FRSD Geometry Curriculum Grade 8
Collins, Dana; Hering, Carly; McAnlis, Melissa
Unit
Essential
Questions
Enduring
Knowledge/ Assess
Understandings Skills
ments
Building
Blocks of
Geometry
(Week 1,
2 Weeks)
How can
you use
dynamic
geometry
software to
visualize
geometric
concepts?
How can
you measure
and construct a
line segment?
How can
you find the
midpoint, length
of a line
segment,
perimeter and
area in a
coordinate
plane?
How can
you measure
and classify an
angle?
How can
you describe
angle pair
relationships
and use these
Students
will be
able to:
The
undefined
concepts of
point, line,
and plane
are the basis
of geometry.
Geometric
concepts
can be
better
explained
and
understood
by using
construction
s.
Understan
d the
undefined
concepts of
point, line,
and plane.
Apply the
undefined
concepts of
point, line,
and plane
to define
and use
collinear
points,
coplanar
points, line
segment,
ray,
opposite
rays,
intersection
s of lines,
planes,
and
Learning Experiences
Learning Activities
Basic Geometry Language Video
https://www.khanacademy.org/math/geometry/intro_euclid
/v/language-and-notation-of-basic-geometry OR
Resources
Exploring Geometry with
GeoGebra
Big Ideas Textbook
Chromebooks
http://tube.geogebra.org/student/m98533 (Links
Attached)
Angle Bisector and Perpendicular Bisector of a Line
Segment GeoGebra Exploration Perpendicular bisector
and Angle Bisector.pdf
Modern Art Project with Geometer's Sketchpad (adapt
from Introduction Activity pg. 8 - 10 Introduction to
GeoGebra.pdf)
https://www.khanacademy.org/math/geometry/intro_euclid
/v/language-and-notation-of-basic-geometry
http://tube.geogebra.org/student/m98533
Perpendicular bisector and Angle Bisector.pdf
Introduction to GeoGebra.pdf
http://www.mathwarehouse.com/algebra/distance_formula
/interactive-distance-formula.php
https://www.khanacademy.org/math/basic-geo/basicgeo-pythagorean-topic/basic-geo-pythagoreantheorem/v/soccer-thiago
Unit Review and Answers
(*attached) Ch1 Test
Review.docx Ch1 Test
Review Answers.docx
Quiz Review Answers
(*attached) Quiz Review
sheet Answers.pdf
Solving Equations in One
Variable Video Review
(*link attached)
https://www.khanacademy.
org/math/algebra/solvinglinear-equations-andinequalities/complicated_e
quations/v/multi-stepequations
Teacher created materials
Ch1 Test Review.docx
Differen
tiation
Unit
Essential
Questions
descriptions to
find angle
measures?
Enduring
Knowledge/ Assess
Understandings Skills
ments
segments.
Use the
Ruler
Postulate
to
understand
measurem
ent and
length
.
Understan
d and use
the
Segment
Addition
Postulate
to
determine
lengths of
segments.
Copy
segments
and
compare
segments
for
congruenc
e.
Students
will be able
Learning Experiences
Resources
Ch1 Test Review
Answers.docx
Quiz Review sheet
Answers.pdf
https://www.khanacademy.
org/math/algebra/solvinglinear-equations-andinequalities/complicated_e
quations/v/multi-stepequations
Differen
tiation
Unit
Essential
Questions
Enduring
Knowledge/ Assess
Understandings Skills
ments
to
compare,
contrast,
and
classify
polygons.
Define an
angle and
identify its
parts.
Compare,
contrast,
ad classify
angles
obtuse,
acute,
right,
straight,
and reflex)*
Define and
identify
congruent
angles and
angle
bisectors.
Define and
identify
compleme
ntary and
supplemen
tary
Learning Experiences
Resources
Differen
tiation
Unit
Essential
Questions
Enduring
Knowledge/ Assess
Understandings Skills
ments
Learning Experiences
Resources
angles.
Define and
identify a
linear pair
and vertical
angles.
Use
dynamic
geometry
software to
visualize
and
represent
geometric
concepts.
Reasonin
g and
Proofs
(Week 3,
4 Weeks)
When is a
conditional
statement true
or false?
