Texas Administrative Code
Title 19 - EDUCATION
Part 2 - TEXAS EDUCATION AGENCY
Chapter 111 - TEXAS ESSENTIAL KNOWLEDGE AND SKILLS FOR MATHEMATICS
Subchapter B - MIDDLE SCHOOL
Section 111.28 - Grade 8, Adopted 2012
Universal Citation: 19 TX Admin Code ยง 111.28
Current through Reg. 49, No. 38; September 20, 2024
(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 [PI] 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 is not equal to
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
(C) use models and diagrams to explain the
Pythagorean theorem.
(7)
Expressions, equations, and relationships. The student applies mathematical
process standards to use geometry to solve problems. The student is expected
to:
(A) solve problems involving the volume of
cylinders, cones, and spheres;
(B)
use previous knowledge of surface area to make connections to the formulas for
lateral and total surface area and determine solutions for problems involving
rectangular prisms, triangular prisms, and cylinders;
(C) use the Pythagorean Theorem and its
converse to solve problems; and
(D)
determine the distance between two points on a coordinate plane using the
Pythagorean Theorem.
(8)
Expressions, equations, and relationships. The student applies mathematical
process standards to use one-variable equations or inequalities in problem
situations. The student is expected to:
(A)
write one-variable equations or inequalities with variables on both sides that
represent problems using rational number coefficients and constants;
(B) write a corresponding real-world problem
when given a one-variable equation or inequality with variables on both sides
of the equal sign using rational number coefficients and constants;
(C) model and solve one-variable equations
with variables on both sides of the equal sign that represent mathematical and
real-world problems using rational number coefficients and constants;
and
(D) use informal arguments to
establish facts about the angle sum and exterior angle of triangles, the angles
created when parallel lines are cut by a transversal, and the angle-angle
criterion for similarity of triangles.
(9) Expressions, equations, and
relationships. The student applies mathematical process standards to use
multiple representations to develop foundational concepts of simultaneous
linear equations. The student is expected to identify and verify the values of
x and y that simultaneously satisfy two
linear equations in the form y = mx + b from the intersections
of the graphed equations.
(10)
Two-dimensional shapes. The student applies mathematical process standards to
develop transformational geometry concepts. The student is expected to:
(A) generalize the properties of orientation
and congruence of rotations, reflections, translations, and dilations of
two-dimensional shapes on a coordinate plane;
(B) differentiate between transformations
that preserve congruence and those that do not;
(C) explain the effect of translations,
reflections over the x- or y- axis, and
rotations limited to 90°, 180°, 270°, and 360° as applied to
two-dimensional shapes on a coordinate plane using an algebraic representation;
and
(D) model the effect on linear
and area measurements of dilated two-dimensional shapes.
(11) Measurement and data. The student
applies mathematical process standards to use statistical procedures to
describe data. The student is expected to:
(A) construct a scatterplot and describe the
observed data to address questions of association such as linear, non-linear,
and no association between bivariate data;
(B) determine the mean absolute deviation and
use this quantity as a measure of the average distance data are from the mean
using a data set of no more than 10 data points; and
(C) simulate generating random samples of the
same size from a population with known characteristics to develop the notion of
a random sample being representative of the population from which it was
selected.
(12) Personal
financial literacy. The student applies mathematical process standards to
develop an economic way of thinking and problem solving useful in one's life as
a knowledgeable consumer and investor. The student is expected to:
(A) solve real-world problems comparing how
interest rate and loan length affect the cost of credit;
(B) calculate the total cost of repaying a
loan, including credit cards and easy access loans, under various rates of
interest and over different periods using an online calculator;
(C) explain how small amounts of money
invested regularly, including money saved for college and retirement, grow over
time;
(D) calculate and compare
simple interest and compound interest earnings;
(E) identify and explain the advantages and
disadvantages of different payment methods;
(F) analyze situations to determine if they
represent financially responsible decisions and identify the benefits of
financial responsibility and the costs of financial irresponsibility;
and
(G) estimate the cost of a
two-year and four-year college education, including family contribution, and
devise a periodic savings plan for accumulating the money needed to contribute
to the total cost of attendance for at least the first year of
college.
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