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Math Standards Document
Geometry
Final Draft
Hawaii School Districts
Prepared by Marzano and Associates
1
Geometry Summary
Chapter
Strand(s)
Topic(s)
Basics of
Geometry and
Geometry
Spatial Sense
Standard(s)
5
Reasoning and
Proof
Geometry and
Spatial Sense
5
Perpendicular
and Parallel
Lines
Congruent
Triangles
Geometry and
Spatial Sense
5
Geometry and
Spatial Sense
5
Geometric
Shapes and
Their Properties
and
Relationships
Quadrilaterals
Geometry and
Spatial Sense
5
Geometry and
Spatial Sense
5
Transformations
Numbers and
Operation
1,3,8
Similarity
Geometry and
Spatial Sense
5
Right Triangles
and
Trigonometry
Circles
Measurement,
Geometry and
Spatial Sense
Geometry and
Spatial Sense
4
Areas of
Polygons and
Circles
Surface Area
and Volume
Measurement
4
Measurement
4, 7
5
Number of
Elements
Level 4.0- 1
Level 3.0- 1
Level 2.0- 1
Level 4.0- 1
Level 3.0- 3
Level 2.0- 3
Level 4.0- 1
Level 3.0- 3
Level 2.0- 3
Level 4.0- 1
Level 3.0- 3
Level 2.0- 2
Level 4.0- 2
Level 3.0- 4
Level 2.0- 4
Level 4.0- 1
Level 3.0- 2
Level 2.0- 1
Level 4.0- 4
Level 3.0- 2
Level 2.0- 3
Level 4.0- 1
Level 3.0- 2
Level 2.0- 2
Level 4.0- 2
Level 3.0- 4
Level 2.0- 4
Level 4.0- 1
Level 3.0- 2
Level 2.0- 2
Level 4.0- 1
Level 3.0- 2
Level 2.0- 3
Level 4.0-2
Level 3.0- 4
Level 2.0- 5
32
Total of Levels 3.0
2
Chapter Topic: Basics of Geometry
Strand: Geometry and Spatial Sense
Standard 5: PROPERTIES AND RELATIONSHIPS: Analyze properties of objects
and relationships among the properties.
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 using logic skills, deduces what kind of figure to draw
Level 3.5
Level 3.0
While engaged in tasks regarding geometric shapes and their properties and
relationships the student will:
 (MA.G.5.1) use inductive and deductive reasoning to create and defend
geometric conjectures (e.g., write a logically sound proof (two-column,
paragraph form) to defend conjectures)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
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 point
o line
o plane
o ray
o line segment
o inductive reasoning
o deductive reasoning
 performs basic processes such as:
o coming up with rational explanations to defend a geometric
conjecture
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.
3
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0
 Given certain conditions, ask students to use logical deduction to draw a
geometric shape.
Level 3.0
 Ask students to use inductive and deductive reasoning to create and defend
geometric conjectures.
Level 2.0
 Ask students to define “point,” “line,” “plane,” “ray,” “line segment.”
 Ask students to come up with rational explanations to defend a geometric
conjecture.
4
Chapter Topic: Reasoning and Proof
Strand: Geometry and Spatial Sense
Standard 5: PROPERTIES AND RELATIONSHIPS: Analyze properties of objects
and relationships among the properties.
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 proves geometric conjectures
Level 3.5
Level 3.0
While engaged in tasks regarding geometric shapes and their properties and
relationships the student will:
 (MA.G.5.1) use inductive and deductive reasoning to create and defend
geometric conjectures (e.g., write a logically sound proof (two-column,
paragraph form) to defend conjectures)
 (MA.G.5.3) explain properties and characteristics of angle bisectors,
perpendicular bisectors, and parallel lines (e.g., use a straight edge and
compass to construct angle bisectors, perpendicular bisectors and parallel
lines) (First Quarter)
 (MA.G.5.4) use the relationship between pairs of angles (complimentary,
supplementary, vertical, exterior, interior) to determine unknown angle
measures or definitions of properties (e.g., use complimentary, supplementary,
vertical, exterior, and interior angles that are formed when two parallel lines
are cut by a transversal to find the measure of an unknown angle) (First
Quarter)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
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 bisect
o complementary angles
o supplementary angles
o congruent angles
 performs basic processes such:
o coming up with rational explanations to defend a geometric
conjecture
o defining perpendicular and bisector; explaining properties and
characteristics of angle bisectors and parallel lines
o defining and recognizing or recalling examples of complimentary,
supplementary, vertical, interior and exterior angles
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.