How can you
use reasoning
to solve
problems?
In a diagram,
what can be
assumed and
what needs to
be labeled?
How can
algebraic
Proofs of
theorems
are a form
of deductive
reasoning.
Reasoning
skills allow
one to
successfully
prove ideas
and solve
problems.
Students
will be
able to:
Write
conditional
and
bicondition
al
statements
.
Use and
understand
definitions
Exploring Geometry with
GeoGebra
Big Ideas Textbook
Chromebooks
Teacher created materials
Differen
tiation
Unit
Essential
Questions
properties
help you solve
an equation?
How can you
prove a
mathematical
statement?
Enduring
Knowledge/ Assess
Understandings Skills
ments
as
bicondition
als.
Compare
and
contrast
inductive
and
deductive
reasoning.
Identify
postulates
using
diagrams.
Sketch and
interpret
diagrams
of points,
lines,
planes
Apply
Algebraic
Properties
and the
Distributive
Property to
justify
steps in
solving
equations
and
Learning Experiences
Resources
Differen
tiation
Unit
Essential
Questions
Enduring
Knowledge/ Assess
Understandings Skills
ments
Learning Experiences
Resources
involving
segment
lengths
and angle
measures.
Develop
and write
two-column
proofs on
segment
and angle
relationship
s.
Use
dynamic
geometry
software to
visualize
and
represent
geometric
concepts.
Parallel
and
Perpendic
ular Lines
(Week 7,
3 Weeks)
● What does it
mean when two
lines are
parallel,
intersecting,
coincident or
skew?
● Certain
relationships
exist between
lines and
angles.
● Logical
arguments can
Students
will be
able to:
https://www.khanacademy.org/math/geometry/paralleland-perpendicular-lines/triang_prop_tut/v/proofcorresponding-angle-equivalence-implies-parallel-lines
Identify
lines and
planes,
parallel
http://www.pleasanton.k12.ca.us/avhsweb/kiyoi/Sketchpa
d/Constructing_Parallel_Lines_Guide.pdf
https://www.khanacademy.org/math/geometry/geometric-
Exploring Geometry with
GeoGebra
Big Ideas Textbook
Chromebooks
Differen
tiation
Unit
Essential
Questions
● When two
parallel lines are
cut by a
transversal,
which of the
resulting pairs of
angles are
congruent?
Supplementary?
● For which of
the theorems
involving parallel
lines and
transversals is
the converse
true?
● What
conjectures can
you make about
perpendicular
lines?
● How can you
write an
equation of a
line that is
parallel or
perpendicular to
a given line
passing through
a given point?
Enduring
Knowledge/ Assess
Understandings Skills
ments
be made
based on
known
information or
deduced
information
and
perpendicu
lar lines
and pairs
of angles
formed by
transversal
s.
Use
properties
to prove
theorems
about
parallel
and
perpendicu
lar lines
and apply
these
properties
to real-life
problems.
Construct
parallel
and
perpendicu
lar lines.
Use slope
to partition
directed
line
segments
Learning Experiences
constructions/geo-bisectors/v/constructing-aperpendicular-line-using-a-compass-and-straightedge
http://tube.geogebra.org/student/mETI8RCVi?mobile=true
Resources
Teacher created materials
Differen
tiation
Unit
Essential
Questions
Enduring
Knowledge/ Assess
Understandings Skills
ments
Learning Experiences
Resources
and to find
the
distance
from a
point to a
line.
Write
equations
of parallel
and
perpendicu
lar lines.
Use
dynamic
geometry
software to
visualize
and
represent
geometric
concepts.
Transform
ations
(Week 10,
3 Weeks)
How can you
translate, reflect,
and rotate a
figure in a
coordinate
plane?
What
conjectures can
● Rigid
motions are
connected to
congruence.
Students
will be
able to:
● Dilations are
connected to
similarity.
Perform
translations
,
reflections,
rotations,
Exploring Geometry with
GeoGebra
Geogebra Exploring TransformationsGEOGEBRA
.docx
Geogebra Transformations.ggb
investigate rotation.doc
Big Ideas Textbook
Chromebooks
Teacher created materials
Differen
tiation
Unit
Essential
Questions
you make about
a figure
reflected in two
lines?
