(a) General requirements. Students shall be awarded
one credit for successful completion of this course. This course is
recommended for students in Grade 8 or 9. Prerequisite: Mathematics,
Grade 8 or its equivalent.
(b) Introduction.
(1) The desire to achieve educational excellence is
the driving force behind the Texas essential knowledge and skills
for mathematics, guided by the college and career readiness standards.
By embedding statistics, probability, and finance, while focusing
on fluency and solid understanding, Texas will lead the way in mathematics
education and prepare all Texas students for the challenges they will
face in the 21st century.
(2) The process standards describe ways in which students
are expected to engage in the content. The placement of the process
standards at the beginning of the knowledge and skills listed for
each grade and course is intentional. The process standards weave
the other knowledge and skills together so that students may be successful
problem solvers and use mathematics efficiently and effectively in
daily life. The process standards are integrated at every grade level
and course. When possible, students will apply mathematics to problems
arising in everyday life, society, and the workplace. Students will
use a problem-solving model that incorporates analyzing given information,
formulating a plan or strategy, determining a solution, justifying
the solution, and evaluating the problem-solving process and the reasonableness
of the solution. Students will select appropriate tools such as real
objects, manipulatives, paper and pencil, and technology and techniques
such as mental math, estimation, and number sense to solve problems.
Students will effectively communicate mathematical ideas, reasoning,
and their implications using multiple representations such as symbols,
diagrams, graphs, and language. Students will use mathematical relationships
to generate solutions and make connections and predictions. Students
will analyze mathematical relationships to connect and communicate
mathematical ideas. Students will display, explain, or justify mathematical
ideas and arguments using precise mathematical language in written
or oral communication.
(3) In Algebra I, students will build on the knowledge
and skills for mathematics in Grades 6-8, which provide a foundation
in linear relationships, number and operations, and proportionality.
Students will study linear, quadratic, and exponential functions and
their related transformations, equations, and associated solutions.
Students will connect functions and their associated solutions in
both mathematical and real-world situations. Students will use technology
to collect and explore data and analyze statistical relationships.
In addition, students will study polynomials of degree one and two,
radical expressions, sequences, and laws of exponents. Students will
generate and solve linear systems with two equations and two variables
and will create new functions through transformations.
(4) Statements that contain the word "including" reference
content that must be mastered, while those containing the phrase "such
as" are intended as possible illustrative examples.
(c) Knowledge and skills.
(1) Mathematical process standards. The student uses
mathematical processes to acquire and demonstrate mathematical understanding.
The student is expected to:
(A) apply mathematics to problems arising in everyday
life, society, and the workplace;
(B) use a problem-solving model that incorporates analyzing
given information, formulating a plan or strategy, determining a solution,
justifying the solution, and evaluating the problem-solving process
and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives,
paper and pencil, and technology as appropriate, and techniques, including
mental math, estimation, and number sense as appropriate, to solve
problems;
(D) communicate mathematical ideas, reasoning, and
their implications using multiple representations, including symbols,
diagrams, graphs, and language as appropriate;
(E) create and use representations to organize, record,
and communicate mathematical ideas;
(F) analyze mathematical relationships to connect and
communicate mathematical ideas; and
(G) display, explain, and justify mathematical ideas
and arguments using precise mathematical language in written or oral
communication.
(2) Linear functions, equations, and inequalities.
The student applies the mathematical process standards when using
properties of linear functions to write and represent in multiple
ways, with and without technology, linear equations, inequalities,
and systems of equations. The student is expected to:
(A) determine the domain and range of a linear function
in mathematical problems; determine reasonable domain and range values
for real-world situations, both continuous and discrete; and represent
domain and range using inequalities;
(B) write linear equations in two variables in various
forms, including *y = mx + b, Ax + By = C, * and *y - y*_{1 } = *m **(x - x*_{1 }), given one point and the slope and
given two points;
(C) write linear equations in two variables given a
table of values, a graph, and a verbal description;
(D) write and solve equations involving direct variation;
(E) write the equation of a line that contains a given
point and is parallel to a given line;
(F) write the equation of a line that contains a given
point and is perpendicular to a given line;
(G) write an equation of a line that is parallel or
perpendicular to the X or Y axis and determine whether the slope of
the line is zero or undefined;
(H) write linear inequalities in two variables given
a table of values, a graph, and a verbal description; and
(I) write systems of two linear equations given a table
of values, a graph, and a verbal description.
(3) Linear functions, equations, and inequalities.
