Geometry Benchmark Task Cards MA.912.D.6.2
BENCHMARK: MA.912.D.6.2 Find the converse, inverse, and contrapositive of a statement.






Academic Voc
converse
inverse
contrapositive
conditional
hypothesis
conclusion
HIGH ORDER QUESTION STEMS



How would you make the
statement converse, inverse or
contrapostive?
How do you find a
counterexample?
Is your answer reasonable/ How
do you know?
Cognitive Complexity
MODERATE
SAMPLE ITEMS
Which of the following is the converse of the following statement?
“If today is Sunday, then tomorrow is Monday.”
★ A. If tomorrow is Monday, then today is Sunday.
B. If tomorrow is not Monday, then today is Sunday.
C. If today is not Sunday, then tomorrow is not Monday.
D. If tomorrow is not Monday, then today is not Sunday
STUDENT SCALE QUESTIONS
EOC TEST ITEM SPECIFICATION
 How have I used this benchmark in my
Also assesses MA.912.D.6.3 Determine whether two
reading/math?
propositions are logically equivalent.
 How did the benchmark help me better
This benchmark will be assessed using MC items.
understand __________?
 Where is my learning on the scale?
(Clarification) The student will:
___ I can teach someone else.

Identify the converse, inverse, or contrapositive
___ I can do it on my own.
of a given statement.
___ I understand, but have questions.

Determine whether two propositions are logically
equivalent.
STUDENT SUMMATIVE WRITING TASK
After completing___________, the evidence from
the lesson that helps me understand and answer
the essential question is ____________. This
relates to the essential question because
______________________.
THINKING MAPS CORRELATION
Cognitive Process: Comparing and Contrasting
Product: Double Bubble Map
Cognitive Process: Classifying
Product: Tree Map
Teaching and Learning, Lake County School District
Content Limits

Truth tables or validity of a given statement will
not be assessed.

Items must present propositions as a sentence,
and not by using
symbols,
Additional Information on page 31 of Geometry
EOC Item Specification Document
Geometry Benchmark Task Cards MA.912.G.1.1
BENCHMARK: MA.912.G.1.1 Find the lengths and midpoints of line segments in two-dimensional
coordinate systems
Academic Voc

midpoint

line segment

distance formula

coordinate plane
HIGH ORDER QUESTION STEMS




How would you find the length or end
points of a segment?
How are averages used to find the
midpoint of a segment?
Why is the distance formula helpful?
Is your answer reasonable? How do you
know?
Cognitive Complexity
MODERATE
SAMPLE ITEMS
The circle shown below is centered at the origin
On a coordinate grid, AB has end point B at (24,
and contains the point (-4, -2).
16). The midpoint of AB is P(4, -3). What is the
y-coordinate of Point A?
Which of the following is closest to the length of
the diameter of the circle?
A. 13.41
B. 11.66
★ C. 8.94
D. 4.47
STUDENT SCALE QUESTIONS
 How have I used this benchmark in my
reading/math?
 How did the benchmark help me better
understand __________?
 Where is my learning on the scale?
___ I can teach someone else.
___ I can do it on my own.
___ I understand, but have questions.
EOC TEST ITEM SPECIFICATION
This benchmark will be assessed using
MC and FR items
STUDENT SUMMATIVE WRITING TASK
Content Limits

Items may require multiple steps.

Items may include both distance and
midpoint.
After completing___________, the evidence from the
lesson that helps me understand and answer the
essential question is ____________. This relates to
the essential question because
______________________.
THINKING MAPS CORRELATION
Cognitive Process: Sequencing
Product: Flow Map
Teaching and Learning, Lake County School District
(Clarification) The student will:

Find the length or midpoint or one of
the end points of a segment.

Justify lengths of segments
Additional Information on page 32-33
of Geometry EOC Item Specification
Document
Geometry Benchmark Task Cards MA.912.G.1.3
BENCHMARK: MA.912.G.1.3 Identify and use the relationships between special pairs of angles
formed by parallel lines and transversals
Academic Voc

parallel lines

transversals

alternate
interior angles

alternate
exterior angles

corresponding
angles

same-side
interior angles
Cognitive Complexity
MODERATE
SAMPLE ITEMS
Highlands Park is located between two parallel streets, Walker
Street and James Avenue. The park faces Walker Street and is
bordered by two brick walls that intersect James Avenue at point
C, as shown below.
What is the measure, in degrees, of <ACB, the angle formed by
the park’s two brick walls?
HIGH ORDER
QUESTION STEMS

What kinds of
angels can be
formed from
parallel lines
and
transversals?
Explain

Describe the
relationship
between the
various types of
angles that are
formed when 2
parallel lines
are cut by a
transversal.

How can
applying
properties of
angles help you
find the
measure of a
missing angle?
STUDENT SCALE QUESTIONS
EOC TEST ITEM SPECIFICATION
How have I used this benchmark in my
reading/math?
 How did the benchmark help me better
understand __________?
 Where is my learning on the scale?
___ I can teach someone else.
___ I can do it on my own.
___ I understand, but have questions.
This benchmark will be assessed using MC and FR items

STUDENT SUMMATIVE WRITING TASK
After completing___________, the evidence from the
lesson that helps me understand and answer the
essential question is ____________. This relates to
the essential question because
______________________.
THINKING MAPS CORRELATION
Cognitive Process: Seeing Analogies
Product: Bridge Map
Cognitive Process: Defining in Context
Product: Circle Map
Teaching and Learning, Lake County School District
(Clarification) The student will:

Recognize, represent, apply, and/or explain properties of
angles formed by parallel lines and transversals.
Content Limits

Items may have multiple sets of parallel lines.