What does it
mean to dilate a
figure?
When a figure is
translated,
reflected,
rotated or
dilated in a
plane, is the
image always
congruent
and/or similar to
the original
figure?
Enduring
Knowledge/ Assess
Understandings Skills
ments
● There are
certain
relationships
that exist
between
figures before
and after
transformation
s
are applied.
dilations,
and
compositio
ns of
transformat
ions.
Solve reallife
problems
involving
transformat
ions.
Identify
lines of
symmetry
and
rotational
symmetry.
Describe
and
perform
congruenc
e
transformat
ions and
similarity
transformat
ions.
Use
dynamic
geometry
Learning Experiences
Resources
Differen
tiation
Unit
Essential
Questions
Enduring
Knowledge/ Assess
Understandings Skills
ments
Learning Experiences
Resources
software to
visualize
and
represent
geometric
concepts.
● How are the
angle measures
of a triangle
related?
Congruent
Triangles
(Week 13,
5 Weeks)
● Given two
congruent
triangles, how
can you use
rigid motions to
map one
triangle to the
other triangle?
● What can you
conclude about
two triangles
when you know
that two pairs of
corresponding
sides and the
corresponding
included angles
are congruent?
● What
● Congruence
and rigid
transformation
s are related.
● Triangles
can be prove
congruent in
several ways
with certain
given
information.
● There is a
relationship
between the
sides and
angles of
triangles.
● Properties of
congruent
triangles can
be used to
solve real-life
Students
will be
able to
Identify
and use
correspond
ing parts of
triangles
prove or
show that
triangles
are
congruent.
Use
theorems
about the
angles of a
triangle
Use SAS,
SSS, HL,
ASA and
AAS to
prove two
Exploring Geometry with
GeoGebra
http://illuminations.nctm.org/activity.aspx?id=3504
explore triangle congruenceHandsON.doc
Exploring Congruent TrianglesHANDSON.docx
http://tube.geogebra.org/student/mc9xn98go?mobile=true
Big Ideas Textbook
Chromebooks
Teacher created materials
Differen
tiation
Unit
Essential
Questions
conjectures can
you make about
the side lengths
and angle
measures of an
isosceles
triangle?
Enduring
Knowledge/ Assess
Understandings Skills
ments
problems.
Learning Experiences
Resources
triangles
congruent
Construct
an
equilateral
triangle
and
explore its
properties.
● What can you
conclude about
two triangles
when you know
that the
corresponding
sides are
Write
coordinate
proofs.
Use
dynamic
geometry
software to
visualize
and
represent
geometric
concepts.
congruent?
● What
information is
sufficient to
determine
whether two
triangles are
congruent?
● How can you
use congruent
triangles to
make an indirect
measurement?
Relationsh
What
● Sides and
Students
Exploring Geometry with
Differen
tiation
Unit
ips Within
Triangles
(Week 18,
4 Weeks)
Essential
Questions
conjectures can
you make about
a point on the
perpendicular
bisector of a
segment and
on the bisector
of an angle?
What
conjectures can
you make about
the
perpendicular
bisectors and
the angle
bisectors of a
triangle?
What
conjectures can
you make about
the medians and
altitudes of a
triangle?
How are the
midsegments of
a triangle
related to the
sides of a
triangle?
Enduring
Knowledge/ Assess
Understandings Skills
ments
angles of a
triangle are
related to each
other.
● Indirect
proof is an
alternate way
of explaining
or reasoning.
will be
able to:
Understan
d and use
angle
bisectors
and
perpendicu
lar
bisectors to
find
measures.
Find and
use the
circumcent
er,
incenter,
centroid
and
orthocenter
of a
triangle.
Understan
d, use and
apply the
Triangle
Midsegme
nt Theorem
and the
Triangle
Inequality
Learning Experiences
Resources
http://tube.geogebra.org/student/mVhBlIUTF?mobile=true
GeoGebra
http://tube.geogebra.org/student/mGWqCQCEN?mobile=t
rue
Big Ideas Textbook
Chromebooks
http://tube.geogebra.org/student/mJ7BkiwqL?mobile=true
Teacher created materials
Differen
tiation
Unit
Essential
Questions
How are the
sides of a
triangle related
to the angles of
the triangle?
