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Chapter 1 - Essentials of Geometry
Start Date – 8/19/14
End Date – 08/29/14
Section Number
and Topic
Standards
Learning Target
Introduction/Syllabus
1.1 Identifying
Points, Lines,
and Planes
MAFS.912.G.CO.1
1.2 Use
Segments and
Congruence
MAFS.912.G.CO.1
1.3 Use Distance
and Midpoint
Formulas
MAFS.
912.G.GPE.7
1.4 Measure and
Classify Angles
MAFS.912.G.CO.1
1.5 Describe
Angle Pair
Relationship
MAFS.912.G.CO.1
Name and sketch geometric
figures.
Know precise definitions of
angle, circle, perpendicular
line, parallel line, and line
segment, based on the
undefined notions of point,
line, distance along a line, and
distance around a circle arc.
Will use segment postulates to
identify congruent segments.
Know precise definitions of
angle, circle, perpendicular
line, parallel line, and line
segment, based on the
undefined notions of point,
line, distance along a line, and
distance around a circle arc.
Will find lengths of segments in
the coordinate plane.
Use coordinates to compute
perimeters of polygons and
areas of triangles and
rectangles, e.g., using the
distance formula.
Will name, measure, and
classify angles.
Know precise definitions of
angle, circle, perpendicular
line, parallel line, and line
segment, based on the
undefined notions of point,
line, distance along a line, and
distance around a circle arc.
Will use special angle
relationships to find angle
measures.
Know precise definitions of
angle, circle, perpendicular
line, parallel line, and line
segment, based on the
undefined notions of point,
line, distance along a line, and
Instructional
Time Frame
1 Day
Additional
Resources
1 Day
Parallel,
Intersecting,
and Skew Lines
1 Day
Constructing
Congruent
Segments and
Angles
1 Day
Distance
Formula Activity A
1 Day
Constructing
Congruent
Segments and
Angles
1 Day
Investigating
Angle
Theorems Activity B
1.6 Classify
Polygons
MAFS.912.G.MG.1
distance around a circle arc.
Will classify polygons.
Use geometric shapes, their
measures, and their properties
to describe objects (e.g.,
modeling a tree trunk or a
human torso as a cylinder.)
1 Day
Polygon Angle
Sum
Classifying
Triangles
Classifying
Quadrilaterals Activity B
Chapter Test
1 Day
Total
8 Days
Chapter 2 - Reasoning and Proof
Start Date – XX/XX/14
End Date – XX/XX/14
Section
Number and
Topic
2.1 Use
Inductive
Reasoning
Standards
SMP3
2.2 Analyze
Conditional
Statements
SMP3
2.3 Apply
Deductive
Reasoning
SMP3
2.4 Use
Postulates and
Diagrams
MAFS.912.G.CO.9
Learning Target
Will describe patterns and use
inductive reasoning.
Construct viable arguments and
critique the reasoning of others.
Will write definitions as
conditional statements.
Construct viable arguments and
critique the reasoning of others.
Will use deductive reasoning to
form a logical argument.
Construct viable arguments and
critique the reasoning of others.
Will use postulates involving
points, lines, and planes.
Prove theorems about lines and
angles.
Quiz
Additional
Resources
1 Day
2 Days
Conditional
Statements
2 Days
1 Day
1 Day
2.5 Reason
Using Properties
from Algebra
MAFS.912.G.REI.1
2.6 Prove
Statements
about Segments
and Angles
2.7 Prove Angle
Pair
Relationships
MAFS.912.G.CO.9
Test
Instructional
Time Frame
MAFS.912.G.CO.9
Will use algebraic properties in
logical arguments too.
Explain each step in solving a
simple equation as following from
the equality of numbers asserted
at the previous step, starting
from the assumption that the
original equation has a solution.
Construct a viable argument to
justify a solution method.
Will write proofs using geometric
theorems.
Prove theorems about lines and
angles.
Will use properties of special
pairs of angles.
Prove theorems about lines and
angles.
