(a) General requirements. Students shall be awarded
onehalf to one credit for successful completion of this course. Prerequisites:
Geometry and Algebra II.
(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 problemsolving model that incorporates analyzing given information,
formulating a plan or strategy, determining a solution, justifying
the solution, and evaluating the problemsolving 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 Advanced Quantitative Reasoning, students will
develop and apply skills necessary for college, careers, and life.
Course content consists primarily of applications of high school mathematics
concepts to prepare students to become welleducated and highly informed
21st century citizens. Students will develop and apply reasoning,
planning, and communication to make decisions and solve problems in
applied situations involving numerical reasoning, probability, statistical
analysis, finance, mathematical selection, and modeling with algebra,
geometry, trigonometry, and discrete mathematics.
(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 problemsolving model that incorporates analyzing
given information, formulating a plan or strategy, determining a solution,
justifying the solution, and evaluating the problemsolving 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) Numeric reasoning. The student applies the process
standards in mathematics to generate new understandings by extending
existing knowledge. The student generates new mathematical understandings
through problems involving numerical data that arise in everyday life,
society, and the workplace. The student extends existing knowledge
and skills to analyze realworld situations. The student is expected
to:
(A) use precision and accuracy in reallife situations
related to measurement and significant figures;
(B) apply and analyze published ratings, weighted averages,
and indices to make informed decisions;
(C) solve problems involving quantities that are not
easily measured using proportionality;
(D) solve geometric problems involving indirect measurement,
including similar triangles, the Pythagorean Theorem, Law of Sines,
Law of Cosines, and the use of dynamic geometry software;
(E) solve problems involving large quantities using
combinatorics;
(F) use arrays to efficiently manage large collections
of data and add, subtract, and multiply matrices to solve applied
problems, including geometric transformations;
(G) analyze various voting and selection processes
to compare results in given situations; and
(H) select and apply an algorithm of interest to solve
reallife problems such as problems using recursion or iteration involving
population growth or decline, fractals, and compound interest; the
validity in recorded and transmitted data using checksums and hashing;
sports rankings, weighted class rankings, and search engine rankings;
and problems involving scheduling or routing situations using vertexedge
graphs, critical paths, Euler paths, and minimal spanning trees and
communicate to peers the application of the algorithm in precise mathematical
and nontechnical language.
(3) Algebraic reasoning (expressions, equations, and
generalized relationships). The student applies the process standards
in mathematics to create and analyze mathematical models of everyday
situations to make informed decisions related to earning, investing,
spending, and borrowing money by appropriate, proficient, and efficient
use of tools, including technology. The student uses mathematical
relationships to make connections and predictions. The student judges
the validity of a prediction and uses mathematical models to represent,
analyze, and solve dynamic realworld problems. The student is expected
to:
(A) collect numerical bivariate data to create a scatterplot,
select a function to model the data, justify the model selection,
and use the model to interpret results and make predictions;
(B) describe the degree to which uncorrelated variables
may or may not be related and analyze situations where correlated
variables do or do not indicate a causeandeffect relationship;
(C) determine or analyze an appropriate growth or decay
model for problem situations, including linear, exponential, and logistic
functions;
(D) determine or analyze an appropriate cyclical model
for problem situations that can be modeled with periodic functions;
(E) determine or analyze an appropriate piecewise model
for problem situations;
(F) create, represent, and analyze mathematical models
for various types of income calculations to determine the best option
for a given situation;
(G) create, represent, and analyze mathematical models
for expenditures, including those involving credit, to determine the
best option for a given situation; and
(H) create, represent, and analyze mathematical models
and appropriate representations, including formulas and amortization
tables, for various types of loans and investments to determine the
best option for a given situation.
(4) Probabilistic and statistical reasoning. The student
uses the process standards in mathematics to generate new understandings
of probability and statistics. The student analyzes statistical information
and evaluates risk and return to connect mathematical ideas and make
informed decisions. The student applies a problemsolving model and
statistical methods to design and conduct a study that addresses one
or more particular question(s). The student uses multiple representations
to communicate effectively the results of studentgenerated statistical
studies and the critical analysis of published statistical studies.
The student is expected to:
(A) use a twoway frequency table as a sample space
to identify whether two events are independent and to interpret the
results;
(B) use the Addition Rule, P(A or B) = P(A) + P(B)  P(A and B), in mathematical and realworld problems;
(C) calculate conditional probabilities and probabilities
of compound events using tree diagrams, Venn diagrams, area models,
and formulas;
(D) interpret conditional probabilities and probabilities
of compound events by analyzing representations to make decisions
in problem situations;
(E) use probabilities to make and justify decisions
about risks in everyday life;
(F) calculate expected value to analyze mathematical
fairness, payoff, and risk;
(G) determine the validity of logical arguments that
include compound conditional statements by constructing truth tables;
(H) identify limitations and lack of relevant information
in studies reporting statistical information, especially when studies
are reported in condensed form;
(I) interpret and compare statistical results using
appropriate technology given a margin of error;
(J) identify potential misuses of statistics to justify
particular conclusions, including assertions of a causeandeffect
relationship rather than an association, and missteps or fallacies
in logical reasoning;
(K) describe strengths and weaknesses of sampling techniques,
data and graphical displays, and interpretations of summary statistics
and other results appearing in a study, including reports published
in the media;
(L) determine the need for and purpose of a statistical
investigation and what type of statistical analysis can be used to
answer a specific question or set of questions;
(M) identify the population of interest for a statistical
investigation, select an appropriate sampling technique, and collect
data;
(N) identify the variables to be used in a study;
(O) determine possible sources of statistical bias
in a study and how bias may affect the validity of the results;
(P) create data displays for given data sets to investigate,
compare, and estimate center, shape, spread, and unusual features
of the data;
(Q) analyze possible sources of data variability, including
those that can be controlled and those that cannot be controlled;
(R) report results of statistical studies to a particular
audience, including selecting an appropriate presentation format,
creating graphical data displays, and interpreting results in terms
of the question studied;
(S) justify the design and the conclusion(s) of statistical
studies, including the methods used; and
(T) communicate statistical results in oral and written
formats using appropriate statistical and nontechnical language.
