Download Standards addressed in Geometry Unit

Standards addressed in Geometry Unit
Common Core Standards
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For Grade 6:
1. 6.NS.8 – Solve real-world and mathematical problems by graphing points in all four
quadrants of the coordinate plane. Include use of coordinates and absolute value to
find distances between points with the same first coordinate or the same second
coordinate.
2. 6.G.3 – Draw polygons in the coordinate plane given coordinates for the vertices;
use coordinates to find the length of a side joining points with the same first
coordinate or the same second coordinate. Apply these techniques in the context of
solving real-world and mathematical problems.
For Grade 7:
1. 7.G.4 – Know the formulas for the area and circumference of a circle and use them
to solve problems.
2. 7.G.5 – Use facts about supplementary, complementary, vertical, and adjacent
angles in a multi-step problem to write and solve simple equations for an unknown
angle in a figure.
3. 7.G.6 – Solve real-world and mathematical problems involving area, volume and
surface are of two-and three-dimensional objects composed of triangles,
quadrilaterals, polygons, cubes, and right prisms.
For Grade 8:
1. 8.G.1 – Verify experimentally the properties of rotations, reflections, and
translations.
2. 8.G.3 – Describe the effect of dilations, translations, rotations, and reflections on
two-dimensional figures using coordinates.
3. 8.G.5 – Use informal arguments to establish facts about the angle sum and exterior
angle of triangles, about the angles created when parallel lines are cut by a
transversal, and the angle-angle criterion similarity of triangles.
4. 8.G.7 – Apply the Pythagorean Theorem to determine unknown side lengths in right
triangles in real-world and mathematical problems in two and three dimensions.
5. 8.G.9 – Know the formulas for the volumes of cones, cylinders, and spheres and use
them to solve real-world and mathematical problems.
For High School Geometry:
1. G.CO - Congruence
G.CO.2 – Represent transformations in the plane.
G.CO.3 – Given a rectangle, parallelogram, trapezoid, or regular polygon, describe
the rotations and reflections that carry it onto itself.
G.CO.4 – Develop definitions of rotations, reflections, and translations in terms of
angles, circles, perpendicular lines, parallel lines, and line segments.
G.CO.6 – Use geometric descriptions of rigid motions to transform figures and to
predict the effect of a given rigid motion on a given figure.
G.CO.8 – Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow
from the definition of congruence in terms of rigid motion.
G.CO.9 – Prove theorems about lines and angles.
G.CO.10 – Prove theorems about triangles.
G.CO.12 – Make formal geometric constructions with a variety of tools and methods
(…paper folding).
2. G.SRT – Similarity, Right Triangles, and Trigonometry
G.SRT.8 – Use trigonometric ratios and the Pythagorean Theorem to solve right
triangles in applied problems.
3. G.GPE – Expressing Geometric Properties with Equations
G.GPE.4 – Use coordinates to prove simple geometric theorems algebraically.
G.GPE.7 – Use coordinates to compute perimeters of polygons and areas of triangles
and rectangles, e.g., using the distance formula.
4. G.GMD – Geometric Measurement and Dimension
G.GMD.3 – Use volume formulas for cylinders, pyramids, cones, and spheres to solve
problems.
TEKS – TX Essential Knowledge and Skills
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For Grade 6
(1) 6.b.1 – The student uses mathematical processes to acquire and demonstrate
mathematical understanding. (All standards A-G)
(2) 6.b.8 – The student applies mathematical process standards to use geometry to
represent relationships and solve problems.
A. TSIET extend previous knowledge of triangles and their properties to include
the sum of angles of a triangle, the relationship between the lengths of sides and
measures of angles in a triangle, and determining when three lengths form a
triangle.
B. TSIET model area formulas for parallelograms, trapezoids, and triangles by
decomposing and rearranging parts of these shapes.
C. TSIET write equations that represent problems related to the area of
rectangles, parallelograms, trapezoids, and triangles and volume of right
rectangular prisms where dimensions are positive rational numbers.
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D. TSIET determine solutions for problems involving the area of rectangles,
parallelograms, trapezoids, and triangles and volume of right rectangular prisms
where dimensions are positive rational numbers.
