Presentation on theme: "Common Core Algebra 1 Topics Crosswalk Writing and Solving Equations and Inequalities – Explain and prove methods of solution, more robust applications."— Presentation transcript:
Common Core Algebra 1 Topics Crosswalk Writing and Solving Equations and Inequalities – Explain and prove methods of solution, more robust applications Solving Systems of Linear Equations – Explain and prove methods of solution Polynomial Expressions, Functions, and Equations – Solve by factoring, including factoring by grouping and factoring trinomials with leading coefficients – Solve quadratics by completing the square; use and prove the quadratic formula – Add, Subtract, and Multiply Polynomials of any degree Statistics – Measures of Central Tendency: Mean, Median, Mode – Measures of Spread: Range, Interquartile Range, Standard deviation – Conditional Relative Frequencies and Association – Linear Modeling: Correlation Coefficient, Residual Analysis Functions and Modeling – Domain and Range of a Function, in a modeling context – Arithmetic and Geometric Sequences – Behavior of a Function (Increasing, Decreasing, Positive, Negative, Roots) – Solving Equations Using the Graphs of Functions, Including Absolute Value Equations – Graphing Linear, Exponential, Absolute Value, Quadratic, Cubic, Square Root, Cube Root, and Piecewise Functions, and Modeling with all types of functions – Transformations of Graphs of Functions Red Topics are traditionally taught in Algebra 2/Trig Blue Topics are traditionally taught in Precalculus Green topics are traditionally taught in AP Statistics Purple Topics are topics presented in much greater depth in the Common Core
Comparison of Standards Example: Factoring and Quadratic Equations 2005 Standards A.A.19 Identify and factor the difference of two perfect squares A.A.20 Factor algebraic expressions completely, including trinomials with a lead coefficient of one (after factoring a GCF) A.A.27 Understand and apply the multiplication property of zero to solve quadratic equations with integral coefficients and integral roots Common Core Standards A-SSE.A.2 Use the structure of an expression to identify ways to rewrite it. For example, see x 4 – y 4 as (x 2 ) 2 – (y 2 ) 2, thus recognizing it as a difference of squares that can be factored as (x 2 – y 2 )(x 2 + y 2 ). A-REI.B.4 Solve quadratic equations in one variable. – Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p) 2 = q that has the same solutions. Derive the quadratic formula from this form. – Solve quadratic equations by inspection (e.g., for x 2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation.