STATE STANDARDS
ALGEBRA I |

NUMBER AND QUANTITY |

The Real Number System |

B. Use properties of rational and
irrational numbers |

N.RN.B.3 |
Explain why the sum or product of two rational
numbers is rational; that the sum of a rational number and an irrational
number is irrational; and that the product of a nonzero rational number
and an irrational number is irrational. |

Quantities |

A. Reason quantitatively and use units to
solve problems |

N.Q.A.1 |
Use units as a way to understand problems and to
guide the solution of multi-step problems; choose and interpret units
consistently in formulas; choose and interpret the scale and the origin
in graphs and data displays. |

N.Q.A.2 |
Define appropriate quantities for the purpose of
descriptive modeling. |

N.Q.A.3 |
Choose a level of accuracy appropriate to
limitations on measurement when reporting quantities. The greatest
precision for a result is only at the level of the least precise data
point. *For example, if units are tenths and hundredths, then
the appropriate level of precision is tenths.* Calculation of
relative error is not included in this standard. |

ALGEBRA |

Seeing Structure in Expressions |

A. Interpret the structure of expressions |

A.SSE.A.1 |
Interpret expressions that
represent a quantity in terms of its context. |

a |
Interpret parts of an
expression, such as terms, factors, coefficients, degree of polynomial,
leading coefficient, constant term and the standard form of a polynomial
(linear, exponential, quadratic). |

b |
Interpret complicated expressions by viewing one or
more of their parts as a single entity. *For example, interpret P(1+r*)^{n}*
as the product of P and a factor not depending on P* (linear,
exponential, quadratic) |

A.SSE.A.2 |
Use the structure of an
expression to identify ways to rewrite it. *For example, see x*^{4}
– y^{4} as (x^{2})^{2} – (y^{2})^{2},
thus recognizing it as a difference of squares that can be factored as
(x^{2} – y^{2})(x^{2} + y^{2})
(linear, exponential, quadratic). Does not include factoring by
grouping and factoring the sum and difference of cubes. |

B. Write expressions in equivalent forms to
solve problems |

A.SSE.B.3 |
Choose and produce an equivalent form of an
expression to reveal and explain properties of the quantity represented
by the expression. |

a |
Factor a quadratic expression to reveal the zeros of
the function it defines. Includes trinomials with leading
coefficients other than 1. |

b |
Complete the square in a quadratic expression to
reveal the maximum or minimum value of the function it defines. |

c |
Use the properties of exponents to transform
expressions for exponential functions. *For example the
expression 1.15*^{t} can be rewritten as (1.15^{1/12})^{12t}
≈ 1.012^{12t} to reveal the approximate equivalent monthly
interest rate if the annual rate is 15%. |

Arithmetic with Polynomials & Rational
Expressions |

A. Perform arithmetic operations on
polynomials |

A.APR.A.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 (linear, quadratic). |

B. Understand the relationship between
zeros and factors of polynomials |

A.APR.B.3 |
Identify zeros of polynomials when suitable
factorizations are available, and use the zeros to construct a rough
graph of the function defined by the polynomial. |

Creating Equations |

A. Create equations that describe numbers
or relationships |

A.CED.A.1 |
Create equations and inequalities in one variable
and use them to solve problems (linear, quadratic, exponential (integer
inputs only)). |

A.CED.A.2 |
Create equations in two or more variables to
represent relationships between quantities; graph equations on
coordinate axes with labels and scales (linear, quadratic, exponential
(integer inputs only)). |

A.CED.A.3 |
Represent constraints by equations or inequalities,
and by systems of equations and/or inequalities, and interpret solutions
as viable or nonviable options in a modeling context. *For
example, represent inequalities describing nutritional and cost
constraints on combinations of different foods* (linear). |

A.CED.A.4 |
Rearrange formulas to highlight a quantity of
interest, using the same reasoning as in solving equations. *
For example, rearrange Ohm’s law V = IR to highlight resistance R*
(linear, quadratic, exponential (integer inputs only)). |

