Algebra I

Topic A introduces polynomial expressions.  In Module 1, students learned the definition of a polynomial and how to add, subtract, and multiply polynomials.  Here, their work with multiplication is extended and connected to factoring polynomial expressions and solving basic polynomial equations (A-APR.A.1, A-REI.D.11).  They analyze, interpret, and use the structure of polynomial expressions to multiply and factor polynomial expressions (A-SSE.A.2).  They understand factoring as the reverse process of multiplication.  In this topic, students develop the factoring skills needed to solve quadratic equations and simple polynomial equations by using the zero-product property (A-SSE.B.3a).  Students transform quadratic expressions from standard form, ax² + bx + c, to factored form, f(x) = a(x - n)(x - m), and then solve equations involving those expressions.  They identify the solutions of the equation as the zeros of the related function.  Students apply symmetry to create and interpret graphs of quadratic functions (F-IF.B.4, F-IF.C.7a). They use average rate of change on an interval to determine where the function is increasing or decreasing (F-IF.B.6).  Using area models, students explore strategies for factoring more complicated quadratic expressions, including the product-sum method and rectangular arrays.  They create one- and two-variable equations from tables, graphs, and contexts and use them to solve contextual problems represented by the quadratic function (A-CED.A.1, A-CED.A.2).  Students then relate the domain and range for the function to its graph and the context (F-IF.B.5).