MAFS.912.A-APR.1.1
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

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**Content Complexity:**
Level 1: Recall

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Perform arithmetic operations on...__

Remarks/Examples:

**Algebra 1 - Fluency Recommendations**

Fluency in adding, subtracting, and multiplying polynomials supports students throughout their work in algebra, as well as in their symbolic work with functions. Manipulation can be more mindful when it is fluent.

MAFS.912.A-APR.4.6
Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Rewrite rational expressions. (Algebra 2 -...__

MAFS.912.A-APR.4.7
Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Rewrite rational expressions. (Algebra 2 -...__

MAFS.912.A-CED.1.1
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Create equations that describe numbers or...__

MAFS.912.A-CED.1.3
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

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**Content Complexity:**
Level 3: Strategic Thinking & Complex Reasoning

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Create equations that describe numbers or...__

MAFS.912.A-REI.1.1
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

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**Content Complexity:**
Level 3: Strategic Thinking & Complex Reasoning

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Understand solving equations as a process of...__

MAFS.912.A-REI.2.4
Solve quadratic equations in one variable. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x p) = q that has the same solutions. Derive the quadratic formula from this form.Solve quadratic equations by inspection (e.g., for x = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a bi for real numbers a and b.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Solve equations and inequalities in one...__

MAFS.912.A-REI.3.7
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = 3x and the circle x + y = 3.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Solve systems of equations. (Algebra 1 -...__

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