Items will not include more than six lines in the graphic.

Items should not be set in the context of a parallelogram.
Additional Information on page 34-36 of Geometry EOC Item
Specification Document
Geometry Benchmark Task Cards MA.912.G.2.2
BENCHMARK: MA.912.G.2.2 Determine the measures of interior and exterior angles of polygons,
justifying the method used.
Academic Voc

interior angles

exterior angles

regular polygon

polygon angle- sum theorem

polygon exterior angle- sum
theorem
SAMPLE ITEMS
A regular hexagon and a regular heptagon share one Claire is drawing a regular polygon. She has
side, as shown in the diagram below.
drawn two of the sides with an interior angle of
140°, as shown below.
Which of the following is closest to the measure of x,
the angle formed by one side of the hexagon and
one side of the heptagon?
HIGH ORDER QUESTION STEMS
STUDENT SCALE QUESTIONS




Describe the method used to
determine the measure of the
interior/exterior angles.
How could you use the sum of the
interior angles to determine the
number of sides of a polygon?
Is your answer reasonable? How do
you know?
Cognitive Complexity
MODERATE
How have I used this benchmark in my
reading/math?
 How did the benchmark help me better
understand __________?
 Where is my learning on the scale?
___ I can teach someone else.
___ I can do it on my own.
___ I understand, but have questions.
STUDENT SUMMATIVE WRITING TASK
After completing___________, the evidence from the
lesson that helps me understand and answer the
essential question is ____________. This relates to
the essential question because
______________________.
THINKING MAPS CORRELATION
Cognitive Process: Sequencing
Product: Flow Map
Teaching and Learning, Lake County School District
When Claire completes the regular polygon,
what should be the sum, in degrees, of the
measures of the interior angles?
EOC TEST ITEM SPECIFICATION
This benchmark will be assessed using MC and
FR items
(Clarification) The student will:

Determine the measures of interior and
exterior angles of polygons.
Additional Information on page 37-38 of
Geometry EOC Item Specification Document
Geometry Benchmark Task Cards MA.912.G.2.3
BENCHMARK: MA.912.G.2.3 Use properties of congruent and similar polygons to solve mathematical
or real-world problems.
Academic Voc

congruent

similar

corresponding
points

scale model

ratio

proportion
Cognitive Complexity
HIGH
SAMPLE ITEMS
HIGH ORDER
QUESTION STEMS
STUDENT SCALE QUESTIONS
EOC TEST ITEM SPECIFICATION

 How have I used this benchmark in my reading/math?
 How did the benchmark help me better understand __________?
 Where is my learning on the scale?
___ I can teach someone else.
___ I can do it on my own.
___ I understand, but have questions.
Also assesses MA.912.G.2.1 Identify and describe convex,
concave, regular, and irregular polygons.
Also assesses MA.912.G.4.1 Classify, construct, and describe
triangles that are right, acute, obtuse, scalene, isosceles,
equilateral, and equiangular.
Also assesses MA.912.G.4.2 Define, identify, and construct
altitudes, medians, angle bisectors, perpendicular bisectors,
orthocenter, centroid, incenter, and circumcenter.
Also assesses MA.912.G.4.4 Use properties of congruent and
similar triangles to solve problems involving lengths and areas.
Also assesses MA.912.G.4.5 Apply theorems involving
segments divided proportionally.
This benchmark will be assessed using MC and FR items


Describe the
properties of
congruent figures/
similar figures?
How do congruent
figures differ from
similar figures?
How can you
apply properties of
polygons to solve
real world
problems?
STUDENT SUMMATIVE WRITING TASK
After completing___________, the evidence from the lesson that helps me
understand and answer the essential question is ____________. This relates to
the essential question because ______________________.
THINKING MAPS CORRELATION
Cognitive Process: Describing Qualities
Product: Bubble Map
Cognitive Process: Cause and Effect
Product: Multi-Flow Map
Teaching and Learning, Lake County School District
(Clarification) The student will:

Use properties of congruent and/or similar polygons
to solve problems.

Identify characteristics of a triangle based on given
information.

Identify characteristics of a polygon based on given
information.

Identify altitudes, medians, angle bisectors,
perpendicular bisectors, orthocenter, centroid,
incenter, and circumcenter based on given
information.

Use the properties of altitudes, medians, angle
bisectors, and perpendicular bisectors of triangles
to solve problems.

