J.O. Combs Unified School District #44
Geometry
Table of Contents for Geometry
Logic.................................................................................................................................................. 4
Points, Segments, Lines, and Planes ................................................................................................. 6
Angles................................................................................................................................................ 8
Triangle Congruence ......................................................................................................................... 10
Similarity........................................................................................................................................... 12
Polygons ............................................................................................................................................ 14
Right Triangles.................................................................................................................................. 16
Circles................................................................................................................................................ 18
Perimeter and Area............................................................................................................................ 20
Surface Area...................................................................................................................................... 22
Volume .............................................................................................................................................. 24
Transformational Geometry .............................................................................................................. 26
Organizing and Analyzing Data........................................................................................................ 28
Probability and Counting Rules ........................................................................................................ 30
2
Logic
3
Logic
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5
In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0
While engaged in grade appropriate tasks involving logic, the student:
• writes converse, inverse, contrapositive, and biconditional (as applicable) of a
conditional statement (required: statements and symbols)
• writes conclusions using laws of syllogism and detachment (required: statements and
symbols)
• uses inductive reasoning to make a conjecture based on a given pattern
• uses deductive reasoning to construct a 2-column proof
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o hypothesis and conclusion, conjecture, and counterexample
o inductive and deductive reasoning
o negation, symbols of logic, if- then statements
o conditional and biconditional
o converses, inverses
o contrapositive
o postulates, theorems, definition
o reflexive, symmetric, and transitive properties
o 2-column proof
o law of detachment, law of syllogism, congruence
• recognizes or recalls the accuracy of basic solutions or information and performs
basic operations such as:
o identifying accurate statements about the converse, inverse,
contrapositive, and biconditional
o identifying accurate statements about the laws of syllogism and
detachment
o using inductive reasoning in basic situations
o using deductive reasoning in basic situations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
4
Points, Segments, Lines, and Planes
5
Points, Segments, Lines and Planes
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5
In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0
While engaged in grade appropriate tasks involving points, segments, lines and
planes, the student:
• calculates the midpoint of segments (required: midpoint formula)
• calculates the length of segments (required: distance formula)
• applies postulates and theorems to find unknown lengths
• writes the equation of parallel and perpendicular lines given critical information
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o midpoint, midpoint formula
o endpoint, point, line, plane, line segment
o distance formula
o skew lines, parallel lines, perpendicular lines
o parallel planes, perpendicular planes, slope, opposite reciprocal,
perpendicular bisector
o Cartesian plane, ordered pair
o transversal, intersection
o collinear, coplanar
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
6
Angles
7
Angles
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5
In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0
While engaged in grade appropriate tasks involving angles, the student:
• applies postulates and theorems to find unknown angle measures
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o acute, right, obtuse, and straight angles
o ray, vertex, degree
o vertical angles, linear pair
o complementary angles, supplementary angles, corresponding angles,
adjacent angles, alternate interior angles, consecutive interior angles,
alternate exterior angles, consecutive exterior angles
o angle bisectors
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
8
Triangle Congruence
9
Triangle Congruence
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5
In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0
While engaged in grade appropriate tasks involving triangle congruence, the
student:
• uses congruence postulates and theorems to identify congruent triangles
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o equilateral, equiangular
o acute, right, obtuse, scalene, equilateral, isosceles triangles
o median, altitude
o Triangle inequality theorem, midsegment theorem, SAS, SSS, ASA,
AAS, HL postulate and congruence theorems
o corresponding parts
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
10
Similarity
11
Similarity
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5
In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0
While engaged in grade appropriate tasks involving similarity, the student:
• uses similarity postulates and theorems to identify similar polygons
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o SAS, AA, SSS
o similarity postulate and theorems
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
12
Polygons
13
Polygons
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5
In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0
While engaged in grade appropriate tasks involving polygons, the student:
• applies postulates and theorems to find unknown angle measures and segment lengths
(required: triangles, quadrilaterals, and regular polygons)
• differentiates quadrilaterals based on the definition
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o polygon, consecutive angles, interior angle, exterior angle, diagonal