5
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0
 Ask students to prove a geometric conjecture (in a statement – reason or
paragraph form).
 Ask students to explain/justify why their constructions are bisected or parallel by
naming the appropriate angle relationship.
Level 3.0
 Ask students to use inductive and deductive reasoning to create and defend
geometric conjectures.
 Ask students to explain properties and characteristics of angle bisectors,
perpendicular bisectors, and parallel lines.
 Ask students to use the relationship between pairs of angles (complimentary,
supplementary, vertical, exterior, interior) to determine unknown angle measures
or definitions of properties.
Level 2.0
 Ask students to define “bisect,” “complementary angles,” “supplementary
angles,” “congruent angles.”
 Ask students to come up with rational explanations to defend a geometric
conjecture.
 Ask students to define perpendicular and bisector; be able to explain the
properties and characteristics of angle bisectors and parallel line.
 Ask students to define and recognize or recall examples of complimentary,
supplementary, vertical, interior and exterior angles.
6
Topic: Perpendicular and Parallel Lines
Strand: Geometry and Spatial Sense
Standard 5: PROPERTIES AND RELATIONSHIPS: Analyze properties of objects
and relationships among the properties.
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 explains/justifies why their constructions are bisected or parallel by naming
the appropriate angle relationship
Level 3.5
Level 3.0
While engaged in tasks regarding geometric shapes and their properties and
relationships the student will:
 (MA.G.5.1) use inductive and deductive reasoning to create and defend
geometric conjectures (e.g., write a logically sound proof (two-column,
paragraph form) to defend conjectures)
 (MA.G.5.3) explain properties and characteristics of angle bisectors,
perpendicular bisectors, and parallel lines (e.g., use a straight edge and
compass to construct angle bisectors, perpendicular bisectors and parallel
lines)
 (MA.G.5.4) use the relationship between pairs of angles (complimentary,
supplementary, vertical, exterior, interior) to determine unknown angle
measures or definitions of properties (e.g., use complimentary, supplementary,
vertical, exterior, and interior angles that are formed when two parallel lines
are cut by a transversal to find the measure of an unknown angle)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
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 bisect
o complementary angles
o supplementary angles
o congruent angles
 performs basic process such as:
o coming up with rational explanations to defend a geometric
conjecture
o defining perpendicular and bisector; explaining properties and
characteristics of angle bisectors and parallel lines
o defining and recognizing or recalling examples of complimentary,
supplementary, vertical, interior and exterior angles
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.
7
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0
 Ask students to explain/justify why their constructions are bisected or parallel by
naming the appropriate angle relationship.
Level 3.0
 Ask students to use inductive and deductive reasoning to create and defend
geometric conjectures.
 Ask students to explain properties and characteristics of angle bisectors,
perpendicular bisectors, and parallel lines.
 Ask students to use the relationship between pairs of angles (complimentary,
supplementary, vertical, exterior, interior) to determine unknown angle measures
or definitions of properties.
Level 2.0
 Ask students to define “bisect,” “complementary angles,” “supplementary
angles,” “congruent angles.”
 Ask students to come up with rational explanations to defend a geometric
conjecture.
 Ask students to define perpendicular and bisector; be able to explain the
properties and characteristics of angle bisectors and parallel line.
 Ask students to define and identify complimentary, supplementary, vertical,
interior and exterior angles.
8
Chapter Topic: Congruent Triangles
Strand: Geometry and Spatial Sense
Standard 5: PROPERTIES AND RELATIONSHIPS: Analyze properties of objects
and relationships among the properties.
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 uses the knowledge of interior angles of a polygon to determine unknown
angle measures
Level 3.5
Level 3.0
While engaged in tasks regarding geometric shapes and their properties and
relationships the student will:
 (MA.G.5.1) use inductive and deductive reasoning to create and defend
geometric conjectures (e.g., write a logically sound proof (two-column,
paragraph form) to defend conjectures)
 (MA.G.5.2) use the concept of corresponding parts to prove that triangles and
other polygons are congruent (e.g., identify enough corresponding parts to
determine if two shapes are congruent)
 (MA.G.5.4) use the relationship between pairs of angles (complimentary,
supplementary, vertical, exterior, interior) to determine unknown angle
measures or definitions of properties (e.g., use complimentary, supplementary,
vertical, exterior, and interior angles that are formed when two parallel lines
are cut by a transversal to find the measure of an unknown angle)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
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 corresponding parts
o congruent shapes
 performs basic processes such as:
o coming up with rational explanations to defend a geometric
conjecture
o recognizing or recalling examples of corresponding parts of
polygons; proving triangles are congruent; recognizing or
recalling accurate statements about the difference between
similarity and congruence
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.
