Algebra 1 Description

The differences between an expression and an equation are further highlighted at the beginning of Algebra I.  Properties, including the distributive property, are used to simplify expressions, and used to factor basic expressions.  The concept of absolute value is extended to studying equations in one variable with an absolute value term.  The concept of infinity is introduced, and is linked with the number of solutions of linear equations in one and two variables.  Graphs of linear equations are used to develop the concept of systems of linear equations.  Methods of solving systems of linear equations are explored.  The concepts of function and exponent are expanded to the study of quadratic functions.  Quadratic functions are analyzed and quadratic equations are solved.  Connections are made between the x-intercepts of a quadratic function and the solutions to a quadratic equation.  The concepts of expression and exponent are further expanded to include polynomials.  Polynomials are added, subtracted, and multiplied.  Methods of factoring polynomials, especially quadratics, are discussed in depth, and the need for factoring is highlighted.  The concept of the rational numbers is used to develop the concept of rational expressions with polynomials in the numerator and denominator.  Operations on rational expressions are performed.  The concept of inequalities is then introduced as a way to solidify understanding and link many previous concepts.  Mathematical reasoning is weaved throughout the course both in justifying the steps to simplify expressions, solve equations and inequalities and in solving applied problems requiring solving for unknowns.