Algebra I
These standards require students to use algebra as a tool for representing and solving a variety of practical problems. Tables and
graphs will be used to interpret algebraic expressions, equations, and inequalities and to analyze behaviors of functions.
Expressions and Operations
A.1 The student will represent verbal quantitative
situations algebraically and evaluate these expressions for given replacement
values of the variables.
Performance Assessments:
Equations and Inequalities
A.4 The student will solve multistep linear and
quadratic equations in two variables, including
a) solving literal equations (formulas) for a given
variable;
b) justifying steps used in simplifying expressions and
solving equations, using field properties and axioms of equality that are valid
for the set of real numbers and its subsets;
c) solving quadratic equations
algebraically and graphically;
d) solving multistep linear
equations algebraically and graphically;
e) solving systems of two linear
equations in two variables algebraically and graphically; and
f) solving realworld problems involving equations and
systems of equations.
Graphing
calculators will be used both as a primary tool in solving problems and to
verify algebraic solutions.
Performance Assessments:
A.5 The student will solve multistep linear inequalities in two variables, including
a) solving multistep linear inequalities algebraically and graphically;
b) justifying steps used in solving inequalities, using axioms of inequality and properties of
order that are valid for the set of real numbers and its subsets;
c) solving realworld problems involving inequalities; and
d) solving systems of inequalities.
Performance Assessments:
A.6 The student will graph linear equations and linear inequalities in two variables, including
a) determining the slope of a line when given an equation of the line, the graph of the line, or
two points on the line. Slope will be described as rate of change and will be positive, negative, zero, or undefined; and
b) writing the equation of a line when given the graph of the line, two points on the line, or the
slope and a point on the line.
Performance Assessments:
Functions
A.7 The student will investigate and analyze function (linear and quadratic) families and their
characteristics both algebraically and graphically, including
a) determining whether a relation is a function;
b) domain and range;
c) zeros of a function;
d) x and yintercepts;
e) finding the values of a function for elements in its domain; and
f) making connections between and among multiple representations of functions including
concrete, verbal, numeric, graphic, and algebraic.
Performance Assessments:
Statistics
A.9 The
student, given a set of data, will interpret variation in realworld contexts
and calculate and interpret mean absolute deviation, standard deviation, and
zscores.
Performance Assessments:
A.10 The student will compare and contrast multiple
univariate data sets, using boxandwhisker plots.
Performance Assessments:
A.11 The student will collect
and analyze data, determine the equation of the curve of best fit in order to
make predictions, and solve realworld
problems, using mathematical models. Mathematical models will include linear
and quadratic functions.
Performance Assessments:
Algebra II
These standards include a transformational approach to graphing functions. Transformational graphing uses translation, reflection,
dilation, and rotation to generate a “family of graphs” from a given graph and builds a strong connection between algebraic and
graphic representations of functions. Students will vary the coefficients and constants of an equation, observe the changes in
the graph of the equation, and make generalizations that can be applied to many graphs.
Expressions and Operations
AII.2 The student will investigate and apply the properties of arithmetic and geometric sequences and
series to solve realworld problems, including writing the first n terms, finding the nth term, and
evaluating summation formulas. Notation will include Σ and an.
Performance Assessments:
Equations and Inequalities
AII.4 The student will solve, algebraically and
graphically,
a) absolute value equations and inequalities;
b) quadratic equations over the set of complex numbers;
c) equations containing rational algebraic expressions;
and
d) equations containing radical expressions.
Graphing calculators will be used for solving and for
confirming the algebraic solutions.
Performance Assessments:
AII.5 The student will solve nonlinear systems of equations, including linearquadratic and quadraticquadratic,
algebraically and graphically. Graphing calculators will be used as a tool to visualize
graphs and predict the number of solutions.
Performance Assessments:
Functions
AII.6 The student will recognize the general shape of
function (absolute value, square root, cube root, rational, polynomial,
exponential, and logarithmic) families and will convert between graphic and
symbolic forms of functions. A transformational approach to graphing will be
employed. Graphing calculators will be used as a tool to investigate the shapes
and behaviors of these functions.