9
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0
 Ask students to use knowledge of interior angles of a polygon to determine
unknown angle measures.
Level 3.0
 Ask students to use inductive and deductive reasoning to create and defend
geometric conjectures.
 Ask students to use the concept of corresponding parts to prove that triangles and
other polygons are congruent.
Level 2.0
 Ask students to define “corresponding parts,” “congruent shapes.”
 Ask students to come up with rational explanations to defend a geometric
conjecture.
 Ask students to recognize or recall examples of corresponding parts of polygons;
prove triangles are congruent; recognize or recall accurate statements about the
difference between similarity and congruence.
10
Chapter Topic: Geometric Shapes and Their Properties and Relationships
Strand: Geometry and Spatial Sense
Standard 5: PROPERTIES AND RELATIONSHIPS: Analyze properties of objects
and relationships among the properties.
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 explains/justifies why their constructions are bisected or parallel by naming
the appropriate angle relationship
 uses the knowledge of interior angles of a polygon to determine unknown
angle measures
 applies the properties of angle, perpendicular bisectors, parallel lines and pairs
of angles in a given situation
Level 3.5
Level 3.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
While engaged in tasks regarding geometric shapes and their properties and
relationships the student will:
 (MA.G.5.1) use inductive and deductive reasoning to create and defend
geometric conjectures (e.g., write a logically sound proof (two-column,
paragraph form) to defend conjectures) (Throughout the year)
 (MA.G.5.2) use the concept of corresponding parts to prove that triangles and
other polygons are congruent (e.g., identify enough corresponding parts to
determine if two shapes are congruent) (Second Quarter)
 (MA.G.5.3) explain properties and characteristics of angle bisectors,
perpendicular bisectors, and parallel lines (e.g., use a straight edge and
compass to construct angle bisectors, perpendicular bisectors and parallel
lines) (First Quarter)
 (MA.G.5.4) use the relationship between pairs of angles (complimentary,
supplementary, vertical, exterior, interior) to determine unknown angle
measures or definitions of properties (e.g., use complimentary, supplementary,
vertical, exterior, and interior angles that are formed when two parallel lines
are cut by a transversal to find the measure of an unknown angle) (First
Quarter)
The student exhibits no major errors or omissions.
Level 2.5
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
11
Level 2.0
There are no major errors or omissions regarding the simpler details and
processes as the student:
 recognizes or recalls specific terminology such as:
o corresponding parts
o congruent shapes
o bisect
o complementary angles
o supplementary angles
o congruent angles
o chords
o tangents
o circumference
o arcs
o radius
o diameter
o inscribe
o circumscribe
 performs basic processes such as:
o coming up with rational explanations to defend a geometric
conjecture (all 4 quarters)
o recognizing or recalling examples of corresponding parts of
polygons; proving triangles are congruent; recognizing or
recalling accurate statements about the difference between
similarity and congruence (second quarter)
o defining perpendicular and bisector; explaining properties and
characteristics of angle bisectors and parallel lines (first quarter)
o defining and recognizing or recalling examples of complimentary,
supplementary, vertical, interior and exterior angles (first quarter)
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
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0
 Ask students to use knowledge of interior angles of a polygon to determine
unknown angle measures.
 Ask students to explain/justify why their constructions are bisected or parallel by
naming the appropriate angle relationship.
 Ask students to apply the properties of angle bisectors, perpendicular bisectors,
parallel lines and pairs of angles in a given situation.
Level 3.0
 Ask students to use inductive and deductive reasoning to create and defend
geometric conjectures.
 Ask students to use the concept of corresponding parts to prove that triangles and
other polygons are congruent.
Level 2.0
 Ask students to define “corresponding parts,” “congruent shapes.”
 Ask students to come up with rational explanations to defend a geometric
conjecture.
 Ask students to recognize or recall examples of corresponding parts of polygons;
prove triangles are congruent; recognize or recall accurate statements about the
difference between similarity and congruence.
 Ask students define perpendicular and bisector; explain properties and
characteristics of angle bisectors and parallel lines.
