1. Numbers and Polynomials:Students will develop and apply concepts of polynomials to investigate and describe relationships and solve problems.

Students will : A. Understand the use of parameters and variables, including appropriate replacement sets.
For example:Students will identify which symbols represent parameters and which represent variables.Students will represent situations with polynomials or equations, and identify appropriate replacement sets for the variables, and connect these to domain & range for equations.For classes of situations, students will also identify appropriate replacement sets for the parameters.

B. Show procedural fluency with polynomial expressions focusing on basic operations and simple factoring.
For example: Students will use fundamental properties of numbers to simplify and expand polynomial expressions.Students will identify the equivalence between a polynomial and its factored form.Students will write limited types of polynomials in factored form, such as common factor and difference of squares.

C. Use equations, inequalities, and systems of equations & inequalities to represent situations and find solutions via symbolic, numeric and graphic methods.
For example:Students will represent a situation with an equation or inequality in one variable, and find solutions by multiple methods (symbolic, numeric, and graphic).Students will represent a situation with a system of linear equations or inequalities involving two or three variables; the resulting system is to be solved by multiple methods for two variable systems of equations (all 3 – numeric, symbolic, and graphic) … for other systems, numeric and graphic methods will be used.

D. Use exponential and power equations to represent situations and find solutions via numeric and graphic methods.
For example:Students will represent a situation with an exponential equation or power equation in one variable, and find solutions by numeric & graphic methods.Students will recognize when an exponential equation is appropriate, when a power equation is appropriate, or when a linear equation is an appropriate model.Optional: Inclusion of comparable logarithmic equations.

E. Use symbolic procedures to manipulate simple formulas and literal equations.
For example: Students will solve for another variable with formulas employing the 4 standard operations on variables.Students will paraphrase a given equation into alternate forms (with or without parentheses, with or without fractional expressions).

F. To prepare for STEM pathways, these outcomes might be needed:Algebraic solution of power equations; basics of radical expressions; basic simplification of roots (indices 2 and 3); rational exponent notation; algebraic solution of radical and rational equations with limited complexity; additional factoring, such as trinomials.

1. Numbers and Polynomials:Students will develop and apply concepts of polynomials to investigate and describe relationships and solve problems.Students will :

A. Understand the use of parameters and variables, including appropriate replacement sets.For example:Students will identify which symbols represent parameters and which represent variables.Students will represent situations with polynomials or equations, and identify appropriate replacement sets for the variables, and connect these to domain & range for equations.For classes of situations, students will also identify appropriate replacement sets for the parameters.

B. Show procedural fluency with polynomial expressions focusing on basic operations and simple factoring.For example: Students will use fundamental properties of numbers to simplify and expand polynomial expressions.Students will identify the equivalence between a polynomial and its factored form.Students will write limited types of polynomials in factored form, such as common factor and difference of squares.

C. Use equations, inequalities, and systems of equations & inequalities to represent situations and find solutions via symbolic, numeric and graphic methods.For example:Students will represent a situation with an equation or inequality in one variable, and find solutions by multiple methods (symbolic, numeric, and graphic).Students will represent a situation with a system of linear equations or inequalities involving two or three variables; the resulting system is to be solved by multiple methods for two variable systems of equations (all 3 – numeric, symbolic, and graphic) … for other systems, numeric and graphic methods will be used.

D. Use exponential and power equations to represent situations and find solutions via numeric and graphic methods.For example:Students will represent a situation with an exponential equation or power equation in one variable, and find solutions by numeric & graphic methods.Students will recognize when an exponential equation is appropriate, when a power equation is appropriate, or when a linear equation is an appropriate model.Optional: Inclusion of comparable logarithmic equations.

E. Use symbolic procedures to manipulate simple formulas and literal equations.For example: Students will solve for another variable with formulas employing the 4 standard operations on variables.Students will paraphrase a given equation into alternate forms (with or without parentheses, with or without fractional expressions).

F. To prepare for STEM pathways, these outcomes might be needed:Algebraic solution of power equations; basics of radical expressions; basic simplification of roots (indices 2 and 3); rational exponent notation; algebraic solution of radical and rational equations with limited complexity; additional factoring, such as trinomials.