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 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...

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

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

 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 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 work with polynomials with constant coefficients to prove polynomial identities.

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

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

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

 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...

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

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

 Student Outcomes Students will use the factored forms of polynomials to find zeros of a function. Students will use the factored forms of polynomials to sketch the components of graphs between zeros.

 Student Outcomes Students graph polynomial functions and describe end behavior based upon the degree of the polynomial.

 Student Outcomes Students rewrite simple rational expressions in different forms, including representing remainders when dividing.

 Student Outcomes Students know and apply the Remainder Theorem and understand the role zeros play in the theorem.

 Student Outcomes Students learn to fit polynomial functions to data values.

 Student Outcomes Students model a crosssection of a riverbed with a polynomial function and estimate fluid flow with their algebraic model.

 Students solve polynomial, rational, and radical equations, and apply these types of equations to realworld situations. They examine the conditions under which an extraneous solution is introduced...

 Student Outcomes Students define rational expressions and write them in equivalent forms.