Amarillo ISD-Geometry Standards
←
→
Page content transcription
If your browser does not render page correctly, please read the page content below
Amarillo ISD— Geometry Standards
Amarillo Independent School District follows the Texas Essential Knowledge and Skills (TEKS). All of AISD curriculum and documents and resources are
aligned to the TEKS.
The State of Texas State Board of Education has defined the focal points for Geometry in mathematics in the first paragraph of the introduction to the
Texas Essential Knowledge and Skills.
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.
Unit 1 – Lines
Unit 2 – Angles Unit 7 – Circles
Unit 3 – Reasoning Unit 8 – 2-D Figures; Probability
Unit 4 – Polygons and Triangle Basics Unit 9 – Solids 3-D
Unit 5 – Congruent and Similar Triangles Unit 10 – Transformations
Unit 6 – Right Triangles and Trigonometry
2021-22 Amarillo ISD Math Curriculum Page 1 of 11Amarillo ISD— Geometry Standards
Unit 1 – Lines 3 Weeks
•
• Basic Vocabulary, Postulates, and Theorems
G.4 Logical argument and constructions. The (A) distinguish between undefined terms, definitions, postulates, conjectures, and theorems;
student uses the process skills with deductive (D) compare geometric relationships between Euclidean and spherical
reasoning to understand geometric relationships. geometries, including parallel lines and the sum of the angles in a triangle.
The student is expected to:
• Segments
G.2 Coordinate and transformational geometry. (A) determine the coordinates of a point that is a given fractional distance less than one from one
The student uses the process skills to understand end of a line segment to the other in one- and two-dimensional coordinate systems, including
the connections between algebra and geometry finding the midpoint;
and uses the one- and two-dimensional (B) derive and use the distance, slope, and midpoint formulas to verify geometric relationships,
coordinate systems to verify geometric including congruence of segments and parallelism or perpendicularity of pairs of lines; and
conjectures. The student is expected to:
G.5 Logical argument and constructions. The (B) construct congruent segments, congruent angles, a segment bisector, an angle bisector,
student uses constructions to validate conjectures perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given
about geometric figures. The student is expected line through a point not on a line using a compass and a straightedge
to: (C) use the constructions of congruent segments, congruent angles, angle bisectors, and
perpendicular bisectors to make conjectures about geometric relationships;
G.6 Proof and congruence. The student uses the (A) verify theorems about angles formed by the intersection of lines and line segments, including
process skills with deductive reasoning to prove vertical angles, and angles formed by parallel lines cut by a transversal and prove equidistance
and apply theorems by using a variety of methods between the endpoints of a segment and points on its perpendicular bisector and apply these
such as coordinate, transformational, and relationships to solve problems;
axiomatic and formats such as two-column, (E) prove a quadrilateral is a parallelogram, rectangle, square, or rhombus using opposite sides,
paragraph, and flow chart. The student is opposite angles, or diagonals and apply these relationships to solve problems.
expected to:
• Lines
G.2 Coordinate and transformational geometry. (B) derive and use the distance, slope, and midpoint formulas to verify geometric relationships,
The student uses the process skills to understand including congruence of segments and parallelism or perpendicularity of pairs of lines; and
the connections between algebra and geometry (C) determine an equation of a line parallel or perpendicular to a given line that passes through a
and uses the one- and two-dimensional given point.
2021-22 Amarillo ISD Math Curriculum Page 2 of 11Amarillo ISD— Geometry Standards
coordinate systems to verify geometric
conjectures. The student is expected to:
G.4 Logical argument and constructions. The (D) compare geometric relationships between Euclidean and spherical
student uses the process skills with deductive geometries, including parallel lines and the sum of the angles in a triangle.
reasoning to understand geometric relationships.
