Mathematics

As mathematician and author Oleg Gleizer says, "Math is freedom. If we don't know math, our choices are so limited."

Pre Algebra Honors

Pre-Algebra uses a curriculum from Abeka called Pre-Algebra that builds on what students learned in 6th grade. Pre-Algebra eases the transition from arithmetic to algebra. Algebraic expressions and linear equations are applied throughout a thorough review of operations on integers, fractions, decimals, percents, and radicals. Students explore relations and functions using equations, tables, and graphs. Chapters on statistics and geometry extend foundational concepts in preparation for high school courses. Problem-solving and real-life uses of math are featured in each chapter. Dominion through Math exercises regularly illustrate how mathematics can be used to manage God’s creation to His glory.

Algebra 1 Honors

Algebra I is an Honors course using the text Algebra I from Abeka. The goal of Algebra I is threefold: 1) to study the order and absolutes in God’s creation 2) to learn the foundational algebraic processes and skills, and 3) to apply those processes to everyday life and future career situations. This course lays the foundation for studies of higher mathematics and focuses on developing critical thinking skills in both practical and applied situations. Algebra I presents basic algebra concepts founded on the arithmetic principles and skills learned in earlier grades. The concepts are given in a clear, logical order that includes detailed explanations.

In this course we will focus on the following concepts:

  • Algebra Foundations- We will review what we know about real numbers, variables, order of operations, and combining like terms.
  • Functions and Relations- We will define a function and learn about what this means both in an equation and in a graph.
  • Equations- We will learn how to solve two-step and multi-step equations.  We will also learn to set up and solve equations from word problems involving concepts we have already learned such as ratios and proportions.
  • Linear Equations and Functions- We will combine what we have learned about equations and functions to learn more about how algebra relates to the coordinate plane.
  • Polynomials- We will combine what we know about linear equations and exponents to learn about when variables have exponents in an equation.
  • Rational Expressions and Functions- We will add what we know about fractions to learn how to solve problems when the variable is in the denominator.
  • Inequalities- We will learn how to solve for a variable when the equals sign becomes a sign of inequality (<, >, ≤, ≥).
  • Probability and Data Analysis- We will expand what we know about probability by studying measures of central tendency, independent and dependent events.

Geometry Honors

Geometry is an Honors course using the Plane Geometry curriculum, based on Euclid’s Elements. There are three distinctive features of this curriculum. First is a detailed introductory unit, providing the student with tools that lead to the discovery of some of the simpler geometric facts in an informal matter and convinces the student of the need to logically prove conclusions trustworthy while understanding the deceptiveness of the eye. Next is using an analytic- synthetic method of teaching to discover proofs by thinking naturally, logically, and systematically. Finally, there are several Think it Through sections provided in the text that use critical thinking and generalizations to lead the student to understand a broader scope of theorems and discover alternate methods of proof.

Algebra II/Trigonometry Honors

Algebra 2 is an Honors course that reviews algebraic skills from previous courses and introduces topics necessary for success in higher mathematics, including trigonometry. Foundational concepts and procedures of arithmetic and algebra are studied and expanded for the purpose of application. We will use algebra throughout this course to understand relationships among the various laws of God’s creation. As we are using math to discover what God established as laws during the foundation of the universe, we will use our knowledge to solve problems ranging from everyday situations to application in physical and biological sciences.

Pre-Calculus

Precalculus is an Honors course that uses trigonometry and analytic geometry as foundational skills and built upon for furthering the study of the laws God built into the creation of the universe. The purpose of this course is to solve a variety of problems related to real-life situations while whetting the appetite for more advanced study. Since mathematics is the language in which God wrote the universe, and therefore the understanding of the physical world, this course will emphasize problem solving, application, and accurate procedure to develop thinking and working systematically in students.

Statistics

Statistics is an Honors course using Pearson curriculum that is based on concepts and skills learned in Pre-Calculus. In recent years, the skills acquired by taking Statistics and Data Analysis have become much more desirable to both colleges and employers alike. At GV Christian School, even our elementary students are introduced to the basic concepts of probability as early as first grade.

In this course we will focus on the following concepts:

  • Introduction to Statistics- We will get an overview of statistics by discussing data classification, data collection, and experimental design.
  • Descriptive Statistics- We will learn different ways to organize and describe data sets using frequency distributions, measures of central tendency, and measures of variation and position.
  • Probability- We will determine the probability of an event and learn how to use the Counting Principle as well as the Multiplication Rule and the Addition Rule.
  • Discrete Probability Distributions- We will create and use probability distributions, including binomial distributions and other discrete probability distributions.
  • Normal Probability Distributions- We will learn to recognize normal bell-shaped distributions and use their properties in real-life applications.
  • Confidence Intervals- We will introduce inferential statistics by forming confidence intervals to estimate a population parameter.
  • Hypothesis Testing with One Sample- We will test a claim about a parameter by learning about hypothesis tests, testing for the mean for large and small samples as well as for proportions, variance, and standard deviation.
  • Hypothesis Testing with Two Samples- We will test a hypothesis that compares two populations by building on what we learned using one sample.
  • Correlation and Regression- We will describe and test the significance of relationships between two variables when data are presented as ordered pairs.
  • Chi-Square Tests and the F-Distribution- We will test a hypothesis that compares three or more populations by using the goodness-of-fit test and analyzing variance.

AP® Calculus

In this course we will study everything in the Calculus AB guideline as it appears in the AP® Calculus Course Description. The ultimate goal is to introduce students to the major concepts of a first-year college calculus course, with the overall objective of preparing the student for the Advanced Placement® exam in May. Throughout the course, instructional practices to enhance understanding, skills, and use of technology are emphasized to incorporate multiple representations.

Before studying calculus, all students should complete four years of secondary mathematics designed for college-bound students; courses in which they study algebra, geometry, trigonometry, analytic geometry, and elementary functions. These functions include those that are linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise defined. In particular, before studying calculus, students must be familiar with the properties of functions, the algebra of functions (domain and range, even and odd, periodic, symmetry, zeros, intercepts, and so on) and know the values of the trigonometric functions of the numbers 0, π/6, π/4, π/3, π/2, and their multiples.