Apply theorems involving segments divided
proportionally in triangles and parallel lines.
Content Limits

Items may require statements and/or justifications
to complete formal and informal proofs.
Additional Information on page 39-41 of Geometry
EOC Item Specification Document
Geometry Benchmark Task Cards MA.912.G.2.4
BENCHMARK: MA.912.G.2.4 Apply transformations (translations, reflections, rotations, dilations,
Cognitive Complexity
HIGH
and scale factors) to polygons to determine congruence, similarity, and symmetry. Know that
images formed by translations, reflections, and rotations are congruent to the original shape. Create
and verify tessellations of the plane using polygons
Academic Voc
SAMPLE ITEMS
A top view of downtown Rockford is shown on the
Pentagon ABCDE is shown below on a coordinate

transformation
grid below, with Granite Park represented by
grid. The coordinates of A, B, C, D, and E all have

translation
quadrilateral ABCD. The shape of a new park, Mica
integer values.

reflection
Park,
will
be
similar
to
the
shape
of
GranitePark.

rotation
Vertices L and M will be plotted on the grid to form

dilation
quadrilateral JKLM, representing Mica Park.

scale factor



congruence
similarity
symmetry
Which of the following coordinates for L and M could
be vertices of JKLM so that the shape of
Mica Park is similar to the shape of Granite Park?
A. L(4, 4), M(4, 3)
B. L(7, 1), M(6, 1)
C. L(7, 6), M(6, 6)
★D. L(8, 4), M(8, 3)
HIGH ORDER QUESTION STEMS





What would happen to the figure
if…?
How can you change a figure’s
position without changing its size
and shape?
How do you recognize symmetry
in a figure?
Where would you use a scale
factor in the real world?
How could you use coordinate
geometry to perform
transformations?
STUDENT SCALE QUESTIONS
 How have I used this benchmark in my
reading/math?
 How did the benchmark help me better
understand __________?
 Where is my learning on the scale?
___ I can teach someone else.
___ I can do it on my own.
___ I understand, but have questions.
STUDENT SUMMATIVE WRITING TASK
After completing___________, the evidence from the
lesson that helps me understand and answer the
essential question is ____________. This relates to
the essential question because
______________________.
THINKING MAPS CORRELATION
Cognitive Process: Cause and Effect
Product: Multi- Flow Map
Teaching and Learning, Lake County School District
EOC TEST ITEM SPECIFICATION
This benchmark will be assessed using MC and
FR items
(Clarification) The student will:

Describe a transformation applied to a
polygon.

Apply one or more transformations and/or
use the result(s) to determine congruence or
similarity.

Use symmetry to plot a congruent polygon.

Describe the transformation used to create a
tessellation of the plane using polygons.
Content Limits

Items may include using coordinate
geometry to perform transformations in the
plane.
Additional Information on page 42-44 of
Geometry EOC Item Specification Document
Geometry Benchmark Task Cards MA.912.G.3.3
BENCHMARK: MA.912.G.3.3 Use coordinate geometry to prove properties of congruent, regular,
and similar quadrilaterals.
Academic Voc

quadrilateral

congruent quadrilateral

regular quadrilateral

similar quadrilateral
Cognitive Complexity
HIGH
SAMPLE ITEMS
On the coordinate grid below, quadrilateral ABCD has vertices with integer coordinates.
Quadrilateral QRST is similar to quadrilateral ABCD with point S located at (5, -1) and point T
located at (-1, -1). Which of the following could be possible coordinates for point Q?
A. (6, -4)
B. (7, -7)
★ C. (-3, -7)
D. (-2, -4)
HIGH ORDER QUESTION STEMS



Describe the characteristics of
congruent/regular/similar quadrilaterals.
Describe how you could prove a figure is
congruent/ regular/ similar.
How do you determine the measure of an
angle using geometric properties?
STUDENT SCALE QUESTIONS
 How have I used this benchmark in my
reading/math?
 How did the benchmark help me better
understand __________?
 Where is my learning on the scale?
___ I can teach someone else.
___ I can do it on my own.
___ I understand, but have questions.
STUDENT SUMMATIVE WRITING TASK
After completing___________, the evidence from the
lesson that helps me understand and answer the
essential question is ____________. This relates to
the essential question because
______________________.
THINKING MAPS CORRELATION
Cognitive Process: Describing Qualities
Product: Bubble Map
Cognitive Process: Sequencing
Product: Flow Map
Teaching and Learning, Lake County School District
EOC TEST ITEM SPECIFICATION
This benchmark will be assessed using
MC items
(Clarification) The student will:

Use coordinate geometry in applying
properties of quadrilaterals and
determining characteristics of
quadrilaterals.

Use coordinate geometry to classify
a quadrilateral.

Use coordinate geometry to
determine congruency or similarity
of quadrilaterals.
Content Limits

Items may include statements
and/or justifications to complete
formal and informal proofs.

Items may include the use of
coordinate planes.
Additional Information on page 48-49
of Geometry EOC Item Specification
Document
Geometry Benchmark Task Cards MA.912.G.3.4
BENCHMARK: MA.912.G.3.4 Prove theorems involving quadrilaterals.








Academic Voc
quadrilateral
trapezoid
parallelogram
rectangle
rhombus
square
kite
diagonal
Cognitive Complexity
HIGH
SAMPLE ITEMS
Mrs. Linder gave her students the following proof to complete.
Which statement best explains why the equation x + 5 = 2x - 3 can
be used to solve for x?
A. Opposite sides of a rhombus are parallel.
★ B. Diagonals of a rhombus bisect each other.
C. Diagonals of a rhombus are perpendicular.
D. All four sides of a rhombus are congruent.
HIGH ORDER
QUESTION STEMS
STUDENT SCALE QUESTIONS
EOC TEST ITEM SPECIFICATION