2 Days
1.5 Days
2 Days
1 Day
Investigating
Angle
Theorems Activity B
Chapter 3 - Parallel and Perpendicular Lines
Start Date – XX/XX/14
End Date – XX/XX/14
Section Number and
Topic
3.1 Identify Pairs of
Lines and Angles
Standards
Learning Target
MAFS.912.G.CO.1
Will identify angle pairs formed
by three intersecting lines.
Know precise definitions of
angle, circle, perpendicular line,
parallel line, and line segment,
based on the undefined notions
of point, line, distance along a
line, and distance around a circle
arc.
Will use angles formed by
parallel lines and transversals.
Prove theorems about lines and
angles.
Will use angle relationships to
prove that lines are parallel.
Prove theorems about lines and
angles.
3.2 Use Parallel Lines
and Transversals
MAFS.912.G.CO.9
3.3 Prove Lines Parallel
MAFS.912.G.CO.9
Quiz
2 Days
Additional Resources
Constructing Congruent Segmen
Angles
Parallel, Intersecting,
and Skew Lines
2 Days
Constructing Parallel
and Perpendicular Lines
1 Day
3.4 Find and Use
Slopes of Lines
MAFS.912.G.GPE.
5
3.5 Write and Graph
Equations of Lines
MAFS.912.G.GPE.
5
3.6 Prove Theorems
about Perpendicular
Lines
MAFS.912.G.CO.9
Test
Instructional
Time Frame
1 Day
Will find and compare slopes of
lines.
Prove the slope criteria for
parallel and perpendicular lines
and use them to solve geometric
problems (e.g., find the equation
of a line parallel or perpendicular
to a given line that passes
through a given point).
Will find equations of lines.
Prove the slope criteria for
parallel and perpendicular lines
and use them to solve geometric
problems (e.g., find the equation
of a line parallel or perpendicular
to a given line that passes
through a given point).
Will find the distance between a
point and a line.
Prove theorems about lines and
angles.
2 Days
2 Days
2 Days
1 Day
Slope - Activity B
Chapter 4 - Congruent Triangles
Start Date – XX/XX/14
End Date – XX/XX/14
Section Number and Topic
Standards
Learning Target
4.1 Apply Triangle Sum
Properties
MAFS.912.CO.10
4.2 Apply Congruence and
Triangles
MAFS.912.CO.7
4.3 Relate Transformations
and Congruence
MAFS.912.CO.6
Will classify triangles and
find measures of their
angles.
Prove theorems about
triangles.
Will identify congruent
figures.
Use the definition of
congruence in terms of rigid
motions to show that two
triangles are congruent if
and only if corresponding
pairs of sides and
corresponding pairs of
angles are congruent.
Will use transformations to
show congruence.
Use geometric descriptions
of rigid motions to transform
figures and to predict the
effect of a given rigid motion
on a given figure; given two
figures, use the definition of
congruence in terms of rigid
motions to decide if they are
congruent.
Will use the side lengths to
prove triangles are
congruent.
Explain how the criteria for
triangle congruence (ASA,
SAS, and SSS) follow from
the definition of congruence
in terms of rigid motions.
4.4 Prove Triangles
Congruent by SSS
MAFS.912.CO.8
Quiz
Instructional
Time Frame
1 Day
Additional
Resources
Classifying
Triangles
2 Days
Proving
Triangles
Congruent
1 Day
Reflections
Rotations,
Reflections
and
Translations
Translations
1.5 Days
Proving
Triangles
Congruent
1Day
4.5 Prove Triangles
Congruent by SAS and HL
MAFS.912.CO.8
4.6 Prove Triangles
Congruent by ASA and AAS
MAFS.912.CO.8
Will use sides and angles to
prove congruence.
Explain how the criteria for
triangle congruence (ASA,
SAS, and SSS) follow from
the definition of congruence
in terms of rigid motions.
Will use two more methods
to prove congruences.
1.5 Days
Proving
Triangles
Congruent
1.5 Days
Proving
Triangles
4.7 Use Congruent
Triangles
MAFS.912.CO.10
4.8 Use Isosceles and
Equilateral Triangles
MAFS.912.CO.10
4.9 Perform Congruence
Transformations
MAFS.912.CO.2
Test
Explain how the criteria for
triangle congruence (ASA,
SAS, and SSS) follow from
the definition of congruence
in terms of rigid motions.