The student applies the mathematical process standards when using
graphs of linear functions, key features, and related transformations
to represent in multiple ways and solve, with and without technology,
equations, inequalities, and systems of equations. The student is
expected to:
(A) determine the slope of a line given a table of
values, a graph, two points on the line, and an equation written in
various forms, including *y = mx + b, Ax +
By = C, * and *y - y*_{1 } = *m **(x - x*_{1 });
(B) calculate the rate of change of a linear function
represented tabularly, graphically, or algebraically in context of
mathematical and real-world problems;
(C) graph linear functions on the coordinate plane
and identify key features, including *x- *intercept, *y- *intercept, zeros, and slope, in mathematical
and real-world problems;
(D) graph the solution set of linear inequalities in
two variables on the coordinate plane;
(E) determine the effects on the graph of the parent
function *f(x) = x * when *f(x) * is replaced by *af(x),
f(x) + d, f(x - c), f(bx) * for specific values of *a, b, c, * and *d; *
(F) graph systems of two linear equations in two variables
on the coordinate plane and determine the solutions if they exist;
(G) estimate graphically the solutions to systems of
two linear equations with two variables in real-world problems; and
(H) graph the solution set of systems of two linear
inequalities in two variables on the coordinate plane.
(4) Linear functions, equations, and inequalities.
The student applies the mathematical process standards to formulate
statistical relationships and evaluate their reasonableness based
on real-world data. The student is expected to:
(A) calculate, using technology, the correlation coefficient
between two quantitative variables and interpret this quantity as
a measure of the strength of the linear association;
(B) compare and contrast association and causation
in real-world problems; and
(C) write, with and without technology, linear functions
that provide a reasonable fit to data to estimate solutions and make
predictions for real-world problems.
(5) Linear functions, equations, and inequalities.
The student applies the mathematical process standards to solve, with
and without technology, linear equations and evaluate the reasonableness
of their solutions. The student is expected to:
(A) solve linear equations in one variable, including
those for which the application of the distributive property is necessary
and for which variables are included on both sides;
(B) solve linear inequalities in one variable, including
those for which the application of the distributive property is necessary
and for which variables are included on both sides; and
(C) solve systems of two linear equations with two
variables for mathematical and real-world problems.
(6) Quadratic functions and equations. The student
applies the mathematical process standards when using properties of
quadratic functions to write and represent in multiple ways, with
and without technology, quadratic equations. The student is expected
to:
(A) determine the domain and range of quadratic functions
and represent the domain and range using inequalities;
(B) write equations of quadratic functions given the
vertex and another point on the graph, write the equation in vertex
form *(f(x) = a(x - h)*^{2 } + *k), * and rewrite the equation from vertex
form to standard form *(f(x) = ax*^{2 } + *bx + c); * and
(C) write quadratic functions when given real solutions
and graphs of their related equations.
(7) Quadratic functions and equations. The student
applies the mathematical process standards when using graphs of quadratic
functions and their related transformations to represent in multiple
ways and determine, with and without technology, the solutions to
equations. The student is expected to:
(A) graph quadratic functions on the coordinate plane
and use the graph to identify key attributes, if possible, including *x- *intercept, *y- *intercept,
zeros, maximum value, minimum values, vertex, and the equation of
the axis of symmetry;
(B) describe the relationship between the linear factors
of quadratic expressions and the zeros of their associated quadratic
functions; and
(C) determine the effects on the graph of the parent
function *f(x) = x*^{2 } when *f(x) * is replaced by *af(x),
f(x) + d, f(x - c), f(bx) * for specific values of *a, b, c, * and *d. *
(8) Quadratic functions and equations. The student
applies the mathematical process standards to solve, with and without
technology, quadratic equations and evaluate the reasonableness of
their solutions. The student formulates statistical relationships
and evaluates their reasonableness based on real-world data. The student
is expected to:
(A) solve quadratic equations having real solutions
by factoring, taking square roots, completing the square, and applying
the quadratic formula; and
(B) write, using technology, quadratic functions that
provide a reasonable fit to data to estimate solutions and make predictions
for real-world problems.
(9) Exponential functions and equations. The student
applies the mathematical process standards when using properties of
exponential functions and their related transformations to write,
graph, and represent in multiple ways exponential equations and evaluate,
with and without technology, the reasonableness of their solutions.
The student formulates statistical relationships and evaluates their
reasonableness based on real-world data. The student is expected to:
(A) determine the domain and range of exponential functions
of the form *f(x) = ab*^{x } and
represent the domain and range using inequalities;
(B) interpret the meaning of the values of *a * and *b * in
exponential functions of the form *f(x) =
ab*^{x } in real-world problems;
(C) write exponential functions in the form *f(x) = ab*^{x } (where *b * is a rational number) to describe problems
arising from mathematical and real-world situations, including growth
and decay;
(D) graph exponential functions that model growth and
decay and identify key features, including *y- *intercept
and asymptote, in mathematical and real-world problems; and
(E) write, using technology, exponential functions
that provide a reasonable fit to data and make predictions for real-world
problems.
(10) Number and algebraic methods. The student applies
the mathematical process standards and algebraic methods to rewrite
in equivalent forms and perform operations on polynomial expressions.
The student is expected to:
(A) add and subtract polynomials of degree one and
degree two;
(B) multiply polynomials of degree one and degree two;
(C) determine the quotient of a polynomial of degree
one and polynomial of degree two when divided by a polynomial of degree
one and polynomial of degree two when the degree of the divisor does
not exceed the degree of the dividend;
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