How have I used this benchmark in my reading/math?
How did the benchmark help me better understand
__________?
 Where is my learning on the scale?
___ I can teach someone else.
___ I can do it on my own.
___ I understand, but have questions.
Also assesses MA.912.D.6.4 Use methods of direct and indirect
proof and determine whether a short proof is logically valid. Also assesses
MA.912.G.3.1 Describe, classify, and compare relationships among
quadrilaterals including the square, rectangle, rhombus, parallelogram,
trapezoid, and kite. Also assesses MA.912.G.3.2 Compare and contrast
special quadrilaterals on the basis of their properties. Also assesses
MA.912.G.8.5 Write geometric proofs, including proofs by contradiction
and proofs involving coordinate geometry. Use and compare a variety of
ways to present deductive proofs, such as flow charts, paragraphs, twocolumn, and indirect proofs. This benchmark will be assessed using MC
and FR items



How could you
classify
quadrilaterals
based on
properties?
Compare the
relationship
between given
quadrilaterals
How could you
prove your
answer correct by
using geometric
properties?
How could you
use diagonals to
determine the
type of a
quadrilateral?
STUDENT SUMMATIVE WRITING TASK
After completing___________, the evidence from the lesson that
helps me understand and answer the essential question is
____________. This relates to the essential question because
______________________.
THINKING MAPS CORRELATION
Cognitive Process: Describing Qualities
Product: Bubble Map
Cognitive Process: Cause and Effect
Product: Multi- Flow Map
Teaching and Learning, Lake County School District
(Clarification) The student will:

Apply properties of special quadrilaterals to determine measures.

Classify a quadrilateral based on its properties.

Use properties and theorems involving quadrilaterals to complete
proofs.
Content Limits

Items may require statements and/or justifications to complete formal
and informal proofs.
Additional Information on page 50-52 of Geometry EOC Item
Specification Document
Geometry Benchmark Task Cards MA.912.G.4.6
BENCHMARK: MA.912.G.4.6 Prove that triangles are congruent or similar and use the concept
of corresponding parts of congruent triangles.
Academic Voc
SAMPLE ITEM
Nancy wrote a proof about the figure shown below.

congruent

similar

corresponding
parts
Cognitive Complexity
HIGH
In the proof below, Nancy started with the fact that XZ is a perpendicular bisector of WY and proved that LWYZ is
isosceles.
HIGH ORDER
QUESTION STEMS

How do you
identify
corresponding
parts of similar
triangles?

How can you show
that two triangles
are similar/
congruent?

How can you tell if
a triangle is
isosceles,
equilateral, or
scalene?
Which of the following correctly replaces the question mark in Nancy’s proof?
A. ASA
B. SAA
*C. SAS
D. SSS
STUDENT SCALE QUESTIONS
EOC TEST ITEM SPECIFICATION
How have I used this benchmark in my reading/math?
How did the benchmark help me better understand
__________?
 Where is my learning on the scale?
___ I can teach someone else.
___ I can do it on my own.
___ I understand, but have questions.
STUDENT SUMMATIVE WRITING TASK


After completing___________, the evidence from the lesson that
helps me understand and answer the essential question is
____________. This relates to the essential question because
______________________.
THINKING MAPS CORRELATION
Cognitive Process: Cause and Effect
Product: Multi-Flow Map
Teaching and Learning, Lake County School District
Also assesses MA.912.D.6.4 Use methods of direct
and indirect proof and determine whether a short
proof is logically valid.
Also assesses MA.912.G.8.5 Write geometric proofs,
including proofs by contradiction and proofs involving
coordinate geometry. Use and compare a variety of
ways to present deductive proofs, such as flow
charts, paragraphs, two-column, and indirect proofs.
This benchmark will be assessed using MC items
(Clarification) The student will:

Determine the congruency or the similarity of
two triangles.

Apply triangle congruence and CPCTC
(corresponding parts of congruent triangles are
congruent) to determine measurements of
angles or lengths.

Complete proofs on triangle congruence or
similarity.
Content Limits

Items may require statements and/or
justifications to complete formal and informal
proofs.
Additional Information on page 53-54 of
Geometry EOC Item Specification Document
Geometry Benchmark Task Cards MA.912.G.4.7
BENCHMARK: MA.912.G.4.7 Apply the inequality theorems: triangle inequality, inequality in one
triangle, and the Hinge Theorem.
Academic Voc

triangle inequality

Hinge Theorem
Cognitive Complexity
MODERATE
SAMPLE ITEMS
A surveyor took some measurements across a river,
Kristin has two dogs, Buddy and Socks.
as shown below. In the diagram, AC = DF and AB =
She stands at point K in the diagram and
DE.
throws two disks. Buddy catches one at
point B, which is 11 meters (m) from
Kristin. Socks catches the other at point
S, which is 6 m from Kristin.
If KSB forms a triangle, which could be
the length, in meters, of segment SB?
HIGH ORDER QUESTION STEMS




Explain the triangle inequality/ theorem?
What do the sides and angles tell you
about the triangle?
What relationship do you see between
the sides and angles of the triangle?
I can prove my answer by…
Which of the following can he conclude?
A. 5 m
★ B. 8 m
C. 17 m
D. 22 m
STUDENT SCALE QUESTIONS
 How have I used this benchmark in my
reading/math?
 How did the benchmark help me better
understand __________?
 Where is my learning on the scale?
___ I can teach someone else.
___ I can do it on my own.
___ I understand, but have questions.
EOC TEST ITEM SPECIFICATION
This benchmark will be assessed using
MC items
STUDENT SUMMATIVE WRITING TASK
After completing___________, the evidence from the
lesson that helps me understand and answer the
essential question is ____________. This relates to
the essential question because
______________________.
THINKING MAPS CORRELATION
Cognitive Process: Defining in Context
Product: Circle Map
Cognitive Process: Sequencing
Product: Flow Map
Teaching and Learning, Lake County School District
(Clarification) The student will:

Apply the inequality theorems to
determine relationships about sides
and angles within a triangle and
between triangles.
Additional Information on page 55-57
of Geometry EOC Item Specification
Document
Geometry Benchmark Task Cards MA.912.G.5.4
BENCHMARK: MA.912.G.5.4 Solve real-world problems involving right triangles
Academic Voc
right triangle
altitude
Pythagorean
theorem

geometric
mean
Cognitive Complexity
HIGH
SAMPLE ITEMS
Nara created two right triangles. She started with triangle JKL and drew
an altitude from point K to sideJL. The diagram below shows triangle JKL
and some of its measurements, in centimeters (cm).



Based on the information in the diagram, what is the measure of x to the
nearest tenth of a centimeter?
HIGH ORDER
QUESTION
STEMS
STUDENT SCALE QUESTIONS
EOC TEST ITEM SPECIFICATION


How have I used this benchmark in my
reading/math?
 How did the benchmark help me better
understand __________?
 Where is my learning on the scale?
___ I can teach someone else.
___ I can do it on my own.
___ I understand, but have questions.
STUDENT SUMMATIVE WRITING TASK
Also assesses MA.912.G.5.1 Prove and apply the Pythagorean Theorem
and its converse.
Also assesses MA.912.G.5.2 State and apply the relationships that exist
when the altitude is drawn to the hypotenuse of a right triangle.
Also assesses MA.912.G.5.3 Use special right triangles (30° - 60° - 90°
and 45° - 45° - 90°) to solve problems.
This benchmark will be assessed using MC and FR items


How can you
apply the
properties of
right angles to
solve real world
problems?
How is the right
triangle
congruence
different from
other types of
triangle
congruence?
Explain the
properties of
right triangles
After completing___________, the evidence
from the lesson that helps me understand and
answer the essential question is
____________. This relates to the essential
question because ______________________.
THINKING MAPS CORRELATION
Cognitive Process: Defining in Context
Product: Circle Map
Cognitive Process: Sequencing
Product: Flow Map
Teaching and Learning, Lake County School District
(Clarification) The student will:

Apply properties of right triangles to solve real-world problems.
Content Limits

Items may require students to apply one or more of the following:
o Pythagorean theorem and its converse;
o geometric mean;
o 30–60–90 triangles; or
o 45–45–90 triangles.
Additional Information on page 58-60 of Geometry EOC Item
Specification Document
Geometry Benchmark Task Cards MA.912.G.6.5
BENCHMARK: MA.912.G.6.5 Solve real-world problems using measures of circumference, arc length,
Cognitive Complexity
HIGH
and areas of circles and sectors.
Academic Voc
SAMPLE ITEMS
Allison created an embroidery design of a stylized star emblem. The Kayla inscribed kite ABCD in a circle, as shown

circumference
perimeter of the design is made by alternating semicircle and
below.

arc

area
quarter-circle arcs. Each arc is formed from a circle with a

radius
inch diameter. There are 4 semicircle and 4 quarter-circle arcs, as

sector
shown in the diagram below.

arc length






chord
tangent
secant
central angle
inscribed angle
diameter
HIGH ORDER
QUESTION STEMS
STUDENT SCALE QUESTIONS






How do you find
the area of a
circle?
How do you find
the length of an arc
measure?
What would
happen to the
circumference/area
of the circle if…?
How can you use
secants, tangents,
and chords to
determine angle
measures related
to circles?
How have I used this benchmark in my reading/math?
How did the benchmark help me better understand
__________?
 Where is my learning on the scale?
___ I can teach someone else.
___ I can do it on my own.
___ I understand, but have questions.
STUDENT SUMMATIVE WRITING TASK
After completing___________, the evidence from the lesson that
helps me understand and answer the essential question is
____________. This relates to the essential question because
______________________.
THINKING MAPS CORRELATION
Cognitive Process: Sequencing
Product: Flow Map
EOC TEST ITEM SPECIFICATION
Also assesses MA.912.G.6.2 Define and
identify: circumference,
radius, diameter, arc, arc length, chord, secant,
tangent and concentric
circles .Also assesses MA.912.G.6.4 Determine
and use measures of arcs
and related angles (central, inscribed, and
intersections of secants and
tangents).This benchmark will be assessed
using MC and FR items
(Clarification) The student will:

Solve problems related to circles using the
properties of chords, secants, tangents,
and concentric circles.

Solve problems involving circumference,
arc length, area of sectors, and area of
circles.