Will use congruent triangles
to prove corresponding parts
congruent.
Prove theorems about
triangles.
Will use theorems about
isosceles and equilateral
triangles.
Prove theorems about
triangles.
Will create an image
congruent to a given
triangle,
Represent transformations in
the plane using, e.g.,
transparencies and
geometry software; describe
transformations as functions
that take points in the plane
as inputs and give other
points as outputs. Compare
transformations that
preserve distance and angle
to those that do not (e.g.,
translation versus horizontal
stretch).
Congruent
2 Days
2 Days
1.5 Days
Dilations
Reflections
Rotations,
Reflections
and
Translations
Translations
1 Day
Chapter 5 - Relationships within Triangles
Start Date – XX/XX/14
End Date – XX/XX/14
Section Number and
Topic
5.1 Midsegment Theorem
and Coordinate Proof
Standards
Learning Target
MAFS.912.G.GPE.4
Will use properties of
midsegments and write
coordinate proofs.
Use coordinates to prove
simple geometric
theorems algebraically.
Will use perpendicular
bisectors to solve
problems.
Prove theorems about
lines and angles.
Will use angle bisectors to
find distance relationships.
Construct the inscribed
and circumscribed circles
of a triangle, and prove
properties of angles for a
quadrilateral inscribed in a
circle.
Will use medians and
altitudes of triangles.
Prove theorems about
triangles.
5.2 Use Perpendicular
Bisectors
MAFS.912.G.CO.4
5.3 Use Angle Bisectors of
Triangles
MAFS.912.G..C.3
5.4 Use Medians and
Altitudes
MAFS.912.G.CO.10
Review
Additional
Resources
2 Days
Concurrent
Lines,
Medians, and
Altitudes
2 Days
Concurrent
Lines,
Medians, and
Altitudes
1.5 Day
0.5 Day
Quiz
1 Day
5.5 Use Inequalities in a
Triangle
MAFS.912.G.CO.10
5.6 Inequalities in Two
Triangles
MAFS.912.G.CO.10
Test
Instructional
Time Frame
2 Days
Will find possible side
lengths of a triangle.
Prove theorems about
triangles.
Will use inequalities to
make comparisons in two
triangles.
Prove theorems about
triangles.
1 Day
1 Day
1 Day
Triangle
Inequalities
Chapter 6 - Similarity
Start Date –
End Date –
Section Number and
Topic
6.1 Use Similar Polygons
Standards
Learning Target
MAFS.912.G.SRT.5
Will use proportions to
identify similar polygons.
Will identify similarity
transformations called
dilations.
Given two figures, use the
definition of similarity in
terms of similarity
transformations to decide
if they are similar; explain
using similarity
transformations the
meaning of similarity for
triangles as the equality of
all corresponding pairs of
angles and the
proportionality of all
corresponding pairs of
sides.
Will use the AA Similarity
Postulate
Use the properties of
similarity transformations
to establish the AA
criterion for two triangles
to be similar.
Will use the SSS and SAS
Similarity Theorems.
Prove theorems about
triangles.
6.2 Relate Transformations
and Similarity
MAFS.912.G.SRT.2
6.3 Prove Triangles Similar
by AA
MAFS.912.G.SRT.3
6.4 Prove Triangles Similar
by SSS and SAS
MAFS.912.G.SRT.4
Quiz
Instructional
Time Frame
2 Days
Additional
Resources
2 Days
1 Day
Proving
Triangles
Congruent
1. Day
Proving
Triangles
Congruent
1 Day
6.5 Use Proportionality
Theorems
MAFS.912.G.SRT.4
6.6 Perform Similarity
Transformations
MAFS.912.G.CO.2
Will use proportions with a
triangle or parallel lines.
Prove theorems about
triangles.
Will perform dilations.
Represent transformations
in the plane using e.g.,
transparencies and
geometry software;
describe transformations
1 Day
1 Day
Dilations
as functions that take
points in the plane as
inputs and give other point
as outputs. Compare
transformations that
preserve distance and
angle to those that do not
(e.g., translation versus
horizontal stretch).