Theorem.
How are any
two sides of a
triangle related
to the third side?
Use
dynamic
geometry
software to
visualize
and
represent
geometric
concepts.
● What is the
sum of the
measures of the
interior angles of
a polygon?
Quadrilate
rals and
Other
Polygons
(Week 22,
3 Weeks)
Enduring
Knowledge/ Assess
Understandings Skills
ments
● What are the
properties of
parallelograms?
● How can you
prove that a
quadrilateral is a
parallelogram?
● What are the
properties of the
Learning Experiences
Resources
Write
indirect
proofs.
● Knowledge
of
parallelograms
can be
extended to
learn
properties of
special
parallelograms
.
● Information
about
polygons
enables one to
solve realworld
Students
will be
able to:
Find and
use the
interior and
exterior
angle
measures
of polygons
Use
properties
of
parallelogr
ams and
Learning Activity
Is this a Rectangle? Activity
https://www.illustrativemathematics.org/contentstandards/tasks/1302
Pooltastic Task and Student Sheet Pooltastic Task.doc &
Pooltastic Backyard Blueprint.docx
Pooltastic Backyard Blueprint.docx
Pooltastic Task.doc
https://www.illustrativemathematics.org/contentstandards/tasks/1302
Kite Template.docx
Parallelograms Exploration.docx
Rectangles Exploration.docx
Exploring Geometry with
GeoGebra
Big Ideas Textbook
Chromebooks
Teacher created materials
Differen
tiation
Unit
Essential
Questions
diagonals of
rectangles,
rhombuses and
squares?
Enduring
Knowledge/ Assess
Understandings Skills
ments
problems.
special
parallelogr
ams
Prove that
a
quadrilater
al is a
parallelogr
am
● What are the
properties of
trapezoids and
kites?
Learning Experiences
Resources
Trapezoid Exploration.docx
IsoscelesTrapezoid.ggb
Kite.ggb
Parallelogram.ggb
property chart- blankGEOGEBRA.doc
Rectangle.ggb
Rhombus.ggb
Square.ggb
Identify
and use
properties
of
trapezoids
and kites
Use
dynamic
geometry
software to
visualize
and
represent
geometric
concepts.
Similarity
(Week 25,
3 Weeks)
How are similar
polygons
related?
What can you
● Similar
figures and
triangles can
be explored
through
Students
will be
able to:
Use the
http://tube.geogebra.org/student/mLd9sFYbd?mobile=true
http://tube.geogebra.org/student/mkVXuNspo?mobile=tru
e
Exploring Geometry with
GeoGebra
Big Ideas Textbook
Differen
tiation
Unit
Essential
Questions
conclude about
two triangles
when you know
that two pairs of
corresponding
angles are
congruent?
What are two
ways to use
corresponding
sides of two
triangles to
determine that
the triangles
are similar?
What
proportionality
relationships
exist in a
triangle
intersected by
an angle
bisector or by a
line parallel to
one of the
sides?
Enduring
Knowledge/ Assess
Understandings Skills
ments
dilations.
● Proportions
are used to
solve many
real-life
problems,
including
triangle
problems.
● There exist
relationships
between
various
segments in
triangles.
AA, SSS
and SAS
Similarity
Theorems
to prove
triangles
are similar.
Determine
whether
triangles
are similar.
Use
similarity
criteria to
solve
problems
about
lengths,
perimeters
and areas.
Prove the
slope
criteria
using
similar
triangles.
Use the
Triangle
Proportion
ality
Theorem
Learning Experiences
Resources
Chromebooks
http://tube.geogebra.org/student/myZKotF6i?mobile=true
Teacher created materials
Differen
tiation
Unit
Essential
Questions
Enduring
Knowledge/ Assess
Understandings Skills
ments
Learning Experiences
Resources
and other
proportiona
lity
theorems.
Use
dynamic
geometry
software to
visualize
and
represent
geometric
concepts.
● How can you
prove the
Pythagorean
Theorem?