Solve problems related to measures of
arcs and their related angles (central,
inscribed, and intersections of secants and
tangents.)
Content Limits

Items may require statements and/or
justifications to complete formal
and informal proofs.
Additional Information on page 61-63 of
Geometry EOC Item Specification Document
Teaching and Learning, Lake County School District
Geometry Benchmark Task Cards MA.912.G.6.6
BENCHMARK: MA.912.G.6.6 Given the center and the radius, find the equation of a circle in the
coordinate plane or given the equation of a circle in center-radius form, state the center and the
radius of the circle.
Academic Voc
SAMPLE ITEMS

center

radius

equation of a circle
Cognitive Complexity
MODERATE
HIGH ORDER QUESTION
STEMS
STUDENT SCALE QUESTIONS
EOC TEST ITEM SPECIFICATION



How have I used this benchmark in my reading/math?
How did the benchmark help me better understand
__________?
 Where is my learning on the scale?
___ I can teach someone else.
___ I can do it on my own.
___ I understand, but have questions.
Also assesses MA.912.G.6.7 Given the
equation of a circle in center radius form or
given the center and the radius of a circle,
sketch the graph of the circle. This
benchmark will be assessed using MC
items


Describe how to find the
center/radius/graph of a circle
using the equation of a circle?
What does an equation of a
circle tell you? Explain.
What specific information did
you use to write the equation
of the circle?
STUDENT SUMMATIVE WRITING TASK
After completing___________, the evidence from the lesson
that helps me understand and answer the essential question is
____________. This relates to the essential question because
______________________.
THINKING MAPS CORRELATION
Cognitive Process: Part-Whole
Product: Bridge Map
(Clarification) The student will:

Identify the center, radius, and/or
graph of a circle given the equation of
a circle, or write the equation of a
circle given the center, radius, and/or
graph.
Content Limits

Equations of circles must be
presented in center-radius form,
where h and k are rational and r may
be irrational. Items will not require
students to manipulate equations to
or from standard form.
Additional Information on page 64-65 of
Geometry EOC Item Specification
Document
Cognitive Process: Sequencing
Product: Flow Map
Teaching and Learning, Lake County School District
Geometry Benchmark Task Cards MA.912.G.7.1
BENCHMARK: MA.912.G.7.1 Describe and make regular, non-regular, and oblique polyhedra, and
Cognitive Complexity
MODERATE
sketch the net for a given polyhedron and vice versa.
Academic Voc
SAMPLE ITEMS
Below is a net of a polyhedron.
How many faces does a dodecahedron

net
have?

polyhedron

faces

edges

vertices

tetrahedron

hexahedron

cube

octahedron

dodecahedron

icosahedron
How many edges does the polyhedron have?
HIGH ORDER QUESTION STEMS



Describe how to determine the net of a
three dimensional figure.
How can you prove you answer correct?
How do you determine the
faces/edges/vertices of a figure?
A. 6
B. 8
★ C. 12
D. 24
STUDENT SCALE QUESTIONS
 How have I used this benchmark in my
reading/math?
 How did the benchmark help me better
understand __________?
 Where is my learning on the scale?
___ I can teach someone else.
___ I can do it on my own.
___ I understand, but have questions.
STUDENT SUMMATIVE WRITING TASK
After completing___________, the evidence from the
lesson that helps me understand and answer the
essential question is ____________. This relates to
the essential question because
______________________.
THINKING MAPS CORRELATION
Cognitive Process: Part-Whole
Product: Brace Map
EOC TEST ITEM SPECIFICATION
Also assesses MA.912.G.7.2 Describe the
relationships between the faces, edges,
and vertices of polyhedra.
This benchmark will be assessed using
MC and FR items.
(Clarification) The student will:

Identify the net for a give polyhedron
and vice versa.

Identify and determine the types of
faces and/or the numbers of edges,
faces, and vertices of a given
polyhedron or a given net.
Content Limits

Items will only include:
o The five Platonic solids
(tetrahedron, hexahedron or
cube, octahedron,
dodecahedron, a icosahedron);
o Right or oblique prisms or
pyramids with up to 12 edges
on the base or composites;
o Composites of the right or
oblique prisms or pyramids;
and
o Other solids with fewer than 15
faces.

Items must not require use of
formulas relating faces, edges, and
vertices.

Items may not include cones,
spheres, or cylinders.
Additional Information on page 66-67
of Geometry EOC Item Specification
Document
Teaching and Learning, Lake County School District
Geometry Benchmark Task Cards MA.912.G.7.5
BENCHMARK: MA.912.G.7.5 Explain and use formulas for lateral area, surface area, and volume of
solids.
Academic Voc

surface area

lateral area

volume

right prism cylinder

sphere pyramid

cone

composite figure
Cognitive Complexity
MODERATE
SAMPLE ITEMS
Abraham works at the Delicious Cake Factory
The two rectangular prisms shown below are similar to each other.
and packages cakes in cardboard containers
Side corresponds to side and side corresponds to side AB WX, CD
shaped like right circular cylinders with
YZ.
hemispheres on top, as shown in the diagram
below.
What is the surface area of Figure 1, in square units?
Abraham wants to wrap the cake containers
completely in colored plastic wrap and needs
to know how much wrap he will need. What is
the total exterior surface area of the container?
HIGH ORDER QUESTION
STEMS
STUDENT SCALE QUESTIONS
EOC TEST ITEM SPECIFICATION


How have I used this benchmark in my
reading/math?
 How did the benchmark help me better
understand __________?
 Where is my learning on the scale?
___ I can teach someone else.
___ I can do it on my own.
___ I understand, but have questions.
STUDENT SUMMATIVE WRITING TASK
Also assesses MA.912.G.7.4 Identify chords, tangents, radii, and
great circles of spheres.
Also assesses MA.912.G.7.6 Identify and use properties of
congruent and similar solids.
This benchmark will be assessed using MC and FR items



