# Algebra I

## Course Overview

Algebra I covers the study of variables, constants, expressions and equations. Upon successful completion of this course a student will understand linear equations and inequalities, relations & functions, pairs of linear equations & inequalities, exponents and polynomials, quadratic functions, data analysis and probability, exponents and radical functions, and rational functions and equations. The belief that problem solving (investigating, conjecturing, predicting, analyzing, and verifying), followed by a well reasoned presentation of results, is central to the process of learning mathematics, and that this learning happens most effectively in a cooperative, student-centered classroom. The resulting curriculum is problem-centered rather than topic-centered. There is also a continual spiraling throughout the curriculum, so topics are constantly being reinforced.

The purpose of this format is to have students continually encounter mathematics set in meaningful contexts, enabling them to draw, and then verify, their own conclusions. This pedagogy demands that students be active contributors in class each day; they are expected to ask questions, to share their results with their classmates, and to be prime movers of each day’s investigations. They are not necessarily expected to solve the exercise alone, but through collaboration with their peers, they should be able to understand it. The benefit of such participation in the students’ study of mathematics is an enhanced ability to ask effective questions, to answer fellow students’ inquiries, and to critically assess and present their own work. The goal is that the students, not the teacher or a textbook, be the source of mathematical knowledge.

## Course Content (separated by subject as there is no Units)

### Real Numbers

This concept will allow students to define and operate with real numbers, which include solving equations with one variable, apply said equations, working with inequalities, and solving absolute value equations and inequalities. Student will be able to use the foundations of real numbers to solve more complex equations.

### Solving and Graphing Linear Equations

Students will be able to understand and compute linear equations. In this section, students will be able to understand the idea of rate or slope, and how it affects the initial rate. Students will also be able to graph equations and apply it to real world situations. Students can take this information and find other information based on their inferences of the graph or calculation of the linear equation. Furthermore, students will be able to manipulate the equation to find other linear equations related to the original equations, relate distances by using the Pythagorean theorem, and event relate the linear equation to a circle.

### Polynomials

In this concept, students will be introduced to the parts of polynomials including the definition of terms, coefficients, and variables how each of them relate to each other. Students will be able to identify and define a polynomial. Furthermore, students will learn different operations with polynomials including adding and subtracting, multiplying, factoring, dividing, and solving polynomials. This concept will allow them to work with later concepts such as rational expressions and quadratic expressions.

### Rational Expressions

Rational expressions are no more than expressions that also have a denominator. The concept will take expression a step further and introduce simplifying and solving using various techniques. Students will be able to compute, define, and operate with rational expressions. Students will also be able to apply these basics to solving equations, manipulating expressions, and applying to real world situations.

Students should already have a strong concept of the definition of roots. In this concept, students will go beyond memorizing, and compute and simplify them in order to work the roots and radicals in other expressions. Students will be able to understand rational exponents and radicals, and how they relate to each other. Simplifying both roots and radical expressions will allow students to work with it and use operations with radical expressions. Students will also work with equations that have roots and radicals and be able to solve, simplify, and manipulate. Students will also cover complex numbers and real world applications.

### Exponential Functions

Learning to understand, simplify, and calculate with exponential functions is important for other concepts such as quadratics and rationals. Students will be able to define and use the zero and negative exponent rules, and simplify exponential expressions. Furthermore, students will need to apply exponential functions and relate them to situations such as geometric sequences, zero problems, and even quadratics.