Review
1 Day
Test
1 Day
Midterm exam
1 Day
Chapter 7 - Right Triangles and Trigonometry
Start Date –
End Date –
Section Number and
Topic
7.1 Apply the Pythagorean
Theorem
Standards
Learning Target
MAFS.912.G.SRT.8
Will find side lengths in
right triangles.
Use trigonometric ratios
and the Pythagorean
Theorem to solve right
triangles in applied
problems.
7.2 Use the Converse of
the Pythagorean Theorem
MAFS.912.G.SRT.8
7.3 Use Similar Right
Triangles
MAFS.912.G.SRT.5
7.4 Special Right Triangles
MAFS.912.G.SRT.6
7.5 Apply the Tangent
Ratio
MAFS.912.G.SRT.8
Will use its converse to
determine if a triangle is
a right triangle.
Use trigonometric ratios
and the Pythagorean
Theorem in applied
problems.
Will use properties of the
altitude of a right
triangle.
Use congruence and
similarity criteria for
triangles to solve
problems and prove
relationship in geometric
figures.
Will use the relationships
among the sides in
special right triangles.
Understand that by
similarity, side ratios in
right triangles are
properties of the angles
in the triangle, leading to
definitions of
trigonometric ratios for
acute angles.
Will use the tangent ratio
for indirect
measurement.
Use trigonometric ratios
and the Pythagorean
Theorem to solve right
Instructional
Time Frame
.5 Day
Additional
Resources
Pythagorean
Theorem Activity B
Distance
Formula Activity A
.5 Day
Pythagorean
Theorem Activity B
1 Day
Similarity in
Right
Triangles
1.5 Days
1.5 Days
Tangent
Ratio
7.6 Apply the Sine and
Cosine Ratios
MAFS.912.G.SRT.8
7.7 Solve Right Triangles
MAFS.912.G.SRT.8
triangles in applied
problems.
Will use the sine and
cosine ratios.
Use trigonometric ratios
and the Pythagorean
Theorem to solve right
triangles in applied
problems.
Will use inverse tangent,
sine, and cosine ratios.
Use trigonometric ratios
and the Pythagorean
Theorem to solve right
triangles in applied
problems.
1.5 Days
Sine,
Cosine, and
Tangent
Ratios
1.5 Day
Distance
Formula Activity A
Pythagorean
Theorem Activity B
Pythagorean
Theorem
with a
Geoboard
Sine and
Cosine
Ratios Activity A
Tangent
Ratio
Chapter 8 - Quadrilaterals
Start Date –
End Date –
Section Number and
Topic
8.1 Find Angles Measure
in Polygons
8.2. Use Properties of
Parallelograms
Standards
MAFS.912.G.MG.1
MAFS.912.G.CO.11
8.3 Show that a
Quadrilateral is a
Parallelogram
MAFS.912.G.CO.11
8.4 Properties of
Rhombuses, Rectangles,
and Squares
MAFS.912.G.CO.11
8.5 Use Properties of
Trapezoids and Kites
MAFS.912.G.SRT.5
8.6 Identify Special
Quadrilaterals
MAFS.912.G.CO.11
Learning Target
Will find angle measures in
polygons.
Use geometric shapes,
their measure, and their
properties to describe
objects (e.g., modeling a
tree trunk or a human torso
as a cylinder).
Will find angle and side
measures in
parallelograms.
Prove theorems about
parallelograms.
Will use properties to
identify parallelograms.
Prove theorems about
parallelograms.
Will use properties of
rhombuses, rectangles,
and squares.
Prove theorems about
parallelograms.
Will use properties of
trapezoids and kites.
Use congruence and
similarity criteria for
triangles to solve problems
and prove relationship in
geometric figures.
Will identify special
quadrilaterals.
Prove theorems about
parallelograms.
Instructional
Time Frame
1 Day
1 Day
Additional Resources
Parallelogram Conditions
Special Parallelograms
1 Day
Parallelogram Conditions
1 Day
Special Parallelograms
1 Day
Special Parallelograms
1 Day
Chapter 9 - Properties of Transformations
Start Date –
End Date –
Section Number and
Topic
9.1 Translate Figures and
Use Vectors
9.2 Use Properties of
Matrices
9.3 Perform Reflections
9.4 Perform Rotations
Standards
MAFS.912.G.CO.5
MAFS.912.N.VM.8(+)
MAFS.912.G.CO.5
MAFS.912.G.CO.5
Learning Target
Will use a vector to
translate a figure.
