Educational Resource

Algebra I

Course Outline/Objectives

The key content for the Algebra I, involves understanding, writing, solving, and graphing linear and quadratic equations, including systems of two linear equations in two unknowns. Students should also become comfortable with operations on monomial and polynomial expressions. They learn to solve problems employing all of these techniques, and they extend their mathematical reasoning in many important ways, including justifying steps in an algebraic procedure and checking. The main topical objectives are:

Transition from arithmetic to algebra—

  • Be able to connect arithmetic and algebraic principles
    • Be able to translate life problems from mathematical to algebraic expressions
    • Know the sign rules for addition and multiplication of real numbers
    • Know order of operations for evaluating mathematical expressions
    • Know the properties of arithmetic as they apply to algebra
    • Be able to translate from the concrete level of thinking to the abstract level
  • Be able to simplify expressions using real numbers
    • Be able to identify terms, variables, and coefficients
    • Be able to do four operations with real numbers
    • Be able to combine like terms
    • Be able to express fractional coefficients in lowest terms
    • Know and be able to apply order of operations
    • Know associative, commutative, distributive properties
  • Be able to determine, solve, and graph linear equations with one or more variables
    • Be able to use basic operations to isolate variable
    • Be able to translate words into algebraic symbols and equations
    • Be able to graph linear equations by plotting points
    • Be able to recognize and use the slope-intercept form of a line for graphing
  • Understand and be able to use polynomials
    • Be able to identify, add, and subtract types of polynomials and their parts
    • Be able to identify and factor a common monomial factor
    • Be able to multiply and divide polynomials
    • Be able to recognize special binomials (square binomial, perfect squares, difference of squares)
    • Know the zero product property and know how to relate to factors of polynomials
  • Be able to solve and graph linear inequalities
    • Be able to use number line, symbolism (­<, >, ², ³)
    • Know difference between equality and inequality
    • Be able to solve inequalities
    • Be able to graph a line in a coordinate plane
    • Know that multiplying or dividing by a negative reverses the direction of the inequality
  • Be able to solve equations, which contain rational expressions
    • Be able to identify a rational expression
    • Be able to apply operations to rational expressions
    • Be able to identify and solve linear equations
    • Be able to identify/solve equations by substitutions, factoring, and graphing
    • Be able to translate life problems into math language
  • Be able to solve quadratic equations by factoring
    • Be able to recognize quadratic equations
    • Be able to recognize and use distributive property
    • Be able to find the greatest monomial factor
    • Be able to factor through reverse FOIL
    • Be able to apply the zero product property
    • Be able to solve linear equations

Brief Course Description

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. Through practice and applications, students develop skills in dealing with the essentials of a first-year algebra course, including properties of and operation with real numbers, linear and quadratic equations, inequalities, polynomials, rational expressions, radicals, problem solving, factoring, and graphing.

Methods of Assessment
Assessment tools include the following but are not limited to:

1. Student exams
2. Research projects
3. Portfolios
4. Written examinations
5. Student demonstrations
6. Student grades
7. Oral communication
8. Parent facilitator and education specialist observation
9. Periodic review of work by independent study teacher (IST)

Suggested Materials

  • Saxon Algebra 1; 3/e © 1997
  • Prentice Hall Beginning Algebra; 3/e © 2001
  • Glencoe Algebra 1; vol. 1 © 1998