(a) General requirements. Students can be awarded one
credit for successful completion of this course. Prerequisite: Algebra
I.
(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) Mathematical Models with Applications is designed
to build on the knowledge and skills for mathematics in KindergartenGrade
8 and Algebra I. This mathematics course provides a path for students
to succeed in Algebra II and prepares them for various postsecondary
choices. Students learn to apply mathematics through experiences in
personal finance, science, engineering, fine arts, and social sciences.
Students use algebraic, graphical, and geometric reasoning to recognize
patterns and structure, model information, solve problems, and communicate
solutions. Students will select from tools such as physical objects;
manipulatives; technology, including graphing calculators, data collection
devices, and computers; and paper and pencil and from methods such
as algebraic techniques, geometric reasoning, patterns, and mental
math to solve problems.
(4) In Mathematical Models with Applications, students
will use a mathematical modeling cycle to analyze problems, understand
problems better, and improve decisions. A basic mathematical modeling
cycle is summarized in this paragraph. The student will:
(A) represent:
(i) identify the variables in the problem and select
those that represent essential features; and
(ii) formulate a model by creating and selecting from
representations such as geometric, graphical, tabular, algebraic,
or statistical that describe the relationships between the variables;
(B) compute: analyze and perform operations on the
relationships between the variables to draw conclusions;
(C) interpret: interpret the results of the mathematics
in terms of the original problem;
(D) revise: confirm the conclusions by comparing the
conclusions with the problem and revising as necessary; and
(E) report: report on the conclusions and the reasoning
behind the conclusions.
(5) 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) Mathematical modeling in personal finance. The
student uses mathematical processes with graphical and numerical techniques
to study patterns and analyze data related to personal finance. The
student is expected to:
(A) use rates and linear functions to solve problems
involving personal finance and budgeting, including compensations
and deductions;
(B) solve problems involving personal taxes; and
(C) analyze data to make decisions about banking, including
options for online banking, checking accounts, overdraft protection,
processing fees, and debit card/ATM fees.
(3) Mathematical modeling in personal finance. The
student uses mathematical processes with algebraic formulas, graphs,
and amortization modeling to solve problems involving credit. The
student is expected to:
(A) use formulas to generate tables to display series
of payments for loan amortizations resulting from financed purchases;
(B) analyze personal credit options in retail purchasing
and compare relative advantages and disadvantages of each option;
(C) use technology to create amortization models to
investigate home financing and compare buying a home to renting a
home; and
(D) use technology to create amortization models to
investigate automobile financing and compare buying a vehicle to leasing
a vehicle.
(4) Mathematical modeling in personal finance. The
student uses mathematical processes with algebraic formulas, numerical
techniques, and graphs to solve problems related to financial planning.
The student is expected to:
(A) analyze and compare coverage options and rates
in insurance;
(B) investigate and compare investment options, including
stocks, bonds, annuities, certificates of deposit, and retirement
plans; and
(C) analyze types of savings options involving simple
and compound interest and compare relative advantages of these options.
(5) Mathematical modeling in science and engineering.
The student applies mathematical processes with algebraic techniques
to study patterns and analyze data as it applies to science. The student
is expected to:
(A) use proportionality and inverse variation to describe
physical laws such as Hook's Law, Newton's Second Law of Motion, and
Boyle's Law;
(B) use exponential models available through technology
to model growth and decay in areas, including radioactive decay; and
(C) use quadratic functions to model motion.
(6) Mathematical modeling in science and engineering.
The student applies mathematical processes with algebra and geometry
to study patterns and analyze data as it applies to architecture and
engineering. The student is expected to:
(A) use similarity, geometric transformations, symmetry,
and perspective drawings to describe mathematical patterns and structure
in architecture;
(B) use scale factors with twodimensional and threedimensional
objects to demonstrate proportional and nonproportional changes in
surface area and volume as applied to fields;
(C) use the Pythagorean Theorem and special righttriangle
relationships to calculate distances; and
(D) use trigonometric ratios to calculate distances
and angle measures as applied to fields.
(7) Mathematical modeling in fine arts. The student
uses mathematical processes with algebra and geometry to study patterns
and analyze data as it applies to fine arts. The student is expected
to:
(A) use trigonometric ratios and functions available
through technology to model periodic behavior in art and music;
(B) use similarity, geometric transformations, symmetry,
and perspective drawings to describe mathematical patterns and structure
in art and photography;
(C) use geometric transformations, proportions, and
periodic motion to describe mathematical patterns and structure in
music; and
(D) use scale factors with twodimensional and threedimensional
objects to demonstrate proportional and nonproportional changes in
surface area and volume as applied to fields.
(8) Mathematical modeling in social sciences. The student
applies mathematical processes to determine the number of elements
in a finite sample space and compute the probability of an event.
The student is expected to:
(A) determine the number of ways an event may occur
using combinations, permutations, and the Fundamental Counting Principle;
(B) compare theoretical to empirical probability; and
(C) use experiments to determine the reasonableness
of a theoretical model such as binomial or geometric.
(9) Mathematical modeling in social sciences. The student
applies mathematical processes and mathematical models to analyze
data as it applies to social sciences. The student is expected to:
(A) interpret information from various graphs, including
line graphs, bar graphs, circle graphs, histograms, scatterplots,
dot plots, stemandleaf plots, and box and whisker plots, to draw
conclusions from the data and determine the strengths and weaknesses
of conclusions;
(B) analyze numerical data using measures of central
tendency (mean, median, and mode) and variability (range, interquartile
range or IQR, and standard deviation) in order to make inferences
with normal distributions;
(C) distinguish the purposes and differences among
types of research, including surveys, experiments, and observational
studies;
(D) use data from a sample to estimate population mean
or population proportion;
(E) analyze marketing claims based on graphs and statistics
from electronic and print media and justify the validity of stated
or implied conclusions; and
(F) use regression methods available through technology
to model linear and exponential functions, interpret correlations,
and make predictions.
(10) Mathematical modeling in social sciences. The
student applies mathematical processes to design a study and use graphical,
numerical, and analytical techniques to communicate the results of
the study. The student is expected to:
(A) formulate a meaningful question, determine the
data needed to answer the question, gather the appropriate data, analyze
the data, and draw reasonable conclusions; and
(B) communicate methods used, analyses conducted, and
conclusions drawn for a dataanalysis project through the use of one
or more of the following: a written report, a visual display, an oral
report, or a multimedia presentation.