Given a geometric figure
and a rotation, reflection,
or translation, draw the
transformed figure using
e.g., graph paper, tracing
paper, or geometry
software. Specify a
sequence of
transformations that will
carry a given figure onto
another.
Will perform translations
using matrix operations.
Add, subtract, and
multiply matrices of
appropriate dimensions.
Will reflect a figure in any
given line.
Given a geometric figure
and a rotation, reflection,
or translation, draw the
transformed figure using
e.g., graph paper, tracing
paper, or geometry
software. Specify a
sequence of
transformations that will
carry a given figure onto
another.
Will rotate figures about
a point.
Given a geometric figure
and a rotation, reflection,
or translation, draw the
transformed figure using
e.g., graph paper, tracing
paper, or geometry
software. Specify a
sequence of
transformations that will
carry a given figure onto
another.
Instructional
Time Frame
1 Day
Additional
Resources
Reflections
Rotations,
Reflections and
Translations
Translations
1.5 Days
Dilations
Translations
1.5 Days
Reflections
Rotations,
Reflections and
Translations
1.5 Days
Rotations,
Reflections and
Translations
9.5 Apply Compositions of
Transformations
MAFS.912.G.CO.5
9.6 Identify Symmetry
MAFS.912.G.CO.3
9.7 Identify and Perform
Dilations
MAFS.912.G.SRT.1
Will perform
combinations of two or
more transformations.
Given a geometric figure
and a rotation, reflection,
or translation, draw the
transformed figure using
e.g., graph paper, tracing
paper, or geometry
software. Specify a
sequence of
transformations that will
carry a given figure onto
another.
Will identify line and
rotational symmetries of
a figure.
Given a geometric figure
and a rotation, reflection,
or translation, draw the
transformed figure using
e.g., graph paper, tracing
paper, or geometry
software. Specify a
sequence of
transformations that will
carry a given figure onto
another.
Will use drawing tools
and matrices to draw
dilations.
Verify experimentally the
properties of dilations
given by a center and a
scale factor; a. A dilation
takes a line not passing
through the center of the
dilation to a parallel line,
and leaves a line passing
through the center
unchanged. b. The
dilation of a line segment
is longer or shorter in the
ratio given by the scale
factor.
1.5 Days
1 Day
1 Day
Dilations
Chapter 10 - Properties of Circles
Start Date –
End Date –
Section Number and
Topic
10.1 Use Properties of
Tangents
Standards
Learning Target
MAFS.912.G.CO.1
Will use properties of a
tangent to a circle.
Know precise definition of
angle, circle, perpendicular
line, parallel line, and line
segment, based on the
undefined notions of point,
line, distance along a line,
and distance around a
circular arc.
Will use angle measures to
find arc measures.
Know precise definition of
angle, circle, perpendicular
line, parallel line, and line
segment, based on the
undefined notions of point,
line, distance along a line,
and distance around a
circular arc.
Will use relationships of
arcs and chords in a circle.
Identify and describe
relationships among
inscribed angles, radii, and
chords.
Will use inscribed angles of
circles.
Construct the inscribed and
circumscribed circles of a
triangle, and prove
properties of angles for a
quadrilateral inscribed in a
circle.
Will find the measures of
angles inside or outside a
circle.
Identify and describe
relationships among
inscribed angles, radii, and
chords.
Will find segment lengths in
10.2 Find Arc Measures
MAFS.912.G.CO.1
10.3 Apply Properties of
Chords
MAFS.912.G.C.2
10.4 Use Inscribed Angles
and Polygons
MAFS.912.G.C.3
10.5 Apply Other Angles
Relationships in Circles
MAFS.912.G.C.2
10.6 Find Segment Lengths
MAFS.912.G.C.2
Instructional
Time Frame
1.5 Days
Additional
Resources
1 Day
Chords and
Arcs
1.5 Days
Chords and
Arcs
1.5 Days
Inscribed
Angles
1.5 Day
1 5 Days
in Circles
10.7 Write and Graph
Equations of Circles
MAFS.912.G.GPE.