o acute, right, obtuse, scalene, equilateral, and isosceles triangles
o equilateral, equiangular, convex, concave, regular quadrilateral
o kite, trapezoid, isosceles trapezoid
o parallelogram, rhombus, rectangle, square
o pentagon, hexagon, octagon
• performs basic operations such as:
o creating a graphic organizer of the hierarchy of quadrilaterals
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
14
Right Triangles
15
Right Triangles
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5
In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0
While engaged in grade appropriate tasks involving triangle trigonometry, the
student:
• applies the Pythagorean theorem to find unknown side lengths
• calculates unknown side lengths of special right triangles (required: 30-60-90 and 4545-90)
• calculates unknown side lengths and angles measures of right triangles using
trigonometric ratios
• sets up, solves, and analyzes right triangle application problems
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o angle of elevation, angle of depression
o ratio, proportion
o opposite leg, adjacent leg, hypotenuse
o sine, cosine, tangent
o inverse trigonometric functions
o special right triangle relationships
o Pythagorean Theorem
• performs basic operations such as:
o classifying types of triangles using the converse of the Pythagorean
Theorem (required: acute, right, and obtuse)
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
16
Circles
17
Circles
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5
In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0
While engaged in grade appropriate tasks involving circles, the student:
• uses the properties and postulates to find unknown arc lengths, angles, and arc
measures
• graphs a circle from h k form
• writes the equation of a circle given a graph or critical information
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o tangent line, secant line, point of tangency
o chord, radius, diameter, circumference
o arc length, central angle, degree
o geometric definition of a circle
o concentric circles
o inscribed angle, circumscribed angle
o minor arc, major arc, semicircle, intercepted arc
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
18
Perimeter and Area
19
Perimeter and Area
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5
In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0
While engaged in grade appropriate tasks involving perimeter and area, the student:
• calculates the perimeter of planar figures
• calculates the area of planar figures
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o perimeter, circumference
o arc length, pi
o basic area formulas, sector area
o altitude, height
• performs basic operations such as:
o calculating basic area formulas of circles, rectangles, and triangles
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
20
Surface Area
21
Surface Area
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5
In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0
While engaged in grade appropriate tasks involving surface area, the student:
• calculates surface area of a three-dimensional figure
• applies geometric principles to a real life situation (required: surface area)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o surface area, lateral area
o bases, lateral edge, base edge, vertices, faces
o pi, slant height, altitude, height
o basic area formulas
o oblique and right solids
• performs basic operations such as:
o calculating basic surface area formulas of spheres, cylinders, and
rectangular prisms
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
22
Volume
23
Volume
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5
In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0
While engaged in grade appropriate tasks involving volume, the student:
• calculates the volume of a three-dimensional figure
• applies geometric principles to a real life situation (required: volume)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o basic formulas for volume
o cubic units
• performs basic operations such as:
o calculating the volume of right rectangular prisms, cylinders, square
pyramids, cones, and spheres
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
24
Transformational Geometry
25
Transformational Geometry
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5
In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0
While engaged in grade appropriate tasks involving transformational geometry, the
student:
• transforms an image
• differentiates between translations, rotations, and reflections, giving the reflection line
or the direction and angle of rotation, as applicable
• describes translations and reflections using coordinate notation
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o preimage, image
o reflection, rotation, translation, line of reflection, center of rotation
o rigid transformation, isometry, coordinate notation
o line of symmetry, angle of rotation, rotational symmetry
o prime notation
• recognizes and recalls the accuracy of basic solutions and information
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
26
Organizing and Analyzing Data
27
Organizing and Analyzing Data
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5
In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0
While engaged in grade appropriate tasks involving organizing and analyzing data,
the student:
• displays data in an appropriate graphical representation
• calculates measures of central tendency (required: mean, median, and mode)
• calculates measures of variation (required: standard deviation)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o mean
o median
o mode
o histogram
o boxplot
o stem and leaf plot
o central tendency
o variation
o standard deviation
• performs basic processes
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
28
Probability and Counting Rules
29
Probability and Counting Rules
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5
In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0
While engaged in grade appropriate tasks involving organizing and analyzing data,
the student:
• calculates and analyzes the probability of events (required: addition rule and
multiplication rule)
• calculates and analyzes the probability of "at least"/"at most" events (required:
complements)
• calculates and analyzes the probability of events involving counting rules (required:
permutations, combinations, counting principle, and factorials)
• uses permutations and combinations to determine number of total outcomes
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o mutually exclusive
o dependent, independent, conditional
o Law of Large Numbers
o sample space
o equally likely
• performs basic processes
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
30