The student is expected to:
G.5 Logical argument and constructions. The (B) construct congruent segments, congruent angles, a segment bisector, an angle bisector,
student uses constructions to validate conjectures perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given
about geometric figures. The student is expected line through a point not on a line using a compass and a straightedge
to:
G.6 Proof and congruence. The student uses the (E) prove a quadrilateral is a parallelogram, rectangle, square, or rhombus using opposite sides,
process skills with deductive reasoning to prove opposite angles, or diagonals and apply these relationships to solve problems.
and apply theorems by using a variety of methods
such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is
expected to:
Unit 2 – Angles 3 Weeks
• Intro to Angles
G.05 - Logical argument and constructions. The (B) construct congruent segments, congruent angles, a segment bisector, an angle bisector,
student uses constructions to validate conjectures perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given
about geometric figures. The student is expected line through a point not on a line using a compass and a straightedge;
to: (C) use the constructions of congruent segments, congruent angles, angle bisectors, and
perpendicular bisectors to make conjectures about geometric relationships;
G.6 Proof and congruence. The student uses the (A) verify theorems about angles formed by the intersection of lines and line segments, including
process skills with deductive reasoning to prove vertical angles, and angles formed by parallel lines cut by a transversal and prove equidistance
and apply theorems by using a variety of methods between the endpoints of a segment and points on its perpendicular bisector and apply these
such as coordinate, transformational, and relationships to solve problems;
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is
expected to:
• Transversal Angles
2021-22 Amarillo ISD Math Curriculum Page 3 of 11Amarillo ISD— Geometry Standards
G.05 - Logical argument and constructions. The (A) investigate patterns to make conjectures about geometric relationships, including angles
student uses constructions to validate conjectures formed by parallel lines cut by a transversal, criteria required for triangle congruence, special
about geometric figures. The student is expected segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and
to: special segments and angles of circles choosing from a variety of tools;
(B) construct congruent segments, congruent angles, a segment bisector, an angle bisector,
perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given
line through a point not on a line using a compass and a straightedge;
G.6 Proof and congruence. The student uses the (A) verify theorems about angles formed by the intersection of lines and line segments, including
process skills with deductive reasoning to prove vertical angles, and angles formed by parallel lines cut by a transversal and prove equidistance
and apply theorems by using a variety of methods between the endpoints of a segment and points on its perpendicular bisector and apply these
such as coordinate, transformational, and relationships to solve problems;
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is
expected to:
Unit 3 – Reasoning 3 Weeks
• Types of Statements with Truth Value and Validity
G.4 Logical argument and constructions. The (B) identify and determine the validity of the converse, inverse, and contrapositive of a conditional
student uses the process skills with deductive statement and recognize the connection between a biconditional statement and a true
reasoning to understand geometric relationships. conditional statement with a true converse;
The student is expected to: (C) verify that a conjecture is false using a counterexample;
G.05 - Logical argument and constructions. The (A) investigate patterns to make conjectures about geometric relationships, including angles
student uses constructions to validate conjectures formed by parallel lines cut by a transversal, criteria required for triangle congruence, special
about geometric figures. The student is expected segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and
to: special segments and angles of circles choosing from a variety of tools;
• Proofs
G.4 Logical argument and constructions. The (A) distinguish between undefined terms, definitions, postulates, conjectures, and theorems;
student uses the process skills with deductive
reasoning to understand geometric relationships.
The student is expected to:
2021-22 Amarillo ISD Math Curriculum Page 4 of 11Amarillo ISD— Geometry Standards
G.6 Proof and congruence. The student uses the (A) verify theorems about angles formed by the intersection of lines and line segments, including
process skills with deductive reasoning to prove vertical angles, and angles formed by parallel lines cut by a transversal and prove equidistance
and apply theorems by using a variety of methods between the endpoints of a segment and points on its perpendicular bisector and apply these
such as coordinate, transformational, and relationships to solve problems;
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is
expected to:
Unit 4 – Polygons and Triangles Basics 2 Weeks
• Polygon Vocabulary with Interior and Exterior Angles
G.4 Logical argument and constructions. The (A) distinguish between undefined terms, definitions, postulates, conjectures, and theorems;
student uses the process skills with deductive
reasoning to understand geometric relationships.
The student is expected to:
G.05 - Logical argument and constructions. The (A) investigate patterns to make conjectures about geometric relationships, including angles
student uses constructions to validate conjectures formed by parallel lines cut by a transversal, criteria required for triangle congruence, special
about geometric figures. The student is expected segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and
to: special segments and angles of circles choosing from a variety of tools;
• Triangle Vocabulary, Classification, Postulates, and Theorems
G.4 Logical argument and constructions. The (A) distinguish between undefined terms, definitions, postulates, conjectures, and theorems;
student uses the process skills with deductive
reasoning to understand geometric relationships.
