• 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 nonsolution)
under the established constraints.

Reasoning with Equations & Inequalities
A-RE I Reasoning with Equations and Inequalities

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.

A-RE I Solve equations and inequalities in one variable

A-RE I Solve systems of equations

MGSE9-12.A.REI.5 Show and explain why the elimination method works to solve a system of twovariable
equations.

MGSE9-12.A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

A-RE I Represent and solve equations and inequalities graphically.

MGSE9-12.A.REI.10 Understand that the graph of an equation in two variables is the set of all its
solutions plotted in the coordinate plane.

MGSE9-12.A.REI.11 Using graphs, tables, or successive approximations, show that the solution to the
equation f(x) = g(x) is the x-value where the y-values of f(x) and g(x) are the same.

MGSE9-12.A.REI.12 Graph the solution set to a linear inequality in two variables.

GA: HS: Functions
Interpreting Functions
F-IF Understand the concept of a function and use function notation.

MGSE9-12.F.IF.1 Understand that a function from one set (the input, called the domain) to another set (the output, called the range) assigns to each element of the domain exactly one element of the range, i.e. each input value maps to exactly one output value. If f is a function, x is the input (an element of the domain), and f(x) is the output (an element of the range). Graphically, the graph is y = f(x).

MGSE9-12.F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

MGSE9-12.F.IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. (Generally, the scope of high school math defines this subset as the set of natural numbers 1,2,3,4...) By graphing or calculating terms, students should be able to show how the recursive sequence a1=7, an=an-1 +2; the sequence sn = 2(n-1) + 7; and the function f(x) = 2x + 5 (when x is a natural number) all define the same sequence.

F-IF Interpret functions that arise in applications in terms of the context.

MGSE9-12.F.IF.4 Using tables, graphs, and verbal descriptions, interpret the key characteristics of a
function which models the relationship between two quantities. Sketch a graph showing key features
including: intercepts; interval where the function is increasing, decreasing, positive, or negative; relative
maximums and minimums; symmetries; end behavior; and periodicity.

MGSE9-12.F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

F-IF Analyze functions using different representations.

MGSE9-12.F.IF.7 Graph functions expressed algebraically and show key features of the graph both by
hand and by using technology.

MGSE9-12.F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima
(as determined by the function or by context).

Building Functions
F-BF Build a function that models a relationship between two quantities.

MGSE9-12.F.BF.1 Write a function that describes a relationship between two quantities.

MGSE9-12.F.BF.2 Write arithmetic and geometric sequences recursively and explicitly, use them to model situations, and translate between the two forms. Connect arithmetic sequences to linear functions and geometric sequences to exponential functions.
•  Key Vocabulary

Algebra • Arithmetic Sequence • Average Rate of Change • Coefficient • Constant Rate of Change • Continuous • Discrete • Domain • End Behavior • Equation • Explicit Formula • Expression • Factor • Inequality • Interval Notation • Linear Functions • Linear Model • Ordered Pair • Parameter • Range • Recursive Formula • Slope • Substitution • Term • Variable • X-intercept • Y-intercept