Reasoning with Equations & Inequalities |

A. Understand solving equations as a
process of reasoning and explain the reasoning |

A.REI.A.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 (linear). |

B. Solve equations and inequalities in one
variable |

A.REI.B.3 |
Solve linear equations and linear inequalities in
one variable, including equations with coefficients represented by
letters (literal that are linear in the variables being solved for). |

A.REI.B.4 |
Solve quadratic equations in one variable (solutions
may include simplifying radicals). |

a |
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 this form. |

b |
Solve quadratic equations by inspection (e.g., for
*x*^{2} = 49), taking square roots, completing the
square, the quadratic formula and factoring, as appropriate to the
initial form of the equation (real solutions). |

C. Solve systems of equations |

A.REI.C.5 |
Prove that, given a system of two equations in two
variables, replacing one equation by the sum of that equation and a
multiple of the other produces a system with the same solutions. |

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

A.REI.C.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*^{2} + y^{2} =
3. |

D. Represent and solve equations and
inequalities graphically |

A.REI.D.10 |
Understand that the graph of an equation in two
variables is the set of all its solutions plotted in the coordinate
plane, often forming a curve (which could be a line). |

A.REI.D.11 |
Explain why the x-coordinates of the points where
the graphs of the equations *y = f(x)* and *y = g(x)*
intersect are the solutions of the equation *f(x) = g(x)*; find
the solutions approximately, e.g., using technology to graph the
functions, make tables of values, or find successive approximations.
Include cases where *f(x) *and/or *g(x)* are linear and
exponential functions. |

A.REI.D.12 |
Graph the solutions to a linear inequality in two
variables as a half-plane (excluding the boundary in the case of a
strict inequality), and graph the solution set to a system of linear
inequalities in two variables as the intersection of the corresponding
half-planes. |

FUNCTIONS |

Interpreting Functions |

A. Understand the concept of a function and
use function notation |

F.IF.A.1 |
Understand that a function from one set (called the
domain) to another set (called the range) assigns to each element of the
domain exactly one element of the range. If *f *is a function and
*x* is an element of its domain, then *f(x)* denotes the
output of *f* corresponding to the input *x*. The graph of
*f* is the graph of the equation *y = f(x)*. |

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

F.IF.A.3 |
Recognize that sequences are functions, sometimes
defined recursively, whose domain is a subset of the integers. *For
example, the Fibonacci sequence is defined recursively by f(0) = f(1) =
1, f(n+1) = f(n) + f(n-1) for n ≥ 1. * |

B. Interpret functions that arise in
applications in terms of the context |

F.IF.B.4 |
For a function that models a relationship between
two quantities, interpret key features of graphs and tables in terms of
the quantities, and sketch graphs showing key features given a verbal
description of the relationship. *Key features include: intercepts;
intervals where the function is increasing, decreasing, positive, or
negative; relative maximums and minimums; symmetries; end behavior; and
periodicity *(linear, exponential and quadratic). |

F.IF.B.5 |
Relate the domain of a function to its graph and,
where applicable, to the quantitative relationship it describes. *For
example, if the function h(n) gives the number of person-hours it takes
to assemble n engines in a factory, then the positive integers would be
an appropriate domain for the function* y (linear, exponential and
quadratic). |

F.IF.B.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 (linear,
exponential and quadratic). |

C. Analyze functions using different
representations |

F.IF.C.7 |
Graph functions expressed symbolically and show key
features of the graph, by hand in simple cases and using technology for
more complicated cases. |

a |
Graph linear and quadratic functions and show
intercepts, maxima, and minima. |

b |
Graph square root, cube root, and piecewise-defined
functions, including step functions and absolute value functions. |

F.IF.C.8 |
Write a function defined by an expression in
different but equivalent forms to reveal and explain different
properties of the function. |

a |
Use the process of factoring and completing the
square in a quadratic function to show zeros, extreme values, and
symmetry of the graph, and interpret these in terms of a context. |

