to find the
distance between a point and a line and between two parallel lines. The concept of congruence
or equality between shapes will be explored as students “discover” geometric theorems and
use them to complete proofs and solve problems.
Students will use compass and protractor to construct geometric shapes, illustrate
concepts and reinforce classroom learning. Higher achieving students are given more
challenging homework assignments to encourage deeper levels of thinking and the excitement
of learning.
10th Grade - Algebra 2
Algebra 2 is the first higher level math course taught in high school. In large part, the course
builds on concepts introduced in Algebra 1 in middle school - reviewing the material with a
higher level of difficulty and complexity. However, mastery of new concepts in the area of
logarithms and trigonometry and a year-end grade of ‘B’ or higher are a prerequisite for moving
on to the more advanced high school courses of Precalculus and AP Calculus. In Algebra 2, the
numerical and algebraic skills learned in grades 1-8 are meshed with the visual modeling and
analytical tools of graphing and geometry to solve complex problems.
In the second quarter, the class will study matrix addition, subtraction and multiplication and
the heart of the course – polynomials. This section covers the critical algebraic tools that
students will use as they move into higher level courses in Precalculus and Calculus. They will
add, subtract, multiply, divide and factor polynomials; simplify and solve equations involving
roots, radicals (square roots), and rational exponents; and perform operations with numbers.
These skills are essential to solving equations in many areas in both math and physics such as
involving particle motion and optimization.
11th Grade - Precalculus.
At AIAN, Precalculus and Advanced Placement Calculus are taught as a combined two
years course. The goal is for students to achieve a high degree of mastery in order to
successfully challenge the Advanced Placement (AP) Calculus exam at the end of 12th grade. The
Advanced Placement program originated in the US about 40 years ago to enable college level
courses to be taught to advanced high school students. Passing the AP exam enables students
to receive college credit at most US universities and is recognized as a significant academic
achievement for admissions at universities around the world.
During the first half of 11th grade, students’ skills in graphing, algebra, trigonometry and
logarithms are strengthened and the graphing calculator becomes a central tool for problem
solving. In the second half of the year, the course transitions from the Precalculus to the
Calculus textbook and teaches the concepts and mechanics of differentiation and integration.
The senior year is used for in-depth practice, applying calculus concepts and techniques to
difficult real world problems and preparation for the AP Calculus exam in May.
In the second quarter, the class will focus on trigonometry (sine, cosine, tangent, etc.), graphs of
trigonometric functions and trigonometric identities. Many high school students never become
comfortable with these important tools in math and physics. This course spends the time and
emphasis needed to ensure that students are well versed in this area before moving to higher
levels.
Students use the graphing calculator daily to visualize algebraic expressions and analyze
maximum and minimum values. In class, I utilize the Texas Instruments Voyager 200 and Texas
Instrument View screen technology to explore graphing calculator capabilities and calculus
concepts.
Grade 12 Advanced Placement Calculus
Advanced Placement Calculus is the second year of a two-year course combining 11th grade
Precalculus and 12th grade AP Calculus. The concepts and mechanics of differentiation and
integration for calculus are taught in 11th grade during Precalculus. During the first half of 12th
grade Advanced Placement Calculus, students review and practice what they learned in 11th
grade identifying areas where they need more work and practice complicated real world
problems applying calculus concepts and techniques. The course stresses the use of the
graphing calculator as a tool and further explores its capabilities. In the second half of the year,
students take practices exams in a variety of timed situations to build a comfort level with
solving difficult math questions under timed exam conditions
During the second quarter, students will finish differentiation and begin exploring topics and
working problems in the second major component of calculus – integration. Students will solve
both formulaic and real world word problems in finding areas under curves, between curves and
the volume of a shape rotated around an axis to create a solid, integration by parts and of
trigonometric functions. By the end of the quarter, students will be ready to begin practice tests
for the Advanced Placement exam in May.
12th Grade - Advanced Topics
Advanced Topics in Mathematics is designed to move forward the math knowledge and skills of
students who are not enrolled in the Pre-calculus/AP Calculus track, but plan to attend
university. This course supports the students’ need to score well on college entrance exams and
be prepared should they choose to take math or science classes at the college level. The course
involves a review of key Algebra 2 and Geometry skills in preparation for the SAT and other
college entrance exams. It then moves on to trigonometry and logarithms concepts as a strong
base for potential higher level science and math courses in college. Students are taught
mathematical skills and concepts in the context of solving real world problems. They learn to
analyze a problem, identify the appropriate mathematical technique and then utilize technology
such as the graphing calculator to solve it.
In the 2nd Quarter, Advanced Topics will finish Algebra 1 and Geometry concepts (the basic math
content found on college entrance exams such as the SAT) and cover selected topics from
Algebra 2. The goal in this quarter is to finish strengthening skills and laying the foundation for
more advanced topics in the second semester of the course when we move into the Precalculus
textbook.
The topics covered in this in this quarter will be:
Special Right Triangle Relationships;
Right triangle parts and Pythagorean Theorem;
Angles in Parallel and Perpendicular Lines;
Angles in Polygons;
Circles – Solving Problems Using Angles, Arcs, Chords, Seconds and Tangents;
Radical Expressions, Rational Exponents, Rational Equations and Inequalities.