Right
Triangles
and
Trigonom
etry
(Week 28,
5 Weeks)
● What is the
relationship
among the side
lengths of 4545-90 and 3060-90 triangles?
● How are
altitudes and
geometric
means of right
triangles
●
Relationships
exist between
side lengths
and angles of
right triangles.
●
Trigonometry
can help one
to find
unknown
information
about
triangles.
● The Law of
Sines and the
Students
will be
able to:
Use the
Pythagorea
n Theorem
and its
converse
to solve
problems
Understan
d and use
geometric
means
Find side
Hands on activity- Trig River :
https://www.teachengineering.org/view_activity.php?url=c
ollection/cub_/activities/cub_navigation/cub_navigation_le
sson03_activity2.xml
Exploring Geometry with
GeoGebra
http://education.ti.com/en/timathnspired/us/detail?id=C3E
70398468F4DD390DA749899086DA1&t=9D03A938D083
4CEB912366FC09ED1DBE
Big Ideas Textbook
Chromebooks
https://www.teachengineering.org/view_activity.php?url=c
ollection/cub_/activities/cub_navigation/cub_navigation_le
sson03_activity2.xml
http://education.ti.com/en/timathnspired/us/detail?id=C3E
70398468F4DD390DA749899086DA1&t=9D03A938D083
4CEB912366FC09ED1DBE
Teacher created materials
Differen
tiation
Unit
Essential
Questions
related?
● How is a right
triangle used to
find the tangent,
sine and cosine
of a right
triangle?
● What are the
Law of Sines
and the Law of
Cosines?
Enduring
Knowledge/ Assess
Understandings Skills
ments
Law of
Cosines
enable one to
find unknown
information
about
triangles.
lengths
and
tangent,
sine and
cosine
ratios to
solve reallife
problems
involving
right
triangles
Derive the
formula
A=½
absin(c) for
the area of
a triangle
by drawing
an auxiliary
line from a
vertex
perpendicu
lar to the
opposite
side *
Prove the
Law of
Sines and
the Law of
Cosines
and use
them to
Learning Experiences
Daves_NTTI_lesson_plan_1302179828.docx
Explore Sin,Cos,Tan.docx
Special Right Triangles Explore.pdf
http://tube.geogebra.org/student/ml25E2eBn?mobile=true
http://tube.geogebra.org/student/mLxpvJn5x?mobile=true
Resources
Differen
tiation
Unit
Essential
Questions
Enduring
Knowledge/ Assess
Understandings Skills
ments
Learning Experiences
Resources
solve
triangles
and
problems.*
Use
dynamic
geometry
software to
visualize
and
represent
geometric
concepts.
What are the
definitions of the
lines and
segments that
intersect a
circle?
Circles
(Week 33,
5 Weeks)
How are circular
arcs measured?
What are two
ways to
determine when
a chord is a
diameter of a
circle?
How are
● Several
relationships
exist within
circles.
● Segments,
angles, and
triangles can
all be explored
in relation to
circles.
Students
will be
able to:
Define and
identify
chords,
diameters,
radii,
secants
and
tangents of
circles.
Find arc
and angle
measures.
http://tube.geogebra.org/student/mBh173QeH?mobile=tru
e
http://tube.geogebra.org/student/mBoibgqcf?mobile=true
http://tube.geogebra.org/student/mlb6iK8kV?mobile=true
http://tube.geogebra.org/student/me97RO7CE?mobile=tru
e
Exploring Geometry with
GeoGebra
Big Ideas Textbook
Chromebooks
Teacher created materials
Differen
tiation
Unit
Essential
Questions
inscribed angles
related to their
arcs?
What
relationships
exist among the
angles formed
when chords
and tangents
intersect?
What
relationships
exist among the
segments
formed when
chords, secants
and tangents
intersect?
What is the
equation of a
circle with
center (h, k) and
radius r in the
coordinate
plane?
Enduring
Knowledge/ Assess
Understandings Skills
ments
Use
inscribed
angles and
polygons
and use
circumscrib
ed angles
to solve
problems.
Use and
apply
properties
of chords,
tangents
and
secants to
solve
problems.
Write and
graph
equations
of circles.