F.IF.C.9 |
Compare properties of two functions each represented
in a different way (algebraically, graphically, numerically in tables,
or by verbal descriptions). *For example, given a graph of one
quadratic function and an algebraic expression for another, say which
has the larger maximum. * |

Building Functions |

A. Build a function that models a
relationship between two quantities |

F.BF.A.1 |
Write a function that describes a relationship
between two quantities. |

a |
Determine an explicit expression, a recursive
process, or steps for calculation from a context. |

B. Build new functions from existing
functions |

F.BF.B.3 |
Identify the effect on the graph of replacing *
f(x)* by *f(x) + k*, *k f(x)*, *f(kx)*, and *
f(x + k)* for specific values of *k* (both positive and
negative); find the value of *k* given the graphs.
Experiment with cases and illustrate an explanation of the effects on
the graph using technology. Include recognizing even and odd
functions from their graphs and algebraic expressions for them (linear,
exponential, quadratic, and absolute value). |

Linear, Quadratic, & Exponential Models |

A. Construct and compare linear, quadratic,
and exponential models and solve problems |

F.LE.A.1 |
Distinguish between situations that can be modeled
with linear functions and with exponential functions. |

a |
Prove that linear functions grow by equal
differences over equal intervals, and that exponential functions grow by
equal factors over equal intervals. |

b |
Recognize situations in which one quantity changes
at a constant rate per unit interval relative to another. |

c |
Recognize situations in which a quantity grows or
decays by a constant percent rate per unit interval relative to another. |

F.LE.A.2 |
Construct linear and exponential functions,
including arithmetic and geometric sequences, given a graph, a
description of a relationship, or two input-output pairs (include
reading these from a table). |

F.LE.A.3 |
Observe using graphs and tables that a quantity
increasing exponentially eventually exceeds a quantity increasing
linearly, quadratically, or (more generally) as a polynomial function. |

B. Interpret expressions for functions in
terms of the situation they model |

F.LE.B.5 |
Interpret the parameters in a linear or exponential
function in terms of a context (linear and exponential of form *
f(x)=b*^{x}+k). |

Statistics & Probability |

Interpreting Categorical & Quantitative
Data |

A. Summarize, represent, and interpret data
on a single count or measurement variable |

S.ID.A.1 |
Represent data with plots on the real number line
(dot plots, histograms, and box plots). |

S.ID.A.2 |
Use statistics appropriate to the shape of the data
distribution to compare center (median, mean) and spread (interquartile
range, standard deviation) of two or more different data sets. |

S.ID.A.3 |
Interpret differences in shape, center, and spread
in the context of the data sets, accounting for possible effects of
extreme data points (outliers). |

B. Summarize, represent, and interpret data
on two categorical and quantitative variables |

S.ID.B.5 |
Summarize categorical data for two categories in
two-way frequency tables. Interpret relative frequencies in the
context of the data (including joint, marginal, and conditional relative
frequencies). Recognize possible associations and trends in the
data (linear focus, discuss general principle). |

S.ID.B.6 |
Represent data on two quantitative variables on a
scatter plot, and describe how the variables are related (linear focus,
discuss general principle). |

a |
Fit a function to the data; use functions fitted to
data to solve problems in the context of the data. Use given
functions or choose a function suggested by the context. Emphasize
linear, quadratic, and exponential models. Includes the use of the
regression capabilities of the calculator. |

b |
Informally assess the fit of a function by plotting
and analyzing residuals. Includes creating residual plots using
the capabilities of the calculator (not manually). |

c |
Fit a linear function for a scatter plot that
suggests a linear association. Both correlation coefficient and
residuals will be addressed in this standard. |

C. Interpret linear models |

S.ID.C.7 |
Interpret the slope (rate of change) and the
intercept (constant term) of a linear model in the context of the data. |

S.ID.C.8 |
Compute (using technology) and interpret the
correlation coefficient of a linear fit. |

S.ID.C.9 |
Distinguish between correlation and causation. |