Course Descriptions - High School » Math Department

Math Department

The California Content Standard for Algebra 1 has 25 objectives, all of which are covered in this course. A summary of these objectives is: “Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences. In addition, algebraic skills and concepts are developed and used in a wide variety of problem-solving situations.
The California Content Standard for Algebra 1 has 25 objectives, all of which are covered in this course. A summary of these objectives is: “Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences. In addition, algebraic skills and concepts are developed and used in a wide variety of problem-solving situations.
Algebra 1B continues the study of functions begun in Algebra 1A. It builds upon last year’s course work in developing a precise mathematical language and understanding of mathematical structure. Algebra 1B includes such topics as Rational Expressions, Equational Systems, Radicals and higher level equations. The difficulty most students will experience will be in the multiple step processes necessary to answer the questions.  My primary instructional method is lecture, but large amount of class time will be spent on guided practice. Emphasis is placed on the conceptual understanding you have of a problem, and how you arrive at an answer, not just on whether a given answer is correct.
In Geometry, you will develop reasoning and problem-solving skills as you study topics such as congruence and similarity, and apply properties of lines, triangles, quadrilaterals, and circles. You will also develop problem-solving skills by using length, perimeter, area, circumference, surface area, and volume to solve real-world problems.
 
Algebra 2 continues the study of functions begun in Algebra 1. It builds upon Algebra 1 in developing a precise mathematical language and understanding of mathematical structure. Algebra 2 includes such topics as Polynomial, Rational, Inverse, Logarithmic and exponential functions. The Real number system is expanded to include imaginary and complex numbers, and graphing is expanded to include curves called conics. My primary instructional method is lecture. Emphasis is placed on the conceptual understanding you have of a problem, and how you arrive at an answer, not just on whether a given answer is correct.
Precalculus will expand the algebra covered in both algebra 1 and algebra 2. Emphasis will be placed on a graphical approach and will increase the students’ methods in solving a variety of problems. A full course in trigonometry, which covers periodic and cyclical functions, will be studied in the second semester. There is a significant increase in difficulty level as we proceed through the year.
Honors Precalculus will expand on the algebra covered in both algebra 1 and algebra 2. Students enrolled in Honors coursework can expect a much faster-paced presentation, and therefore should enter the course with an excellent understanding of their previous algebra courses. Emphasis will be placed on a graphical approach and will increase the students’ methods in solving a variety of problems. A variety of new functions and graphing systems will be presented and a full course in trigonometry, which covers periodic and cyclical functions. There is a significant increase in difficulty level as we proceed through the year. Topics are specifically emphasized which prepare the student for AP Calculus.
Calculus is the mathematical study of relationships when there is change taking place. It is a very important tool of modern scientists. A variety of different ideas can be studied using calculus such as the orbits of satellites and spacecraft, predicting population sizes, estimating how fast the price of a particular commodity is rising, measuring the cardiac output of the heart and many others. AP Calculus prepares the student to take the AP Calculus AB test. In this course, the student is introduced to the concepts of calculus not only algebraically, but also graphically and numerically.
This is a standard-level course which seeks to introduce students to the science of data analysis. As an elective. it serves the dual purpose of offering an alternative fourth year of math (which is increasingly important to college admissions), while bringing students to math in real life from a different direction. While there is computation and rigorous adherence to procedures, the emphasis is more on the contextual interpretation of the statistics we generate. Why do we use the median when looking at household income? How is it that CNN can project winners in an election when only a few percent of the precincts have reported? We explore the fundamentals of descriptive statistics, the pitfalls of experimental and survey design, the basics of probability and the procedures for inference about populations. In the end, we hope to give students the tools to look at what they see and read in the news with a more discerning and critical eye.
 
Statistics is a unique type of mathematics. Unique in that it serves as a bridge from “high school” math to “college” math. What that means is when one progresses higher in mathematics, that student will be doing less computational work and a greater amount of analytic work. In Statistics, students will be looking at raw numbers or images (data) and using this information to make meaningful commentary about how it describes reality. Students will also be trained in creating a process to take a scenario in real life and assign numbers or symbols to it so that others may see a clearer picture of that scenario. Students will also be given tools to objectively (computational portion of the course) make comments on what the data says. Statistics and Probability are so closely related that it is impossible to learn one without the other. Probability asks the question “If a fair die is rolled n times, how often will 3 appear?” Statistics asks, “If a die is rolled n times and 3 appears k times, is that die fair?” Students cannot answer the latter question without knowledge of the former concept. As this is an Advanced Placement course, students will also have appropriate training for the Exam at the end of the year.