The student is expected to:
G.05 - Logical argument and constructions. The (A) investigate patterns to make conjectures about geometric relationships, including angles
student uses constructions to validate conjectures formed by parallel lines cut by a transversal, criteria required for triangle congruence, special
about geometric figures. The student is expected segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and
to: special segments and angles of circles choosing from a variety of tools;
(D) verify the Triangle Inequality theorem using constructions and apply the theorem to solve
problems.
G.06 - Proof and congruence. The student uses (D) verify theorems about the relationships in triangles, including proof of the Pythagorean
the process skills with deductive reasoning to Theorem, the sum of interior angles, base angles of isosceles triangles, midsegments, and
prove and apply theorems by using a variety of medians, and apply these relationships to solve problems;
methods such as coordinate, transformational,
and axiomatic and formats such as two-column,
2021-22 Amarillo ISD Math Curriculum Page 5 of 11Amarillo ISD— Geometry Standards
paragraph, and flow chart. The student is
expected to:
• Quadritaterals
G.05 - Logical argument and constructions. The (A) investigate patterns to make conjectures about geometric relationships, including angles
student uses constructions to validate conjectures formed by parallel lines cut by a transversal, criteria required for triangle congruence, special
about geometric figures. The student is expected segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and
to: special segments and angles of circles choosing from a variety of tools;
G.06 - Proof and congruence. The student uses (E) prove a quadrilateral is a parallelogram, rectangle, square, or rhombus using opposite sides,
the process skills with deductive reasoning to opposite angles, or diagonals and apply these relationships to solve problems.
prove and apply theorems by using a variety of
methods such as coordinate, transformational,
and axiomatic and formats such as two-column,
paragraph, and flow chart. The student is
expected to:
Unit 5 – Congruent and Similar Triangles 3 Weeks
• Congruent Triangles
G.05 - Logical argument and constructions. The (A) investigate patterns to make conjectures about geometric relationships, including angles
student uses constructions to validate conjectures formed by parallel lines cut by a transversal, criteria required for triangle congruence, special
about geometric figures. The student is expected segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and
to: special segments and angles of circles choosing from a variety of tools;
G.06 - Proof and congruence. The student uses (B) prove two triangles are congruent by applying the Side-Angle-Side, Angle-Side-Angle, Side-Side-
the process skills with deductive reasoning to Side, Angle-Angle-Side, and Hypotenuse-Leg congruence conditions;
prove and apply theorems by using a variety of (C) apply the definition of congruence, in terms of rigid transformations, to identify congruent
methods such as coordinate, transformational, figures and their corresponding sides and angles;
and axiomatic and formats such as two-column, (E) prove a quadrilateral is a parallelogram, rectangle, square, or rhombus using opposite sides,
paragraph, and flow chart. The student is opposite angles, or diagonals and apply these relationships to solve problems.
expected to:
• Similar Triangles
G.07- Similarity, proof, and trigonometry. The (A) apply the definition of similarity in terms of a dilation to identify similar figures and
student uses the process skills in applying their proportional sides and the congruent corresponding angles; and
similarity to solve problems. The student is (B) apply the Angle-Angle criterion to verify similar triangles and apply the proportionality of
expected to: the corresponding sides to solve problems.
2021-22 Amarillo ISD Math Curriculum Page 6 of 11Amarillo ISD— Geometry Standards
G.08 - Similarity, proof, and trigonometry. The (A) prove theorems about similar triangles, including the Triangle Proportionality
student uses the process skills with deductive theorem, and apply these theorems to solve problems; and
reasoning to prove and apply theorems by using a (B) identify and apply the relationships that exist when an altitude is drawn to the hypotenuse of a
variety of methods such as coordinate, right triangle, including the geometric mean, to solve problems.
transformational, and axiomatic and formats such
as two-column, paragraph, and flow chart. The
student is expected to:
DCA December 6-17, 2021 (Units 1-5)
Unit 6– Right Triangles and Trigonometry 5 Weeks
• Pythagorean Theorem, Pythagorean Triples
G.09 - Similarity, proof, and trigonometry. The (B) apply the relationships in special right triangles 30°-60°-90° and 45°-45°-90° and the
student uses the process skills to understand and Pythagorean theorem, including Pythagorean triples, to solve problems.
