| Application |
| 1. Create quadratic or exponential functions. |
The
student will create a quadratic or exponential function or equation that
models a context. The equation will have rational coefficients and may
require multiple steps to simplify or solve the equation. |
| 2. Choose and produce equivalent forms of expressions to reveal
and explain properties of a quantity. |
The
student will, given a context, determine the most suitable form of an
expression or equation to reveal a particular trait. |
| Procedural Skill and Fluency |
| 3. Create equivalent expressions involving radicals and rational
exponents. |
The
student will create equivalent expressions involving rational exponents and
radicals, including simplifying or rewriting in other forms. |
| 4. Create equivalent forms of expressions using structure. |
The
student will create an equivalent form of an algebraic expression by using
structure and fluency with operations. |
| 5. Solve quadratic equations. |
The
student will solve a quadratic equation having rational coefficients. The
equation can be presented in a wide range of forms to reward attending to
algebraic structure and can require manipulation in order to solve. |
| 6. Perform arithmetic operations on polynomials. |
The
student will add, subtract, and multiply polynomial expressions and simplify
the result. The expressions will have rational coefficients. |
| 7. Solve radical and rational equations in one variable,
including examples where there are extraneous solutions. |
The
student will solve an equation in one variable that contains radicals or
contains the variable in the denominator of a fraction. The equation will
have rational coefficients, and the student may be required to identify when
a resulting solution is extraneous. |
| 8. Solve a system of equations consisting of one linear and one
quadratic equation in two variables. |
The
student will solve a system of one linear equation and one quadratic
equation. The equations will have rational coefficients. |
| 9. Rewrite simple rational expressions. |
The
student will add, subtract, multiply, or divide two rational expressions or
divide two polynomial expressions and simplify the result. The expressions
will have rational coefficients. |
| Conceptual Understanding |
| 10. Interpret parts of nonlinear expressions in terms of their
context. |
The
student will make connections between a context and the nonlinear equation
that models the context to identify or describe the real-life meaning of a
constant term, a variable, or a feature of the given equation. |
| 11. Understand the relationship between zeros and factors of
polynomials; use it to sketch graphs. |
The
student will use properties of factorable polynomials to solve conceptual
problems relating to zeros, such as determining whether an expression is a
factor of a polynomial based on other information provided. |
| 12. Understand a nonlinear relationship between two variables by
making connections between their algebraic and graphical representations. |
The
student will select a graph corresponding to a given nonlinear equation,
interpret graphs in the context of solving systems of equations, select a
nonlinear equation corresponding to a given graph, determine the equation of
a curve given a verbal description of a graph, determine key features of the
graph of a linear function from its equation, or determine the impact to a
graph of a change in the defining equation. |
| 13. Use function notation, and interpret statements using function notation. |
The
student will use function notation to solve conceptual problems related to
transformations and compositions of functions. |
| 14. Use structure to isolate or identify a quantity of interest
in an expression or isolate a quantity of interest in an equation. |
The
student will rearrange an equation or formula to isolate a single variable or
a quantity of interest. |