Explain what surface
area/ lateral area /
volume is.
How would you apply the
formula for surface
area/lateral area/volume
to the figure?
What would happen to
the surface area/lateral
area/volume if …?
Explain how you could
determine the surface
area/volume of a
composite figure.
After completing___________, the evidence
from the lesson that helps me understand and
answer the essential question is
____________. This relates to the essential
question because______________________.
THINKING MAPS CORRELATION
Cognitive Process: Defining in Context
Product: Circle Map
Cognitive Process: Part- Whole
Product: Brace Map
Teaching and Learning, Lake County School District
(Clarification) The student will:

Explain and/or apply formulas to determine surface area,
lateral area, and volume of solids

Use properties of congruent solids to determine the lateral
area, surface area, or volume.

Use properties of similar solids to determine the lateral area,
surface area, or volume.
Content Limits

Solids will be limited to right prisms, right-circular cylinders,
spheres, right pyramids, right-circular cones, and/or
composites of these solids.

Items may not include oblique figures.

Items may require students to give a ratio or a scale factor of
the surface area or volume of similar solids.

Items may require students to find a dimension.
Additional Information on page 68-70 of Geometry EOC Item
Specification Document
Geometry Benchmark Task Cards MA.912.G.8.4
BENCHMARK: MA.912.G.8.4 Make conjectures with justifications about geometric ideas.
Distinguish between information that supports a conjecture and the proof of a conjecture.
Academic Voc
SAMPLE ITEMS
In the figure below, line p is parallel to line q.

formal proof

informal proof

conjecture
Cognitive Complexity
HIGH
Janet makes the conjecture that line p is also parallel to line r. What must the value of y be for her
conjecture to be correct?
HIGH ORDER QUESTION STEMS



What statements will guarantee that …?
Explain
How can you prove…?
What evidence can prove your answer
correct?
★ A. 6.75
B. 7.25
C. 8.25
D. 8.75
STUDENT SCALE QUESTIONS
 How have I used this benchmark in my
reading/math?
 How did the benchmark help me better
understand __________?
 Where is my learning on the scale?
___ I can teach someone else.
___ I can do it on my own.
___ I understand, but have questions.
STUDENT SUMMATIVE WRITING TASK
After completing___________, the evidence from the
lesson that helps me understand and answer the
essential question is ____________. This relates to
the essential question because
______________________.
THINKING MAPS CORRELATION
Cognitive Process: Classifying
Product: Tree Map
Teaching and Learning, Lake County School District
EOC TEST ITEM SPECIFICATION
This benchmark will be assessed using
MC items
(Clarification) The student will:

Determine the relationship between
a conjecture and a geometric idea.

Justify conjectures about geometric
ideas.

Determine if the given information
supports or proves a conjecture.
Content Limits

Items must adhere to the content
limits stated in other benchmarks.
Additional Information on page 73-74
of Geometry EOC Item Specification
Document
Geometry Benchmark Task Cards MA.912.T.2.1
BENCHMARK: MA.912.T.2.1 Define and use the trigonometric ratios (sine, cosine, tangent,
cotangent, secant, cosecant) in terms of angles of right triangles.
Academic Voc
A tackle shop and restaurant are located on the

right angle
shore of a lake and are 32 meters (m) apart. A

Pythagorean theorem
boat on the lake heading toward the tackle

sine
shop is a distance of 77 meters from the tackle

cosine
shop. This situation is shown in the diagram

tangent
below, where point T represents the location of

hypotenuse
the tackle shop, point R represents the location

leg
of the restaurant, and point B represents the
location of the boat.
HIGH ORDER QUESTION
STEMS





Describe how to apply the
Pythagorean theorem to real
world problems
What information did you use
to solve the problem?
When would you use right
triangle trigonometry to solve
for a missing quantity in a
triangle?
How do you determine which
trigonometric ratio to use to
solve for the missing variable
in a right triangle?
Is your answer reasonable?
How do you know?
The driver of the boat wants to change
direction to sail toward the restaurant. Which of
the following is closest to the value of x?
★ A. 23
B. 25
C. 65
D. 67
STUDENT SCALE QUESTIONS
How have I used this benchmark in my
reading/math?
 How did the benchmark help me better
understand __________?
 Where is my learning on the scale?
___ I can teach someone else.
___ I can do it on my own.
___ I understand, but have questions.
STUDENT SUMMATIVE WRITING TASK

After completing___________, the evidence
from the lesson that helps me understand and
answer the essential question is
____________. This relates to the essential
question because______________________.
THINKING MAPS CORRELATION
Cognitive Process: Sequencing
Product: Flow Map
Teaching and Learning, Lake County School District
Cognitive Complexity
MODERATE
SAMPLE ITEMS
Mr. Rose is remodeling his house by adding a room to one
side, as shown in the diagram below. In order to determine
the length of the boards he needs for the roof of the room,
he must calculate the distance from point A to point D.
EOC TEST ITEM SPECIFICATION
This benchmark will be assessed using MC and FR items
(Clarification) The student will:

Solve real-world problems involving right-triangle
trigonometry
Content Limits

Items should not include special right triangles (30°60°-90° and 45°-45°-90°) or the Pythagorean
theorem.

