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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,...

 Algebra II Module 1: Polynomial, Rational, and Radical Relationships Students connect polynomial arithmetic to computations with whole numbers and integers. Students learn that the arithmetic of...

 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.

 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...

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

 Student Outcomes Students write explicit polynomial expressions for sequences by investigating successive differences of those sequences.

 Exponential and Logarithmic Functions In this module, students synthesize and generalize what they have learned about a variety of function families. They extend the domain of exponential functions...

 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...

 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...

 The focus in this topic is on polynomial arithmetic and how it is analogous to operations with integers. The module opens with a lively lesson that engages students in writing 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...

 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...

 Student Outcomes Students develop the distributive property for application to polynomial multiplication. Students connect multiplication of polynomials with multiplication of multidigit integers.

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

 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...

 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 develop a division algorithm for polynomials by recognizing that division is the inverse operation of multiplication.

 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 will factor certain forms of polynomial expressions by using the structure of the polynomials.

 Student Outcomes Students connect long division of polynomials with the long division algorithm of arithmetic and use this algorithm to rewrite rational expressions that divide without a remainder.