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 Algebra I Module 1: Relationships Between Quantities and Reasoning with Equations and Their Graphs In this module students analyze and explain precisely the process of solving an equation. Through...

 Algebra I Module 3: Linear and Exponential Functions In earlier grades, students define, evaluate, and compare functions and use them to model relationships between quantities. In this module,...

 Algebra I Module 4: Polynomial and Quadratic Expressions, Equations, and Functions In earlier modules, students analyze the process of solving equations and developing fluency in writing,...

 Student Outcomes Students use the structure of an expression to identify ways to rewrite it. Students use the distributive property to prove equivalency of expressions.

 Student Outcomes Students use the commutative and associative properties to recognize structure within expressions and to prove equivalency of expressions.

 Student Outcomes Students apply knowledge of exponential functions and transformations of functions to a contextual situation.

 Student Outcomes Students use the distributive property to multiply a monomial by a polynomial and understand that factoring reverses the multiplication process. Students use polynomial expressions...

 Student Outcomes Students understand that factoring reverses the multiplication process as they find the linear factors of basic, factorable quadratic trinomials. Students explore squaring a binomial...

 Student Outcomes Students develop strategies for factoring quadratic expressions that are not easily factorable, making use of the structure of the quadratic expression.

 Student Outcomes Students factor quadratic expressions that cannot be easily factored and develop additional strategies for factorization, including splitting the linear term, using graphing...

 Student Outcomes Students solve increasingly complex onevariable equations, some of which need algebraic manipulation, including factoring as a first step and using the zero product property.

 Student Outcomes Students interpret word problems to create equations in onevariable and solve them (i.e., determine the solution set) using factoring and the zero product property.

 Student Outcomes Students rewrite quadratic expressions given in standard form, ax2 + bx + c (with a = 1), in the equivalent completedsquare form, a(x  h)2 + k, and recognize cases for which...

 Student Outcomes Students rewrite quadratic expressions given in standard form, ax2 + bx + c (with a ≠ 1), as equivalent expressions in completed square form, a(x  h)2 + k. They build quadratic...

 Student Outcomes Students solve complex quadratic equations, including those with a leading coefficient other than 1, by completing the square. Some solutions may be irrational. Students draw...

 Student Outcomes Students graph simple quadratic equations of the form y = a(x  h)2 + k (completedsquare or vertex form), recognizing that (h,k) represents the vertex of the graph and use a graph...

 In middle school, students applied the properties of operations to add, subtract, factor, and expand expressions (6.EE.3, 6.EE.4, 7.EE.1, 8.EE.1). Now, in Topic B, students use the structure of...

 In Topic D, students are formally introduced to the modeling cycle (see page 61 of the CCLS) through problems that can be solved by creating equations and inequalities in one variable, systems of...

 In Topic D, students apply and reinforce the concepts of the module as they examine and compare exponential, piecewise, and step functions in a realworld context (FIF.C.9). They create equations...

 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...

 Students apply their experiences from Topic A as they transform quadratic functions from standard form to vertex form, (x) = a(x  h)2 + k in Topic B. The strategy known as completing the square is...