 Ask students to define and recognize or recall examples of complimentary,
supplementary, vertical, interior and exterior angles.
13
Chapter Topic: Quadrilaterals
Strand: Geometry and Spatial Sense
Standard 5: PROPERTIES AND RELATIONSHIPS: Analyze properties of objects
and relationships among the properties.
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 explains/justifies why a quadrilateral is classified as a special quadrilateral by
it’s properties
Level 3.5
Level 3.0
While engaged in tasks regarding geometric shapes and their properties and
relationships the student will:
 (MA.G.5.1) use inductive and deductive reasoning to create and defend
geometric conjectures (e.g., write a logically sound proof (two-column,
paragraph form) to defend conjectures).
 (MA.G.5.2) use the concept of corresponding parts to prove that triangles and
other polygons are congruent (e.g., identify enough corresponding parts to
determine if two shapes are congruent).
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
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 quadrilateral
o parallelogram
o rectangle
o square
o trapezoid
o isosceles trapezoid
o kite
o rhombus
 performs basic processes such as:
o coming up with rational explanations to defend a geometric
conjecture
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
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0
 Ask students to explain/justify why their constructions are bisected or parallel by
naming the appropriate angle relationship.
 Ask students to use knowledge of interior angles of a polygon to determine
unknown angle measures.
Level 3.0
 Ask students to use inductive and deductive reasoning to create and defend
geometric conjectures.
 Ask students to use the concept of corresponding parts to prove that triangles and
other polygons are congruent.
Level 2.0
 Ask students to define “quadrilateral,” “parallelogram,” “rectangle,” “square,”
“rhombus,” “kite,” “trapezoid,” “isosceles trapezoid.”
 Ask students to come up with rational explanations to defend a geometric
conjecture.
15
Chapter Topic: Transformations
Strand: Numbers and Operations
Standard 1: NUMBER SENSE: Understand numbers, ways of representing
numbers, relationships among numbers, and number systems.
Standard 3: COMPUTATION STRATEGIES: Use computational tools and
strategies fluently and, when appropriate, use estimation.
Strand: Geometry and Spatial Sense
Standard 8: REPRESENTATIONAL SYSTEMS: Select and use different
representational systems, including coordinate geometry.
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 justifies why a situation can be represented by vectors
 uses vector addition, subtraction, and scalar multiplication to solve
problems, then justify why their answer(s) is/are correct


applies knowledge of the formulas to solve real-world problems
creates an original Frieze pattern that includes more than one transformation
(TRHVG)
Level 3.5
Level 3.0
While involved in tasks related to vectors the student will:
 (MA.G.1.1) recognize situations that can be represented by vectors (e.g.,
decide if the information in a problem can be represented with vectors, and if
it can, show how to use the vectors)
 (MA.G.3.1) use vector addition, subtraction, and scalar multiplication to solve
problems (e.g., represent the information in a problem with vectors, and
perform the appropriate operation(s) numerically and geometrically to solve
the problem)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
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 direction
o magnitude
o scalar multiplication
o vector
o midpoint
o rotate
o translate
o reflect
 performs basic processes such as:
o defining vector (direction and magnitude)
o using vector addition and subtraction to solve problems
o given coordinates, recognizing or recalling a similar situation and
applying prior knowledge of the appropriate formula
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
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.
16
Level 0.0
Even with help, no understanding or skill demonstrated.
17
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0
 Ask students to justify why a situation can be represented by vectors.
 Ask students to use vector addition, subtraction, and scalar multiplication to solve
problems, then justify why their answer(s) is/are correct.
 Ask students to apply knowledge of the formulas to solve real-world problems.
 Ask students to create an original Frieze pattern that includes more than one
transformation.
Level 3.0
 Ask students to determine if a situation can be represented by vectors.
 Ask students to use vector addition, subtraction, and/or scalar multiplication to
solve word problems.
 Ask students to use coordinate geometry to produce formulas and prove theorems
for the midpoint of a line segment, the distance formula, and forms of equations
of lines and circles.
 Ask the students to describe the concept of rigid motion on figures in the
coordinate plane, including rotation, translation, and reflection.
Level 2.0
 Ask student s to define “direction” and “magnitude” as they relate to vectors.
 Ask students to define vector (must state magnitude and direction in the answer).
 Ask students to define “vector” and “scalar multiplication.”
 Ask students to use vector addition and subtraction to solve problems where the
vectors are given.
