| (a) 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 computational thinking, mathematical 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, algorithms, paper and pencil, and technology
and techniques such as mental math, estimation, number sense, and
generalization and abstraction to solve problems. Students will effectively
communicate mathematical ideas, reasoning, and their implications
using multiple representations such as symbols, diagrams, graphs,
computer programs, 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) The primary focal areas in Grade 8 are proportionality;
expressions, equations, relationships, and foundations of functions;
and measurement and data. Students use concepts, algorithms, and properties
of real numbers to explore mathematical relationships and to describe
increasingly complex situations. Students use concepts of proportionality
to explore, develop, and communicate mathematical relationships. Students
use algebraic thinking to describe how a change in one quantity in
a relationship results in a change in the other. Students connect
verbal, numeric, graphic, and symbolic representations of relationships,
including equations and inequalities. Students begin to develop an
understanding of functional relationships. Students use geometric
properties and relationships, as well as spatial reasoning, to model
and analyze situations and solve problems. Students communicate information
about geometric figures or situations by quantifying attributes, generalize
procedures from measurement experiences, and use the procedures to
solve problems. Students use appropriate statistics, representations
of data, and reasoning to draw conclusions, evaluate arguments, and
make recommendations. While the use of all types of technology is
important, the emphasis on algebra readiness skills necessitates the
implementation of graphing technology.
(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.
(b) 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) Number and operations. The student applies mathematical
process standards to represent and use real numbers in a variety of
forms. The student is expected to:
(A) extend previous knowledge of sets and subsets using
a visual representation to describe relationships between sets of
real numbers;
(B) approximate the value of an irrational number,
including π and square roots of numbers less than 225, and locate
that rational number approximation on a number line;
(C) convert between standard decimal notation and scientific
notation; and
(D) order a set of real numbers arising from mathematical
and real-world contexts.
(3) Proportionality. The student applies mathematical
process standards to use proportional relationships to describe dilations.
The student is expected to:
(A) generalize that the ratio of corresponding sides
of similar shapes are proportional, including a shape and its dilation;
(B) compare and contrast the attributes of a shape
and its dilation(s) on a coordinate plane; and
(C) use an algebraic representation to explain the
effect of a given positive rational scale factor applied to two-dimensional
figures on a coordinate plane with the origin as the center of dilation.
(4) Proportionality. The student applies mathematical
process standards to explain proportional and non-proportional relationships
involving slope. The student is expected to:
(A) use similar right triangles to develop an understanding
that slope, m, given as the rate comparing
the change in y- values to the change
in x- values, (y2 - y1 ) / (x2 - x1 ), is the same for any two points (x1 , y1 ) and (x2, y2) on the
same line;
(B) graph proportional relationships, interpreting
the unit rate as the slope of the line that models the relationship;
and
(C) use data from a table or graph to determine the
rate of change or slope and y- intercept
in mathematical and real-world problems.
(5) Proportionality. The student applies mathematical
process standards to use proportional and non-proportional relationships
to develop foundational concepts of functions. The student is expected
to:
(A) represent linear proportional situations with tables,
graphs, and equations in the form of y =
kx;
(B) represent linear non-proportional situations with
tables, graphs, and equations in the form of y
= mx + b, where b ≠ 0;
(C) contrast bivariate sets of data that suggest a
linear relationship with bivariate sets of data that do not suggest
a linear relationship from a graphical representation;
(D) use a trend line that approximates the linear relationship
between bivariate sets of data to make predictions;
(E) solve problems involving direct variation;
(F) distinguish between proportional and non-proportional
situations using tables, graphs, and equations in the form y = kx or y = mx
+ b, where b ≠ 0;
(G) identify functions using sets of ordered pairs,
tables, mappings, and graphs;
(H) identify examples of proportional and non-proportional
functions that arise from mathematical and real-world problems; and
(I) write an equation in the form y = mx + b to model a linear relationship
between two quantities using verbal, numerical, tabular, and graphical
representations.
(6) Expressions, equations, and relationships. The
student applies mathematical process standards to develop mathematical
relationships and make connections to geometric formulas. The student
is expected to:
(A) describe the volume formula V
= Bh of a cylinder in terms of its base area and its height;
(B) model the relationship between the volume of a
cylinder and a cone having both congruent bases and heights and connect
that relationship to the formulas; and
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