Alg+I+core+and+essential

based on Power Standards
 * Core and Essential Knowledge and Skills in Algebra I**


 * Power Standard 1:**
 * Write, simplify, and find solutions of linear equations, inequalities and systems of equations that represent mathematical or applied situations. Find solutions of quadratic equations and simple equations with powers and roots. (A1.2.1, A1.2.3, A1.2.6)**

1) Write algebraic expressions that represent simple applied linear and quadratic situations and evaluate for given values. (A1.1.1) 2) Write linear equations to represent applied situations. (A1.1.1, A1.2.1) 3) Find solutions of linear equations through various methods, including guess and check and algebraic simplification; explain and justify each method. (L1.1.3, A1.2.1, A1.2.3) 4) Write simple linear inequalities to represent applied situations; use the inequality to answer questions about the situation. (A1.2.1, A1.2.3) 5) Set up and solve applied problems involving simultaneous linear equations in two variables, using various methods. (A1.2.3) //Note: Not three simultaneous equations in three variables.// 6) Recognize the equivalence of quadratic expressions in factored and standard form, and use a given factored form to solve simple quadratic equations. (A1.1.3, A1.2.3) //Note: Students do not need to be able to use the quadratic formula.// 7) Simplify expressions and solve simple equations with exponents and roots. (L2.1.2, A1.1.2, A1.2.6)


 * //Not included://**
 * Solve an equation involving several variables (with numerical or letter coefficients) for a designated variable. Justify steps in the solution. (A1.2.8)
 * Interpret representations that reflect absolute value relationships and solve absolute value equations and inequalities (L1.2.2, A1.2.4)


 * Power Standard 2:**
 * Choose the appropriate family of functions to model a real-world situation, write the symbolic form of the function, and use the specific function to draw conclusions about the situation. (A2.4.1, A2.4.2, A2.4.3)**

1) Use function notation to answer questions about real-world situations: Evaluate expressions to find an output value given an input value; solve equations to find an input value given an output value. (A2.1.2) 2) Write linear functions of the form f(x) = mx + b to represent real-world situations; recognize that these functions represent situations with constant rates of change. (A3.1.1, A2.3.2, A2.3.1) 3) Graph linear functions, relating slope, y-intercept and x-intercept to the symbolic form of the function and to the real-world situation that it models. (A3.1.2, A3.1.3) 4) Recognize exponential functions as modeling real-world situations like compound interest, population growth, radioactive decay, etc., i.e. situations that grow by constant multipliers. (A3.2.5, A2.3.1) 5) Sketch the graph of an exponential function from a table of values; recognize the starting value and the multiplier in the symbolic form of the function. (A3.2.1, A3.2.4) 6) Sketch the graph of a quadratic function, given the symbolic form; explain what the graph shows about a real-world situation that the function models. (A3.3.1, A2.4.3, A2.3.1)

(Students who are working at the core level should know what types of situations are modeled by linear, exponential, and quadratic families of functions but they do not need to use regression analyses on graphing calculators to determine a specific function that most closely models a given situation. )


 * //Not included://**
 * Technical definition of function (only one range value for each domain value) (A2.1.1)
 * Power functions (A1.2.6, A2.7.1-3) and polynomial functions (other than quadratics) (A2.8.1-3)
 * Asymptotic behavior of functions, except as needed to explain the behavior of exponential functions (A2.3.1)
 * Recursive functions; piecewise functions (A2.1.5, A2.1.4)
 * Directly and inversely proportional relationships (A3.4.2)
 * Operations with and transformations of functions, inverses of functions (A2.2.1, A2.2.2, A2.2.3)
 * Bivariate data, scatterplots, correlations, linear regressions (S2.1.1-4, S2.2.1-2)


 * Power Standard 3:**
 * Represent, recognize and analyze the key features of functions in symbols, graphs, tables, diagrams, or words and translate among representations. (A2.1.3, A2.1.6, A2.1.7)**

1) Recognize linear, exponential and quadratic functions from tables of values. (A2.3.2). 2) Recognize graphs of linear, exponential and quadratic functions and describe a real world situation that the graph may model, relating particular aspects of the situation to key features of the graph such as slope, vertex, rate of growth. (A2.3.1)

(Also contained in knowledge and skills for Power Standard 1 and 2, although students working at the core level are not expected to recognize the key features of quadratic equations from symbolic representations or write equations of quadratic equations from verbal descriptions.)


 * //Not included://**
 * Translate between standard form, factored form and vertex form of quadratic functions in order to relate features of the symbolic form to features of the graph and/or situation it models. (A3.3.2-5)