apply relationships in right triangles. The student
is expected to:
• Special Right Triangles
G.09 - Similarity, proof, and trigonometry. The (B) apply the relationships in special right triangles 30°-60°-90° and 45°-45°-90° and the
student uses the process skills to understand and Pythagorean theorem, including Pythagorean triples, to solve problems.
apply relationships in right triangles. The student
is expected to:
• Trigonometry
G.09 - Similarity, proof, and trigonometry. The (A) determine the lengths of sides and measures of angles in a right triangle by applying the
student uses the process skills to understand and trigonometric ratios sine, cosine, and tangent to solve problems;
apply relationships in right triangles. The student
is expected to:
Unit 7– Circles 3 Weeks
• Standard Equation of a Circle
G.12 - Circles. The student uses the process skills (E) show that the equation of a circle with center at the origin and
to understand geometric relationships and apply radius r is x2 + y2 = r2 and determine the equation for the graph of a circle with radius r and
center (h, k), (x - h)2 + (y - k)2 =r2.
2021-22 Amarillo ISD Math Curriculum Page 7 of 11Amarillo ISD— Geometry Standards
theorems and equations about circles. The student
is expected to:
• Special Segments and Angles in Circles
G.05 - Logical argument and constructions. The (A) investigate patterns to make conjectures about geometric relationships, including angles
student uses constructions to validate conjectures formed by parallel lines cut by a transversal, criteria required for triangle congruence, special
about geometric figures. The student is expected segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and
to: special segments and angles of circles choosing from a variety of tools;
G.12 - Circles. The student uses the process skills (A) apply theorems about circles, including relationships among angles, radii, chords, tangents, and
to understand geometric relationships and apply secants, to solve non-contextual problems;
theorems and equations about circles. The student
is expected to:
Unit 8– 2-D Figures; Probability 3 Weeks
• Arc Length & Sector Area
G.12 - Circles. The student uses the process skills (B) apply the proportional relationship between the measure of an arc length of a circle and the
to understand geometric relationships and apply circumference of the circle to solve problems;
theorems and equations about circles. The student (C) apply the proportional relationship between the measure of the area of a sector of a circle and
is expected to: the area of the circle to solve problems;
(D) describe radian measure of an angle as the ratio of the length of an arc intercepted by a central
angle and the radius of the circle; and
• Composite Figures
G.11 - Two-dimensional and three-dimensional (A) apply the formula for the area of regular polygons to solve problems using appropriate units of
figures. The student uses the process skills in the measure;
application of formulas to determine measures of (B) determine the area of composite two-dimensional figures comprised of a combination of
two- and three-dimensional figures. The student is triangles, parallelograms, trapezoids, kites, regular polygons, or sectors of circles to solve
expected to: problems using appropriate units of measure;
• Dimension Change of 2-D Figures
G.10 - Two-dimensional and three-dimensional (B) determine and describe how changes in the linear dimensions of a shape affect its perimeter,
figures. The student uses the process skills to area, surface area, or volume, including proportional and non-proportional dimensional change.
recognize characteristics and dimensional changes
of two- and three-dimensional figures. The
student is expected to:
2021-22 Amarillo ISD Math Curriculum Page 8 of 11Amarillo ISD— Geometry Standards
• Probability
G.13 - Probability. The student uses the process (A) develop strategies to use permutations and combinations to solve contextual problems;
skills to understand probability in real-world (B) determine probabilities based on area to solve contextual problems;
situations and how to apply independence and (C) identify whether two events are independent and compute the probability of the two events
dependence of events. The student is expected to: occurring together with or without replacement;
(D) apply conditional probability in contextual problems; and
(E) apply independence in contextual problems.
DCA April 4 – 15, 2022 (Units 6-8)
Unit 9– Solids 3-D 5 Weeks
• Surface Area and Volume of Solids and Composite Figures
G.10 - Two-dimensional and three-dimensional (A) identify the shapes of two-dimensional cross-sections of prisms, pyramids, cylinders, cones, and
figures. The student uses the process skills to spheres and identify three-dimensional objects generated by rotations of two-
recognize characteristics and dimensional changes dimensional shapes; and
of two- and three-dimensional figures. The
student is expected to:
G.11 - Two-dimensional and three-dimensional (C) apply the formulas for the total and lateral surface area of three-dimensional figures, including
figures. The student uses the process skills in the prisms, pyramids, cones, cylinders, spheres, and composite figures, to solveproblems using
application of formulas to determine measures of appropriate units of measure; and
two- and three-dimensional figures. The student is (D) apply the formulas for the volume of three-dimensional figures, including prisms, pyramids,
expected to: cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of
measure.
• Changing Dimension
G.10 - Two-dimensional and three-dimensional (B) determine and describe how changes in the linear dimensions of a shape affect its perimeter,
figures. The student uses the process skills to area, surface area, or volume, including proportional and non-proportional dimensional change.
recognize characteristics and dimensional changes
of two- and three-dimensional figures. The
student is expected to:
Unit 10– Transformations 1 Week
• Rigid vs. Non-Rigid Transformations
2021-22 Amarillo ISD Math Curriculum Page 9 of 11Amarillo ISD— Geometry Standards
G.03 - Coordinate and transformational (A) describe and perform transformations of figures in a plane using coordinate notation;
geometry. The student uses the process skills to (B) determine the image or pre-image of a given two-dimensional figure under a composition of
generate and describe rigid transformations rigid transformations, a composition of non-rigid transformations, and a composition of
(translation, reflection, and rotation) and non-rigid both, including dilations where the center can be any point in the plane;
transformations (dilations that preserve similarity (C) identify the sequence of transformations that will carry a given pre-image onto an image on and
and reductions and enlargements that do not off the coordinate plane; and
preserve similarity). The student is expected to: (D) identify and distinguish between reflectional and rotational symmetry in a plane figure.
G.06 - Proof and congruence. The student uses (C) apply the definition of congruence, in terms of rigid transformations, to identify congruent
the process skills with deductive reasoning to figures and their corresponding sides and angles;
prove and apply theorems by using a variety of
methods such as coordinate, transformational,
and axiomatic and formats such as two-column,
paragraph, and flow chart. The student is
expected to:
G.07- Similarity, proof, and trigonometry. The (A) apply the definition of similarity in terms of a dilation to identify similar figures and
student uses the process skills in applying their proportional sides and the congruent corresponding angles; and
similarity to solve problems. The student is
expected to:
G.12 - Circles. The student uses the process skills (E) show that the equation of a circle with center at the origin and
to understand geometric relationships and apply radius r is x2 + y2 = r2 and determine the equation for the graph of a circle with radius r and
theorems and equations about circles. The student center (h, k), (x - h)2 + (y - k)2 =r2.
is expected to:
2021-22 Amarillo ISD Math Curriculum Page 10 of 11Amarillo ISD— Geometry Standards
To ensure that every student has an opportunity to learn, understand and demonstrate the Texas Essential Knowledge and Skills. Amarillo Independent
has adopted the following protocols for teachers, curriculum and others to use in reference to Curriculum, Instruction and Assessment.
Curriculum
1) Prioritize essential learning based on AISD written curriculum and adhere to the scope and sequence.
2) Develop deep understandings of the AISD written curriculum with an emphasis on the essential learning outcomes.
3) Create relevant learning environments in every classroom using the AISD written curriculum.
4) Analyze vertical and horizontal alignment to ensure grade level curriculum is being taught.
Instruction
1) Common lessons are developed based on strategically selected grade level TEKS and include learning opportunities for students that:
are at the expected level of thinking and rigor
utilize research based instructional strategies
are actively engaging
have real world applications
2) Collaboratively align instruction to assessment.
3) Individual student instructional needs are considered and addressed in the lessons.
4) Strategic re-teaching when students do not understand.
5) Common lessons are analyzed and strengthened through a continuous improvement process such as the Professional Teaching Model, Lesson
Study or other method for collaborative study and sharing.
Assessment
1) Collaboratively align all assessment to the AISD written curriculum and reflect appropriate rigor.
2) Collaboratively engage in purposeful dialogue about assessment tied to clearly defined essential learning outcomes.
3) Continuously improve and adjust instruction based on common assessment results and student work.
4) Provide feedback to the annual curriculum feedback and revision process.
2021-22 Amarillo ISD Math Curriculum Page 11 of 11You can also read
