# High School Math

Algebra I & II

After successful completion of Pre-algebra, students move into Algebra I, and then into either Geometry or Algebra II. Topics are covered thoroughly as Algebra is at the heart of advanced mathematics including calculus. Many times, calculus students find difficulty not as much in the concepts of calculus itself, but in the algebra that comes inherently in calculus problems. So, the Algebra I and II courses are intended to provide a comprehensive foundation for algebraic problem solving enriched with classroom activities to help balance the studious book work. Often, the algebra classes use college level textbooks for enhanced learning.

Sources

Sullivan Elementary Algebra

Saxon Algebra 2

Martin-Gay Beginning Algebra

Sullivan College Algebra

Methods and Activities

1. Warm up exercises

2. Problem discussion

3. Practice problems at the chalkboard

3. Quizzes and chapter tests

4. Final exam

5. Math projects

Geometry

Geometry is taught between Algebra I and Algebra II, or after both algebra courses have been completed. In recent years, mathematicians have questioned the practicality of geometric proofs. First trimester coursework involves geometry topics that engage the proofing method. However, the second and third trimester coursework relies more on understanding the geometric relationships and less on the protocols of proofs. Geometry curriculum includes using geometric solids to help students visualize shape and symmetry.

Sources

McDougal Geometry for Enjoyment and Challenge

Rusczyk AOPS Introduction to Geometry

Kinsey Symmetry, Space, and Shape – An Introduction to Mathematics Through Geometry

Geometry solids

Methods and Activities

1. Warm up exercises

2. Problem discussion

3. Practice problems at the chalkboard

4. Quizzes and chapter tests

5. Final exam

6. Math projects

Pre-calculus

Pre-calculus mathematics is comprised of advanced algebra and trigonometry and is taught for three trimesters. Examples of topics covered are polynomial, rational, exponential, and logarithmic functions along with graphs of sine and cosine, trig formulas, and trig identities. If students are already confident in the elements of pre-calculus level algebra, having been successful in a higher-level algebra II class, then a dedicated trigonometry course is offered.

Sources

Sullivan Precalculus

Rusczyk AOPS Precalculus

Methods and Activities

1. Warm up exercises

2. Problem discussion

3. Practice problems at the chalkboard

4. Quizzes and chapter tests

5. Final exam

6. Math projects

Trigonometry

Trigonometry is one component of pre-calculus mathematics. If students are calculus bound in high school and confident in the other elements of pre-calculus level math, then a dedicated trigonometry course is offered. This is contingent on Algebra II coursework having been robust and the student being skilled with topics such as polynomial, rational, exponential, and logarithmic functions, complex numbers, and conics. Dedicating an academic year to trigonometry can be very beneficial for success in calculus. Often, for students on this path, calculus topics can be introduced in the final month or so of the trigonometry academic year.

Sources

Sullivan Trigonometry – A Unit Circle Approach

Rusczyk AOPS Precalculus

Methods and Activities

1. Warm up exercises

2. Problem discussion

3. Practice problems at the chalkboard

4. Quizzes and chapter tests

5. Final exam

6. Math projects

Calculus I&II

It has become a rarity that calculus is taught in high school. We offer Calculus at the basic and advanced levels including an AP option. Calculus I introduces the concept of taking a limit and then moves on to derivatives, and integration including calculating the volumes of solids – the course wrapping up at transcendentals. Calculus II picks up with trigonometric integrals, first order differential equations, and moves into parametric equations, polar coordinates, and vectors. Second order differential equations are addressed for advanced students.

Sources

Thomas Calculus

Methods and Activities

1. Warm up exercises

2. Problem discussion

3. Practice problems at the chalkboard

4. Quizzes and chapter tests

5. Final exam

Business Math/Finance

We encourage all students to take Business Math if possible to prepare for everyday adult responsibilities such as balancing a checkbook and calculating compound interest, and to gain a basic understanding of topics like how income taxes are computed. However, Business Math/Finance generally becomes the class that non calculus bound students take in their final years of high school.

Sources

Hansen Business Math

A Beka Consumer Mathematics

Methods and Activities

1. Warm up exercises

2. Problem discussion

3. Practice problems at the whiteboard

4. Quizzes and chapter tests

5. Final exam

High School Math is a student-centric subject which is driven by the level of Math the student has completed at other schools (if entering the "I AM" School from another school), or the levels explored by a student in previous years. For example if a student shows aptitude and attitude to progress beyond their age level year, all efforts are made to accelerate that student. Likewise if a student is focusing more predominantly on other subjects, and the student and parents do not wish to pursue the higher math subjects, we utilize more practical application math, such as Business Math in the High School years.

In general, a student's Math track in the High School years at the "I AM" School would include: Geometry, Algebra I, Algebra II, and Pre-Calculus. However, other Math topics, depending on the direction the student is looking to take after High School, include: Trigonometry, Statistics, Calculus I & II, and/or Business Math/Finance. AP Math subjects are also taught for students requiring, or wanting to complete them for college aspirations.

The "I AM" School requires a student to complete a minimum of three years of High School Math in order to graduate.