Items will assess only sine, cosine, and tangent to
determine the length of a side or an angle measure.
Additional Information on page 75-77 of Geometry EOC
Item Specification Document
Geometry Benchmark Task Cards MA.912.G.2.5
BENCHMARK: MA.912.G.2.5 Explain the derivation and apply formulas for perimeter and area of
Cognitive Complexity
MODERATE
polygons (triangles, quadrilaterals, pentagons, etc.).
Academic Voc
SAMPLE ITEMS
Marisol is creating a custom window frame A square with an area of 144 square centimeters was increased in

perimeter
that is in the shape of a regular hexagon.
length, but not in width, until the resulting rectangle had a

area
She wants to find the area of the hexagon
perimeter that was 4 times the perimeter of the original square. By

apothem
to determine the amount of glass needed.
how many square centimeters did the area of the figure increase?
She measured diagonal d and determined
it was 40 inches. A diagram of the window
frame is shown below.
HIGH ORDER QUESTION
STEMS



How can you apply the
area/ perimeter formula to
solve problems?
Is your answer reasonable?
How do you know?
What would happen to the
area/perimeter of the figure
if…?
Which of the following is closest to the
area, in square inches, of the hexagon?
A. 600
B. 849
★ C. 1,039
D. 1,200
STUDENT SCALE QUESTIONS
How have I used this benchmark in
my reading/math?
 How did the benchmark help me
better understand __________?
 Where is my learning on the scale?
___ I can teach someone else.
___ I can do it on my own.
___ I understand, but have questions.

STUDENT SUMMATIVE WRITING TASK
After completing___________, the
evidence from the lesson that helps me
understand and answer the essential
question is ____________. This relates to
the essential question because
______________________.
THINKING MAPS CORRELATION
Cognitive Process: Cause and Effect
Product: Multi- Flow Map
Cognitive Process: Sequencing
Product: Flow Map
Teaching and Learning, Lake County School District
EOC TEST ITEM SPECIFICATION
Also assesses MA.912.G.2.7 Determine how changes in
dimensions affect the perimeter and area of common geometric
figures.
This benchmark will be assessed using MC and FR items
(Clarification) The student will:

Find the area or perimeter of a polygon or a composite of
common geometric figures by using a formula or deriving the
formula.

Determine how changes in dimensions affect the perimeter or
area of common geometric figures or composite of common
geometric figures.
Content Limits

Items requiring students to calculate area may require the
use of the apothem.
Additional Information on page 45-47 of Geometry EOC Item
Specification Document
Geometry Benchmark Task Cards MA.912.G.7.7
BENCHMARK: MA.912.G.7.7 Determine how changes in dimensions affect the surface area and
volume of common geometric solids.
Academic Voc

perimeter

area

surface area

volume
HIGH ORDER QUESTION STEMS



Describe how changes to parameters of
a figure affect perimeter/area/volume.
What would happen to the
perimeter/area/volume if…?
How could changing one parameter affect
another parameter?
Cognitive Complexity
MODERATE
SAMPLE ITEMS
Kendra has a compost box that has the shape of a
A city is planning to replace one of its
cube. She wants to increase the size of the box by
water storage tanks with a larger one. The
extending every edge of the box by half of its original
city’s old tank is a right circular cylinder
length. After the box is increased in size, which of the
with a radius of 12 feet and a volume of
following statements is true?
10,000 cubic feet. The new tank is a right
circular cylinder with a radius of 15 feet
A. The volume of the new compost box is exactly
and the same height as the old tank. What
112.5% of the volume of the original box.
is the maximum number of cubic feet of
B. The volume of the new compost box is exactly
water the new storage tank will hold?
150% of the volume of the original box.
★ C. The volume of the new compost box is exactly
337.5% of the volume of the original box.
D. The volume of the new compost box is exactly
450% of the volume of the original box.
STUDENT SCALE QUESTIONS
 How have I used this benchmark in my
reading/math?
 How did the benchmark help me better
understand __________?
 Where is my learning on the scale?
___ I can teach someone else.
___ I can do it on my own.
___ I understand, but have questions.
STUDENT SUMMATIVE WRITING TASK
After completing___________, the evidence from the
lesson that helps me understand and answer the
essential question is ____________. This relates to
the essential question because
______________________.
THINKING MAPS CORRELATION
Cognitive Process: Cause and Effect
Product: Multi-Flow Map
Teaching and Learning, Lake County School District
EOC TEST ITEM SPECIFICATION
Also assesses MA.912.G.2.7 Determine
how changes in dimensions affect the
perimeter and area of common geometric
figures.
This benchmark will be assessed using
MC and FR items
(Clarification) The student will:

Determine how changes in
dimension(s) affect surface area or
volume.

Determine how one dimension is
affected by changes in surface area
or volume while other dimensions
remain constant.

Determine how changes to one
dimension will change other
dimensions when the surface area
or volume is held constant.
Content Limits

One or two dimensions may be
changed, resulting in the change of
another dimension.

Solids will be limited to right prisms,
right circular cylinders, spheres, right
pyramids, and right circular cones.

Items may not include oblique
figures.

Changes in dimension may or may
not result in similar figures.
Additional Information on page 71-72
of Geometry EOC Item Specification
Document