Texas Administrative Code › Title 19 - EDUCATION › Part 2 - TEXAS EDUCATION AGENCY › Chapter 111 - TEXAS ESSENTIAL KNOWLEDGE AND SKILLS FOR MATHEMATICS › Subchapter C - HIGH SCHOOL › Section 111.41 - Geometry, Adopted 2012 (One Credit)

Current through Reg. 49, No. 28; July 12, 2024
(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.