 Ask students to define “midpoint,” “rotate,” “translate,” and “reflect” as they
relate to geometry.
 Ask students to recognize or recall a similar situation and apply prior knowledge
of the appropriate formula, when given coordinates.
18
Chapter Topic: Similarity
Strand: Geometry and Spatial Sense
Standard 5: PROPERTIES AND RELATIONSHIPS: Analyze properties of objects
and relationships among the properties.
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 uses the idea of similar triangles to solve complex problems
Level 3.5
Level 3.0
While engaged in tasks regarding geometric shapes and their properties and
relationships the student will:
 (MA.G.5.1) use inductive and deductive reasoning to create and defend
geometric conjectures (e.g., write a logically sound proof (two-column,
paragraph form) to defend conjectures)
 (MA.G.5.2) use the concept of corresponding parts to prove that triangles and
other polygons are congruent or similar (e.g., identify enough corresponding
parts to determine if two shapes are congruent) (Second Quarter)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
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 congruent
o similar
 performs basic processes such as:
o coming up with rational explanations to defend a geometric
conjecture
o recognizing or recalling examples of corresponding parts of
polygons; proving triangles are congruent; recognizing or
recalling accurate statements about the difference between
similarity and congruence
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.
19
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0
 Ask students to use all concepts for polygons to solve nontraditional problems and
defend their solutions.
Level 3.0
 Ask students to use inductive and deductive reasoning to create and defend
geometric conjectures.
 Ask students to use the concept of corresponding parts to prove that triangles and
other polygons are similar.
Level 2.0
 Ask students to define “congruent,” “similar.”
 Ask students to come up with rational explanations to defend a geometric
conjecture.
 Ask students to recognize or recall examples of corresponding parts of polygons;
prove triangles are congruent; recognize or recall accurate statements about the
difference between similarity and congruence.
20
Chapter Topic: Right Triangles and Trigonometry
Strand: Measurement
Standard 4: FLUENCY WITH MEASUREMENT: Understand attributes, units,
and systems of units in measurement and develop and use techniques, tools, and
formulas for measuring.
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 uses right triangle trigonometric ratios to solve for 2 unknown lengths of sides
(given an angle measure and the length of one side)
 solves problems using the formulas for area and volume of two- and threedimensional figures and solids that are made of mixed “shapes”
Level 3.5
Level 3.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
While engaged in tasks involving measurement formulas the student will:
 (MA.G.4.1) use right angle trigonometric ratios to solve for an unknown
length of a side or measure or angle (e.g., use sine, cosine, and tangent to find
the length of a side of a right triangle) (Fourth Quarter)
 (MA.G.4.2) solve problems using the formulas for perimeter, circumference,
area, and volume of two- and three- dimensional figures and solids (e.g., select
and apply the appropriate formula to solve surface area and volume
problems. i.e., calculate the volume of a cone shaped vase to determine the
amount of water needed to fill it) (Fourth Quarter)
 (MA.G.4.3) determine the effect of dimension changes to perimeter, area, and
volume for common geometric figures and solids (e.g., alter the measure of
one of the attributes of a 3-D shape, then determine how that changed affected
the original shape’s surface area and volume. i.e., finds how the volume
changes if the length of the cylinder is doubled.) (Fourth Quarter)
 (MA.G.5.5) apply the concepts of special right triangles to real-world
situations (e.g., recognize if a right triangle is “special” (45-45-90 or 30-6090) and apply the appropriate concepts to find the length of an unknown side)
The student exhibits no major errors or omissions.
Level 2.5
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
21
Level 2.0
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
o area
o circumference
o volume
o 2 and 3 dimensional
o base
o height
o altitude
 performs basic processes such as:
o recognizing or recalling examples of right triangle trig ratio
formulas; placing given information in correct place on right
triangle pictures
o recognizing or recalling examples of formulas for perimeter,
circumference, area, and volume
o plugging information correctly into formulas
o comparing original dimensions calculations to changed dimension
calculations
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
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0
 Ask students to use right triangle trigonometric ratios to solve for 2 unknown
lengths of sides (given an angle measure and the length of one side).
 Ask students to solve problems using the formulas for area and volume of twoand three-dimensional figures and solids that are made of mixed “shapes.”
Level 3.0
 Ask students to use right triangle trigonometric ratios to solve for an unknown
length of a side or measure of an angle.
 Ask students to solve problems using the formulas for perimeter, circumference,
area, and volume of two- and three-dimensional figures and solids.
 Ask student to determine the effect of dimension changes to perimeter, area, and
volume for common geometric figures and solids.
Level 2.0
 Ask students to define “perimeter,” “area,” “circumference,” “volume,” “two- and
three-dimensional,” “base,” “height,” “altitude.”
 Ask students to place given information in the correct place on right triangle
pictures and state the right triangle trigonometric formulas.
 Ask students to write the formulas for perimeter, circumference, area and volume.
 Ask students to plug information correctly into formulas.
 Ask students to compare original dimension calculations to changed dimension
calculations.
23
Chapter Topic: Circles
Strand: Geometry and Spatial Sense
Standard 5: PROPERTIES AND RELATIONSHIPS: Analyze properties of objects
and relationships among the properties.
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 connects two or more circle concepts to solve a complex problem
Level 3.5
Level 3.0
While engaged in tasks regarding geometric shapes and their properties and
relationships the student will:
 (MA.G.5.1) use inductive and deductive reasoning to create and defend
geometric conjectures (e.g., write logically sound proof (two-column,
paragraph form) to defend conjectures)
 (MA.G.5.6) use the relationships among properties of circles (chords,
secants, tangents, arcs, circumference, radius, diameter, inscribed polygons) to
solve problems (e.g., use properties of circles to find the length of the chords
of an inscribed regular hexagon)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
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 chords
o tangents
o circumference
o arcs
o radius
o diameter
o inscribe
o circumscribe
 performs basic processes such as:
o coming up with rational explanations to defend a geometric
conjecture
o recognizing or recalling examples of chords, secants, tangents,
and arcs of circles; solving problems involving one of the above
and either circumference, radius, or diameter
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
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0
 Ask students to use all concepts for circles to solve nontraditional problems and
defend their solutions.
Level 3.0
 Ask students to use inductive and deductive reasoning to create and defend
geometric conjectures.
 Ask students to use the relationships among properties of circles (chords, secants,
tangents, arcs, circumference, radius, diameter, inscribed polygons) to solve
problems.
Level 2.0
 Ask students to define “chords,” “tangents,” “circumference,” “arcs,” “radius,”
“diameter,” “inscribe,” “circumscribe.”
 Ask students to come up with rational explanations to defend a geometric
conjecture.
 Ask students to recognize or recall examples of chords, secants, tangents, and arcs
of circles; solve problems involving one of the above and either circumference,
radius, or diameter.
25
Chapter Topic: Areas of Polygons and Circles
Strand: Measurement
Standard 4: FLUENCY WITH MEASUREMENT: Understand attributes, units,
and systems of units in measurement and develop and use techniques, tools, and
formulas for measuring.
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 solves problems using the formulas for area and volume of two- and threedimensional figures and solids that are made of mixed “shapes”
Level 3.5
Level 3.0
While engaged in tasks involving measurement formulas the student will:
 (MA.G.4.2) solve problems using the formulas for perimeter, circumference,
area, of two- and three- dimensional figures and solids (e.g., select and apply
the appropriate formula to solve surface area problems)
 (MA.G.4.3) determine the effect of dimension changes to perimeter and area
for common geometric figures and solids (e.g., alter the measure of one of the
attributes of a 3-D shape, then determine how that change affected the
original shape’s surface area)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
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
o area
o circumference
o 2 and 3 dimensional
o base
o height
o altitude
 performs basic processes such as:
o recognizing or recalling examples of right triangle trig ratio
formulas; placing given information in correct place on right
triangle pictures
o recognizing or recalling examples of formulas for perimeter,
circumference and area
o plugging information correctly into formulas
o comparing original dimension calculations to changed dimension
calculations
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
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0
 Ask students to use right triangle trigonometric ratios to solve for 2 unknown
lengths of sides (given an angle measure and the length of one side).
 Ask students to solve problems using the formulas for area of two- and threedimensional figures and solids that are made of mixed “shapes.”
Level 3.0
 Ask students to use right triangle trigonometric ratios to solve for an unknown
length of a side or measure of an angle.
 Ask students to solve problems using the formulas for perimeter, circumference
and area of two- and three-dimensional figures and solids.
 Ask students to determine the effect of dimension changes to perimeter and area
for common geometric figures and solids.
Level 2.0
 Ask students to define “perimeter,” “area,” “circumference,” “two- and threedimensional,” “base,” “height,” “altitude.”
 Ask students to place given information in the correct place on right triangle
pictures and state the right triangle trigonometric formulas.
 Ask students to write the formulas for perimeter, circumference and area.
 Ask students to plug the information correctly into formulas.
 Ask students to plug information into the formulas correctly; know how to
compare original dimension calculations to changed dimension calculations.
27
Chapter Topic: Surface Area and Volume
Strand: Measurement
Standard 4: FLUENCY WITH MEASUREMENT: Understand attributes, units,
and systems of units in measurement and develop and use techniques, tools, and
formulas for measuring.
Strand: Geometry and Spatial Sense
Standard 7: VISUAL AND SPATIAL SENSE: Use visualization and spatial
reasoning to solve problems both within and outside of mathematics.
Geometry
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 solves problems using the formulas for area and volume of two- and threedimensional figures and solids that are made of mixed “shapes”
 given a three-dimensional object, designates what other two-dimensional
shapes can be made from cross sections of the object
Level 3.5
Level 3.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
While engaged in tasks involving measurement formulas the student will:
 (MA.G.4.2) solve problems using the formulas for perimeter, circumference,
area, and volume of two- and three- dimensional figures and solids (e.g., select
and apply the appropriate formula to solve surface area and volume
problems. i.e., calculate the volume of a cone shaped vase to determine the
amount of water needed to fill it)
 (MA.G.4.3) determine the effect of dimension changes to perimeter, area, and
volume for common geometric figures and solids (e.g., alter the measure of
one of the attributes of a 3-D shape, then determine how that change affected
the original shape’s surface area and volume. i.e., finds how the volume
changes if the length of the cylinder is doubled)
 (MA.G.7.2) use concrete objects, pictorial representations, computer
software, or graphing calculators to solve geometric problems (e.g., select an
appropriate representation/strategy to solve a geometric problem and show or
explain how the representation/strategy aided in solving the problem)
 (MA.G. 7.1) given a three-dimensional object, designate where to make the
cross section to get a designated two-dimensional shape (e.g., sketch (or uses
computer software) to show two-dimensional drawings of different views,
truncations, and cross-sections of a three-dimensional solid)
The student exhibits no major errors or omissions.
Level 2.5
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
28
Level 2.0
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
o area
o circumference
o volume
o 2 and 3 dimensional
o base
o height
o altitude
o cross section
o truncation
 performs basic processes such as:
o recognizing or recalling examples of triangle trig ratio formulas;
placing given information in correct place on right triangle
pictures
o recognizing or recalling examples of formulas for perimeter,
circumference, area, and volume
o plugging information correctly into formulas
o comparing original dimension calculations to changed dimension
calculations
o given a three-dimensional object, recognizing or recalling what
two-dimensional shape is visible from a designated cross-section
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.
29
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0
 Ask students to use right triangle trigonometric ratios to solve for 2 unknown
lengths of sides (given an angle measure and the length of one side).
 Ask students to solve problems using the formulas for area and volume of twoand three-dimensional figures and solids that are made of mixed “shapes.”
 Ask students to state what other two-dimensional shapes can be made from cross
sections of a three-dimensional object.
Level 3.0
 Ask students to use right triangle trigonometric ratios to solve for an unknown
length of a side or measure of an angle.
 Ask students to solve problems using the formulas for perimeter, circumference,
area, and volume of two- and three-dimensional figures and solids.
 Ask students to determine the effect of dimension changes to perimeter, area, and
volume for common geometric figures and solids.
 Ask students to use concrete objects, pictorial representations, computer software,
or graphing calculators to solve geometric problems.
 Ask students to designate where to make a cross section to get a designated twodimensional shape when given a three-dimensional object.
Level 2.0
 Ask students to define “perimeter,” “area,” “circumference,” “volume,” “two- and
three-dimensional,” “base,” “height,” “altitude.”
 Ask students to place given information in the correct place on right triangle
pictures and state the right triangle trigonometric formulas.
 Ask students to write the formulas for perimeter, circumference, area and volume.
 Ask students to plug the information correctly into formulas.
 Ask students to compare original dimension calculations to changed dimension
calculations.
 Ask students to identify appropriate real-life objects/models that represent the
situation; draw a picture that represents the situation.
 Ask students to define “cross section,” and “truncation” as they relate to threedimensional objects.
 Ask students to recognize or recall what two-dimensional shape is visible from a
designated cross-section when given a three-dimensional object.
30