Performance Assessments:
AII.7 The student will investigate and analyze
functions algebraically and graphically. Key concepts include
a) domain and range, including limited and discontinuous domains
and ranges;
b) zeros;
c) x and yintercepts;
d) intervals in which a function is increasing or decreasing;
e) asymptotes;
f) end behavior;
g) inverse of a function; and
h) composition of multiple functions.
Graphing calculators will be used as a tool to assist in
investigation of functions.
Performance Assessments:
AII.8 The student will investigate and describe the relationships among solutions of an equation, zeros of a function, xintercepts of a graph, and factors of a polynomial expression.
Performance Assessments:
Statistics
AII.9 The student will collect and analyze data,
determine the equation of the curve of best fit, make predictions, and solve
realworld problems, using mathematical models. Mathematical models will
include polynomial, exponential, and logarithmic functions.
Performance Assessments:
AII.10 The student will identify, create, and solve realworld problems involving inverse variation,
joint variation, and a combination of direct and inverse variations.
Performance Assessments:
AII.11 The student will identify properties of a normal distribution and apply those properties to
determine probabilities associated with areas under the standard normal curve.
Performance Assessments:
Algebra, Functions, and Data Analysis
Through the investigation of mathematical models and interpretation/analysis of data from real life situations, students will
strengthen conceptual understandings in mathematics and further develop connections between algebra and statistics. Students
should use the language and symbols of mathematics in representations and communication throughout the course.
These standards include a transformational approach to graphing functions and writing equations when given the graph of the equation.
Transformational graphing builds a strong connection between algebraic and graphic representations of functions.
Algebra and Functions
AFDA.1 The student will investigate and analyze function (linear, quadratic, exponential, and
logarithmic) families and their characteristics. Key concepts include
a) continuity;
b) local and absolute maxima and minima;
c) domain and range;
d) zeros;
e) intercepts;
f) intervals in which the function is increasing/decreasing;
g) end behaviors; and
h) asymptotes.
Performance Assessments:
AFDA.2 The student will use knowledge of transformations to write an equation
given the graph of a function (linear, quadratic, exponential, and logarithmic).
Performance Assessments:
AFDA.3 The student will collect data and generate an
equation for the curve (linear, quadratic, exponential, and logarithmic) of
best fit to model realworld problems or applications. Students will use the
best fit equation to interpolate function values, make decisions, and justify
conclusions with algebraic and/or graphical models.
Performance Assessments:
AFDA.4 The student will transfer between and analyze
multiple representations of functions, including algebraic formulas, graphs,
tables, and words. Students will select and use appropriate representations for
analysis, interpretation, and prediction.
Performance Assessments:
AFDA.5 The student will determine optimal values in problem situations by identifying constraints and
using linear programming techniques.
Performance Assessments:
Data Analysis
AFDA.6 The student will calculate probabilities. Key concepts include
a) conditional probability;
b) dependent and independent events;
c) addition and multiplication rules;
d) counting techniques (permutations and combinations); and
e) Law of Large Numbers.
Performance Assessments:
AFDA.7 The student will analyze the normal distribution.
Key concepts include
a) characteristics of normally distributed data;
b) percentiles;
c) normalizing data, using zscores; and
d) area under the standard normal curve and probability.
Performance Assessments:
AFDA.8 The student will design and conduct an experiment/survey.
Key concepts include
a) sample size;
b) sampling technique;
c) controlling sources of bias and experimental error;
d) data collection; and
e) data analysis and reporting.
Performance Assessments:
Mathematical Analysis
Mathematical Analysis develops students’ understanding of algebraic and transcendental functions, parametric and polar equations,
sequences and series, and vectors.
MA.1 The student will investigate and identify the characteristics of polynomial and rational
functions and use these to sketch the graphs of the functions. This will include determining zeros, upper and lower bounds, yintercepts,
symmetry, asymptotes, intervals for which the function is increasing or decreasing, and maximum or minimum points. Graphing utilities will
be used to investigate and verify these characteristics.
Performance Assessments:
MA.3 The student will investigate and describe the continuity of functions, using graphs and algebraic
methods.
Performance Assessments:
MA.7 The student will find the limit of an algebraic function, if it exists, as the variable approaches
either a finite number or infinity. A graphing utility will be used to verify intuitive reasoning,
algebraic methods, and numerical substitution.
Performance Assessments:

