Algebra I | Content Standards

The Real Number System N.RN

Extend the properties of exponents to rational exponents.

MGSE9-12.N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of

exponents. (i.e., simplify and/or use the operations of addition, subtraction, and multiplication, with radicals

within expressions limited to square roots).

Use properties of rational and irrational numbers.

MGSE9-12.N.RN.3 Explain why the sum or product of rational numbers is rational; why the sum of a rational

number and an irrational number is irrational; and why the product of a nonzero rational number and an

irrational number is irrational.

Quantities N.Q

Reason quantitatively and use units to solve problems.

MGSE9-12.N.Q.1 Use units of measure (linear, area, capacity, rates, and time) as a way to understand

problems:

a. Identify, use, and record appropriate units of measure within context, within data displays, and on

graphs;

b. Convert units and rates using dimensional analysis (English-to-English and Metric-to-Metric without

conversion factor provided and between English and Metric with conversion factor);

c. Use units within multi-step problems and formulas; interpret units of input and resulting units of output.

MGSE9-12.N.Q.2 Define appropriate quantities for the purpose of descriptive modeling. Given a situation,

context, or problem, students will determine, identify, and use appropriate quantities for representing the

situation.

MGSE9-12.N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting

quantities. For example, money situations are generally reported to the nearest cent (hundredth). Also, an

answers’ precision is limited to the precision of the data given.

Seeing Structure in Expressions A.SSE

Interpret the structure of expressions

MGSE9-12.A.SSE.1 Interpret expressions that represent a quantity in terms of its context.

MGSE9-12.A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients, in context.

MGSE9-12.A.SSE.1b Given situations which utilize formulas or expressions with multiple terms and/or

factors, interpret the meaning (in context) of individual terms or factors.

MGSE9-12.A.SSE.2 Use the structure of an expression to rewrite it in different equivalent forms. For example,

see x4 – y

4 as (x2

)

2 - (y2

)

2

, thus recognizing it as a difference of squares that can be factored as (x2 – y

2

) (x2 + y2

).

Write expressions in equivalent forms to solve problems

MGSE9-12.A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties

of the quantity represented by the expression.

MGSE9-12.A.SSE.3a Factor any quadratic expression to reveal the zeros of the function defined by the

expression.

MGSE9-12.A.SSE.3b Complete the square in a quadratic expression to reveal the maximum or minimum

value of the function defined by the expression.

Arithmetic with Polynomials and Rational Expressions A.APR

Perform arithmetic operations on polynomials

MGSE9-12.A.APR.1 Add, subtract, and multiply polynomials; understand that polynomials form a system

analogous to the integers in that they are closed under these operations.

Creating Equations A.CED

Create equations that describe numbers or relationships

MGSE9-12.A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include

equations arising from linear, quadratic, simple rational, and exponential functions (integer inputs only).

MGSE9-12.A.CED.2 Create linear, quadratic, and exponential equations in two or more variables to represent

relationships between quantities; graph equations on coordinate axes with labels and scales. (The phrase “in two

or more variables” refers to formulas like the compound interest formula, in which A = P(1 + r/n)nt has multiple

variables.)

MGSE9-12.A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or

inequalities, and interpret data points as possible (i.e. a solution) or not possible (i.e. a non-solution) under the

established constraints.

MGSE9-12.A.CED.4 Rearrange formulas to highlight a quantity of interest using the same reasoning as in

solving equations. Examples: Rearrange Ohm’s law V = IR to highlight resistance R; Rearrange area of a

circle formula A = π r2 to highlight the radius r.

Reasoning with Equations and Inequalities A.REI

Understand solving equations as a process of reasoning and explain the reasoning

MGSE9-12.A.REI.1 Using algebraic properties and the properties of real numbers, justify the steps of a simple,

one-solution equation. Students should justify their own steps, or if given two or more steps of an equation,

explain the progression from one step to the next using properties.

Solve equations and inequalities in one variable

MGSE9-12.A.REI.3 Solve linear equations and inequalities in one variable including equations with

coefficients represented by letters. For example, given ax + 3 = 7, solve for x.

MGSE9-12.A.REI.4 Solve quadratic equations in one variable.

MGSE9-12.A.REI.4a Use the method of completing the square to transform any quadratic equation in x

into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from ax2

+ bx + c = 0.

MGSE9-12.A.REI.4b Solve quadratic equations by inspection (e.g.,