# Math

*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 Saxon curriculum called ‘Course 3’ that is based on concepts and skills learned in 6th Grade (Course 2). Saxon lessons are ‘distributed and integrated’, which means we do a little at a time on all of the concepts listed below. We rotate and build on each of them, reviewing constantly so the students can build a solid foundation across the board. After a set of five lessons is covered, they are reviewed while we study another set of five lessons before the test is given. This allows the material to really sink in, which in the end reinforces actual learning and even makes studying for midterms and finals less stressful.

In this course we will focus on the following concepts:

Number & Operations- We will review what we know about real numbers (integers, decimals, and fractions) and the operations we can perform on them (addition, subtraction, multiplication, and division).

#### Algebra

We will explore the concept of substituting a variable for an unknown number and then learn to manipulate the equation to solve for a variable.

- Geometry- We will learn about the coordinate plane, how to plot ordered pairs, and how variables and equations may represent a continuous set of ordered pairs that we can then graph as a line. We will also explore the properties of triangles, quadrilaterals, and circles.
- Measurement- We will learn how to convert measures using unit analysis. We will also find perimeters and areas of geometric figures.
- Data Analysis & Probability- We will take what we know about finding an ‘average’ and expand that into other measures of central tendency such as median, mode, and range. We will also explore simple statistics by learning about different types of probability and ways to organize data.
- Problem Solving- Throughout the course we will use the concepts we learn to apply to word problems and real world situations. We will practice determining what we know, what we want to know, and finding the simplest way to use one to find the other by using variables.

#### Algebra 1 Honors

Algebra I is an Honors course using Saxon curriculum that is based on concepts and skills learned in Pre-Algebra (Course 3). Saxon lessons are ‘distributed and integrated’, which means we do a little at a time on all of the concepts listed below. We rotate and build on each of them, reviewing constantly so the students can build a solid foundation across the board. After a set of five lessons is covered, they are reviewed while we study another set of five lessons before the test is given. This allows the material to really sink in, which in the end reinforces actual learning and even makes studying for midterms and finals less stressful.

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 Into Geometry curriculum that will work off of skills and concepts learned in Algebra I. Into Geometry lessons will have “Application Throughout”, which means we will have a conceptual stage that builds understanding, a Conceptual and Procedural stage where concepts and skills connect, and a Procedural stage where concepts are applied and practiced. We will build on each module and review as we move forward, so foundations are all solid and connections are made with each new concept learned. This allows the material to really sink in, which in the end reinforces actual learning and even makes studying for midterms and finals less stressful.

In this course we will focus on the following concepts:

- Geometry Foundations- We will learn definitions of basic geometric terms, explore the properties relating them, and start basic reasoning which will lead to using theorems and writing proofs.
- Logic and Reasoning- We will learn different types of reasoning and write many different types of geometric proofs.
- Construction- We will perform constructions, both with pencil and paper using our geometry set and on Khan Academy.
- Coordinate Geometry- We will apply concepts the students learned in Algebra I to geometric figures using the coordinate plane.
- Triangle Congruence and Similarity- We will learn what it means for triangles to be congruent and similar, and use the properties of triangles to solve problems and write proofs.
- Right Triangles and Trigonometry- We will learn how right triangles and the Pythagorean Theorem opens up a whole different category of math applications as an introduction to Trigonometry.
- Quadrilaterals- We will learn the properties specific to different types of quadrilaterals.
- Polygons- We will explore properties of polygons other than triangles and quadrilaterals.
- Circles- We will go beyond finding the area and circumference of a circle, learning more vocabulary and exploring circles’ special properties. We also celebrate Pi Day on March 14th!
- Solids- We will introduce the third dimension by learning to describe basic solids.

#### Algebra II/Trigonometry Honors

Algebra II/Trigonometry is an Honors course using Saxon curriculum that is based on concepts and skills learned both in Algebra I and Geometry. Saxon lessons are ‘distributed and integrated’, which means we do a little at a time on all of the concepts listed below. We rotate and build on each of them, reviewing constantly so the students can build a solid foundation across the board. After a set of five lessons is covered, they are reviewed while we study another set of five lessons before the test is given. This allows the material to really sink in, which in the end reinforces actual learning and even makes studying for midterms and finals less stressful.

In this course we will focus on the following concepts:

- Number Sense and Foundations of Algebra- We will review some algebra concepts that may be a little rusty and make sure we all start from the same foundation.
- Linear Functions- We will define a function and work more with linear equations and their graphs.
- Matrices- We will learn how to use a matrix to organize data, perform operations with matrices, and relate it to systems of linear equations.
- Polynomials and Polynomial Functions- We will move beyond linear equations into polynomials, and learn how to multiply, divide, and factor polynomials.
- Rational and Radical Functions- We will learn how to simplify and perform operations with rational functions, as well as simplify radical numbers and expressions.
- Linear Systems- We will build on what we know of linear equations and apply it to more than one equation, finding solutions to systems of two or three equations both algebraically and graphically.
- Probability and Statistics- We will expand what we know about probability by studying measures of central tendency, permutations, and combinations.
- Quadratic Functions- We will explore polynomials that are specifically quadratic equations and functions, and relate them to the shape of the parabola and the coordinate plane.
- Trigonometry- We will introduce Trigonometry terms and vocabulary by studying the Pythagorean Theorem and the Distance Formula, and solve basic trigonometric problems.
- Exponential Functions- We will expand what we know about functions by studying what happens when we put the variable into the exponent, learning the equations and graphs of basic exponential functions.

#### 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.

#### Pre-Calculus

Pre-Calculus is an Honors course using Pearson curriculum that is based on concepts and skills learned in Algebra II. Although we do not cover the entire book, the concepts are chosen so that the students may move directly into a Calculus I Course (AB) or Statistics, whether at GV Christian School or at a college level.

In this course we will focus on the following concepts:

- Fundamental Concepts of Algebra- We will review some of the more difficult concepts of Algebra II, such as factoring and solving polynomials, expressions with exponents (scientific notation, rational exponents/radicals), rational expressions, and linear inequalities.
- Functions and Graphs- We will expand on what we know about functions by graphing basic functions and exploring the slope of linear functions. We learn to transform and combine functions, and to evaluate both composite and inverse functions.
- Trigonometric Functions- We will use our introduction to Trigonometry learned in Algebra II to really spend some time on this subject, learning about radian measure, the unit circle, trigonometric functions of special angles and any angle, graphs of trigonometric functions and their inverses. We will also apply these skills to word problems and real-world situations (i.e. Physics).
- Analytic Trigonometry- We will use the trigonometric functions to learn to verify trigonometric identities. We will also learn several formulas that help manipulate trigonometric equations.
- Polynomial and Rational Functions- We will expand on our knowledge of polynomials by introducing complex numbers as possible solutions, graphing polynomial and rational functions, dividing and finding zeros of polynomials, and studying polynomial and rational inequalities.
- Exponential and Logarithmic Functions- We will learn how putting the variable into the exponent results in a specific graph, and how its inverse requires the introduction of the logarithmic function. We will learn how to transform these functions and apply them to real-world problems.
- Conic Sections and Analytic Geometry- We will introduce the special properties and equations of various conic sections such as the circle, ellipse, hyperbola and parabola. We will explore the rotation of axes and parametric equations, as well as introduce polar coordinates.

#### 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, add and even, 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.