(a) General requirements. Students shall 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 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 Statistics, students will build on the knowledge
and skills for mathematics in Kindergarten-Grade 8 and Algebra I.
Students will broaden their knowledge of variability and statistical
processes. Students will study sampling and experimentation, categorical
and quantitative data, probability and random variables, inference,
and bivariate data. Students will connect data and statistical processes
to real-world situations. In addition, students will extend their
knowledge of data analysis.
(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, or justify mathematical ideas
and arguments using precise mathematical language in written or oral
communication.
(2) Statistical process sampling and experimentation.
The student applies mathematical processes to apply understandings
about statistical studies, surveys, and experiments to design and
conduct a study and use graphical, numerical, and analytical techniques
to communicate the results of the study. The student is expected to:
(A) compare and contrast the benefits of different
sampling techniques, including random sampling and convenience sampling
methods;
(B) distinguish among observational studies, surveys,
and experiments;
(C) analyze generalizations made from observational
studies, surveys, and experiments;
(D) distinguish between sample statistics and population
parameters;
(E) formulate a meaningful question, determine the
data needed to answer the question, gather the appropriate data, analyze
the data, and draw reasonable conclusions;
(F) communicate methods used, analyses conducted, and
conclusions drawn for a data-analysis project through the use of one
or more of the following: a written report, a visual display, an oral
report, or a multi-media presentation; and
(G) critically analyze published findings for appropriateness
of study design implemented, sampling methods used, or the statistics
applied.
(3) Variability. The student applies the mathematical
process standards when describing and modeling variability. The student
is expected to:
(A) distinguish between mathematical models and statistical
models;
(B) construct a statistical model to describe variability
around the structure of a mathematical model for a given situation;
(C) distinguish among different sources of variability,
including measurement, natural, induced, and sampling variability;
and
(D) describe and model variability using population
and sampling distributions.
(4) Categorical and quantitative data. The student
applies the mathematical process standards to represent and analyze
both categorical and quantitative data. The student is expected to:
(A) distinguish between categorical and quantitative
data;
(B) represent and summarize data and justify the representation;
(C) analyze the distribution characteristics of quantitative
data, including determining the possible existence and impact of outliers;
(D) compare and contrast different graphical or visual
representations given the same data set;
(E) compare and contrast meaningful information derived
from summary statistics given a data set; and
(F) analyze categorical data, including determining
marginal and conditional distributions, using two-way tables.
(5) Probability and random variables. The student applies
the mathematical process standards to connect probability and statistics.
The student is expected to:
(A) determine probabilities, including the use of a
two-way table;
(B) describe the relationship between theoretical and
empirical probabilities using the Law of Large Numbers;
(C) construct a distribution based on a technology-generated
simulation or collected samples for a discrete random variable; and
(D) compare statistical measures such as sample mean
and standard deviation from a technology-simulated sampling distribution
to the theoretical sampling distribution.
(6) Inference. The student applies the mathematical
process standards to make inferences and justify conclusions from
statistical studies. The student is expected to:
(A) explain how a sample statistic and a confidence
level are used in the construction of a confidence interval;
(B) explain how changes in the sample size, confidence
level, and standard deviation affect the margin of error of a confidence
interval;
(C) calculate a confidence interval for the mean of
a normally distributed population with a known standard deviation;
(D) calculate a confidence interval for a population
proportion;
(E) interpret confidence intervals for a population
parameter, including confidence intervals from media or statistical
reports;
(F) explain how a sample statistic provides evidence
against a claim about a population parameter when using a hypothesis
test;
(G) construct null and alternative hypothesis statements
about a population parameter;
(H) explain the meaning of the p-value in relation
to the significance level in providing evidence to reject or fail
to reject the null hypothesis in the context of the situation;
(I) interpret the results of a hypothesis test using
technology-generated results such as large sample tests for proportion,
mean, difference between two proportions, and difference between two
independent means; and
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