| (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 Geometry, students will build on the knowledge
and skills for mathematics in Kindergarten-Grade 8 and Algebra I to
strengthen their mathematical reasoning skills in geometric contexts.
Within the course, students will begin to focus on more precise terminology,
symbolic representations, and the development of proofs. Students
will explore concepts covering coordinate and transformational geometry;
logical argument and constructions; proof and congruence; similarity,
proof, and trigonometry; two- and three-dimensional figures; circles;
and probability. Students will connect previous knowledge from Algebra
I to Geometry through the coordinate and transformational geometry
strand. In the logical arguments and constructions strand, students
are expected to create formal constructions using a straight edge
and compass. Though this course is primarily Euclidean geometry, students
should complete the course with an understanding that non-Euclidean
geometries exist. In proof and congruence, students will use deductive
reasoning to justify, prove and apply theorems about geometric figures.
Throughout the standards, the term "prove" means a formal proof to
be shown in a paragraph, a flow chart, or two-column formats. Proportionality
is the unifying component of the similarity, proof, and trigonometry
strand. Students will use their proportional reasoning skills to prove
and apply theorems and solve problems in this strand. The two- and
three-dimensional figure strand focuses on the application of formulas
in multi-step situations since students have developed background
knowledge in two- and three-dimensional figures. Using patterns to
identify geometric properties, students will apply theorems about
circles to determine relationships between special segments and angles
in circles. Due to the emphasis of probability and statistics in the
college and career readiness standards, standards dealing with probability
have been added to the geometry curriculum to ensure students have
proper exposure to these topics before pursuing their post-secondary
education.
(4) These standards are meant to provide clarity and
specificity in regards to the content covered in the high school geometry
course. These standards are not meant to limit the methodologies used
to convey this knowledge to students. Though the standards are written
in a particular order, they are not necessarily meant to be taught
in the given order. In the standards, the phrase "to solve problems"
includes both contextual and non-contextual problems unless specifically
stated.
(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 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) Coordinate and transformational geometry. The student
uses the process skills to understand the connections between algebra
and geometry and uses the one- and two-dimensional coordinate systems
to verify geometric conjectures. The student is expected to:
(A) determine the coordinates of a point that is a
given fractional distance less than one from one end of a line segment
to the other in one- and two-dimensional coordinate systems, including
finding the midpoint;
(B) derive and use the distance, slope, and midpoint
formulas to verify geometric relationships, including congruence of
segments and parallelism or perpendicularity of pairs of lines; and
(C) determine an equation of a line parallel or perpendicular
to a given line that passes through a given point.
(3) Coordinate and transformational geometry. The student
uses the process skills to generate and describe rigid transformations
(translation, reflection, and rotation) and non-rigid transformations
(dilations that preserve similarity and reductions and enlargements
that do not preserve similarity). The student is expected to:
(A) describe and perform transformations of figures
in a plane using coordinate notation;
(B) determine the image or pre-image of a given two-dimensional
figure under a composition of rigid transformations, a composition
of non-rigid transformations, and a composition of both, including
dilations where the center can be any point in the plane;
(C) identify the sequence of transformations that will
carry a given pre-image onto an image on and off the coordinate plane;
and
(D) identify and distinguish between reflectional and
rotational symmetry in a plane figure.
(4) Logical argument and constructions. The student
uses the process skills with deductive reasoning to understand geometric
relationships. The student is expected to:
(A) distinguish between undefined terms, definitions,
postulates, conjectures, and theorems;
(B) identify and determine the validity of the converse,
inverse, and contrapositive of a conditional statement and recognize
the connection between a biconditional statement and a true conditional
statement with a true converse;
(C) verify that a conjecture is false using a counterexample;
and
(D) compare geometric relationships between Euclidean
and spherical geometries, including parallel lines and the sum of
the angles in a triangle.
(5) Logical argument and constructions. The student
uses constructions to validate conjectures about geometric figures.
The student is expected to:
(A) investigate patterns to make conjectures about
geometric relationships, including angles formed by parallel lines
cut by a transversal, criteria required for triangle congruence, special
segments of triangles, diagonals of quadrilaterals, interior and exterior
angles of polygons, and special segments and angles of circles choosing
from a variety of tools;
Cont'd... |