Construct a
tangent
line from a
point
outside a
given circle
to the
circle. *
Use
Learning Experiences
Resources
Differen
tiation
Unit
Essential
Questions
Enduring
Knowledge/ Assess
Understandings Skills
ments
Learning Experiences
Resources
dynamic
geometry
software to
visualize
and
represent
geometric
concepts.
● How can you
find the length of
a circular arc?
Students
will be
able to:
● How can you
find the area of
a sector of a
circle?
Measure
angles in
radians *
Circumfer
ence,
Area and
Volume
● How can you
find the area of
a regular
polygon?
(Week 38,
3 Weeks)
● What is the
relationship
between the
numbers of
vertices, edges
and faces of a
polyhedron?
● How can you
find the volume
● Area and
volume can be
used in reallife situations.
Find arc
lengths
and areas
of sectors.
Find and
use the
areas of
rhombuses
, kites and
regular
polygons.
Find and
use
volumes of
http://tube.geogebra.org/student/mgAftSMzd?mobile=true
http://tube.geogebra.org/student/mWk1fxp9z?mobile=true
http://tube.geogebra.org/student/mx4NVGB2q?mobile=tru
e
http://tube.geogebra.org/student/mftRPdDWg?mobile=tru
e
Exploring Geometry with
GeoGebra
Big Ideas Textbook
Chromebooks
Teacher created materials
Differen
tiation
Unit
Essential
Questions
Enduring
Knowledge/ Assess
Understandings Skills
ments
of a prism or
cylinder that is
not a right
prism/cylinder?
Describe
crosssection and
solids of
revolution.
● How can you
find the surface
area and
volume of a
cone and a
sphere?
Probability
(Week 38,
3 Weeks)
How can you
determine
whether two
evens are
independent or
Resources
prisms,
cylinders,
pyramids,
cones and
spheres.
● How can you
find the volume
of a pyramid?
How can you list
the possible
outcomes in the
sample space of
an experiment?
Learning Experiences
Use
dynamic
geometry
software to
visualize
and
represent
geometric
concepts.
Probabi
lity can
be used
to solve
real
world
problem
s.
There is
a
differen
Students
will be
able to:
Find
sample
spaces.
Find
theoretical
probabilitie
http://tube.geogebra.org/student/mZd5fLRjA?mobile=true
Exploring Geometry with
GeoGebra
http://tube.geogebra.org/student/mOmL9WRU2?mobile=tr
ue
Big Ideas Textbook
http://tube.geogebra.org/student/mwmc9YZqU?mobile=tru
e
http://tube.geogebra.org/student/mGXy6rGjJ?mobile=true
Chromebooks
Teacher created materials
Differen
tiation
Unit
Essential
Questions
dependent?
How can you
construct and
interpret a twoway table?
How can you
find probabilities
of disjoint and
overlapping
events?
How can a tree
diagram help
you visualize the
number of ways
in which two or
more events can
occur?
How can you
determine the
frequency of
each outcome of
an event?
Enduring
Knowledge/ Assess
Understandings Skills
ments
ce
betwee
n
theoreti
cal and
experim
ental
probabil
ity.
s.
Find
experiment
al
probabilitie
s.
Determine
whether
events are
independe
nt events.
Find
probabilitie
s of
independe
nt and
dependent
events.
Find
conditional
probabilitie
s.
Make twoway tables.
Find
relative
and
conditional
relative
Learning Experiences
Resources
Differen
tiation
Unit
Essential
Questions
Enduring
Knowledge/ Assess
Understandings Skills
ments
frequencie
s.
Use
conditional
relative
frequencie
s to find
conditional
probabilitie
s.
Find
probabilitie
s of
compound
events.
Use more
than one
probability
rule to
solve reallife
problems.
Use the
formula for
the number
of
permutatio
ns.
Use the
formula for
Learning Experiences
Resources
Differen
tiation
Unit
Essential
Questions
Enduring
Knowledge/ Assess
Understandings Skills
ments
Learning Experiences
Resources
Differen
tiation
the number
of
combinatio
ns.
Use
combinatio
ns and the
Binomial
Theorem to
expand
binomials.
Construct
and
interpret
probability
distribution
s.
Construct
and
interpret
binomial
distribution
s.
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