(3) 6.b.11 – The student applies mathematical process standards to use coordinate
geometry to identify locations on a plane. TSIET graph points in all four quadrants using
ordered pairs of rational numbers.
For Grade 7:
(1) 7.b.1 – The student uses mathematical processes to acquire and demonstrate
mathematical understanding. (All standards A-G)
(2) 7.b.5 – The student applies mathematical process standards to use geometry to
describe or solve problems involving proportional relationships.
A. TSIET generalize the critical attributes of similarity, including ratios within and
between similar shapes.
B. TSIET describe π as the ratio of the circumference of a circle to its diameter.
(3) 7.b.9 – The student applies mathematical process standards to solve geometric
problems.
A. TSIET solve problems involving the volume of rectangular prisms, triangular
prisms, rectangular pyramids, and triangular pyramids.
B. TSIET determine the circumference and area of circles.
C. TSIET solve problems involving the lateral and total surface area of a rectangular
prism, rectangular pyramid, triangular prism, and triangular pyramid by
determining the area of the shape’s net.
For Grade 8:
(1) 8.b.1 – The student uses mathematical processes to acquire and demonstrate
mathematical understanding. (All standards A-G)
(2) 8.b.3 – The student applies mathematical process standards to use proportional
relationships to describe dilations.
A. TSIET generalize that the ratio of corresponding sides of similar shapes are
proportional, including a shape and its dilation.
B. TSIET compare and contrast the attributes of a shape and its dilation(s) on a
coordinate plane.
C. TSIET 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.
(3) 8.b.6 – The student applies mathematical process standards to develop
mathematical relationships and make connections to geometric formulas.
A. TSIET describe the volume formula V = Bh of a cylinder in terms of its base area
and its height.
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B. TSIET model relationship between the volume of a cylinder and a cone having
both congruent bases and heights and connect that relationship to the formulas.
C. TSIET use models and diagrams to explain the Pythagorean Theorem.
(4) 8.b.7 – The student applies mathematical process standards to use geometry to
solve problems.
A. TSIET solve problems involving the volume of cylinders, cones, and spheres.
B. TSIET 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. TSIET use the Pythagorean Theorem and its converse to solve problems.
D. TSIET determine the distance between two points on a coordinate plane using
the Pythagorean Theorem.
(5) 8.b.8 – The student applies mathematical process standards to use one-variable
equations or inequalities in problem situations.
E. TSIET 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 similar triangles.
(6) 8.b.10 – The student applies mathematical process standards to develop
transformational geometry concepts.
A. TSIET generalize the properties of orientation and congruence of rotations,
reflections, translations, and dilations of two-dimensional shapes on a
coordinate plane.
B. TSIET 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.
For High School Geometry:
(1) c.1 – The student uses mathematical processes to acquire and demonstrate
mathematical understanding. (All standards A-G)
(2) c.3 – 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).
A. TSIET describe and perform transformations of figures in a plane use coordinate
notation.
B. TSIET identify and distinguish between reflectional and rotational symmetry in a
plane figure.
(3) c.5 – The student uses constructions to validate conjectures about geometric figures.
A. TSIET 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.
(4) c.6 – The student uses the process skills with deductive reasoning to 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.
A. TSIET verify theorems about angles formed by the intersection of lines and line
segments, including vertical angles, and angles formed by parallel lines cut by a
transversal.
B. TSIET prove two triangles are congruent by applying the SAS, ASA, SSS, AAS, and
HL congruence conditions.
C. TSIET apply the definition of congruence, in terms of rigid transformations, to
identify congruent figures and their corresponding sides and angles.
(5) c.11 – The student uses the process skills in the application of formulas to determine
measures of two- and three-dimensional figures.
A. TSIET apply the formula for the area of regular polygons to solve problems using
appropriate units of measure.
C. TSIET apply the formulas for the total and lateral surface area of threedimensional figures, including prisms, pyramids, cones, cylinders, spheres, and
composite figures, to solve problems using appropriate units of measure.
D. TSIET apply the formulas for the volume of three-dimensional figures, including
prisms, cones, cylinders, spheres, and composite figures to solve problems using
appropriate units of measure.