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Common Core: Standard
Common Core: ELA
Common Core: Math
CCLS  Math: A.SSE.2
 Category
 Seeing Structure In Expressions
 SubCategory
 Interpret The Structure Of Expressions
 State Standard:
 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).
28 Results

 Student Outcomes Students will use the structure of polynomials to identify factors.

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

 This topic focuses on factoring polynomials and the advantages of factored form of a polynomial to both solve equations and sketch graphs of polynomial functions. Students solve problems involving...

 Student Outcomes Students find solutions to polynomial equations where the polynomial expression is not factored into linear factors. Students construct a polynomial function that has a specified set...

 Student Outcomes Students explore the difference of two squares identity x2 − y2 = (x − y)(x + y) in the context of finding Pythagorean triples.

 Student Outcomes Students understand that the sum of two square roots (or two cube roots) is not equal to the square root (or cube root) of their sum. Students convert expressions to simplest radical...

 Student Outcomes Students apply polynomial identities to the detection of prime numbers.

 Student Outcomes Students perform arithmetic by using polynomial identities to describe numerical relationships.

 Student Outcomes Students work with polynomials with constant coefficients to prove polynomial identities.

 Student Outcomes Students perform arithmetic operations on polynomials and write them in standard form. Students understand the structure of polynomial expressions by quickly determining the first...

 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.

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

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

 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...

 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...

 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...

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

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