1
circles.
Identify and describe
relationships among
inscribed angles, radii, and
chords.
Will write equations of
circles in the coordinate
plane.
Derive the equation of a
circle of given center and
radius using the
Pythagorean theorem;
complete the square to find
the center and radius of a
circle given by an equation.
1 Day
Circles
Chapter 11 - Measurements of Figures and
Solids
Start Date –
End Date –
Section Number and
Topic
11.1 Circumference and
Arc
Standards
MAFS.912.G.C.5
11.2 Areas of Circles and
Sectors
MAFS.912.G.C.5
11.3 Areas of Regular
Polygons
MAFS.912.G.SRT.8
11.4 Use Geometric
Probability
SMP 4
11.5 Explore Solids
MAFS.912.G.GMD.4
Learning Target
Will find arc lengths and
other measures.
Derive using similarity the
fact that the length of the
arc intercepted by an angle
is proportional to the
radius, and define the
radian measure of the
angle as the constant of
proportionality; derive the
formula for the area of a
sector.
Will find the areas of circles
and sectors.
Derive using similarity the
fact that the length of the
arc intercepted by an angle
is proportional to the
radius, and define the
radian measure of the
angle as the constant of
proportionality; derive the
formula for the area of a
sector.
Will find areas of regular
polygons inscribed in
circles.
Use trigonometric ratios
and the Pythagorean
Theorem to solve right
triangles in applied
problems.
Will use lengths and areas
to find geometric
probabilities.
Model with mathematics
Will identify solids.
Identify the shapes of twodimensional cross-sections
Instructional
Time Frame
1 Day
Additional
Resources
Circles:
Circumference and
Area
1 Day
Circles:
Circumference and
Area
1 Day
1 Day
1 Day
Geometric
Probability - Activity
A
11.6 Volume of Prisms and
Cylinders
MAFS.912.G.GMD.3
11.7 Volume of Pyramids
and Cones
MAFS.912.G.GMD.3
11.8 Surface Area and
Volume of Spheres
MAFS.912.G.GMD.3
11.9 Exploring Similar
Solids
MAFS.912.G.GMD.3
of three-dimensional
objects, and identify threedimensional objects
generated by rotations of
two-dimensional objects.
Will find volumes of prisms
and cylinders.
Use volume formulas for
cylinders, pyramids, cones,
and spheres to solve
problems.
Will find volumes of
pyramids and cones.
Use volume formulas for
cylinders, pyramids, cones,
and spheres to solve
problems.
Will find surface areas and
volumes of spheres.
Use volume formulas for
cylinders, pyramids, cones,
and spheres to solve
problems.
Will use properties of
similar solids.
Use volume formulas for
cylinders, pyramids, cones,
and spheres to solve
problems.
1 Day
Prisms and Cylinders
- Activity A
1 Day
Pyramids and Cones
- Activity B
1 Day
1 Day
Chapter 12 - Probability
Start Date –
End Date –
Section Number and
Topic
12.1 Find Probability and
Odds
Standards
Learning Target
MAFS.912.G.CP.1
Will find sample spaces and
probabilities.
Describe events as subsets of
a sample space (the set of
outcomes) using
characteristics (or categories)
of the outcomes, or as unions,
intersections, or complements
of other events (“or,” “and,”
“not”).
Will use the formula for the
number of permutations.
Use permutations and
combinations of compound
events and solve problems.
Will use combinations to count
possibilities.
Use permutations and
combinations of compound
events and solve problems.
Will find probabilities of
compound events
Apply the Addition Rule, P(A
or B)=P(A) + P(B) - P(A and
B), and interpret the answer in
terms of the model.
Will examine independent and
dependent events.
Apply the Addition Rule, P(A
or B)=P(A) + P(B) - P(A and
B), and interpret the answer in
terms of the model.
12.2 Find Probability Using
Permutations
MAFS.912.G.CP.9
12.3 Find Probability Using
Combinations
MAFS.912.G.CP.9
12.4 Find Probabilities of
Disjoint and Overlapping
Events
MAFS.912.G.CP.7
12.5 Find Probabilities of
Independent and
Dependent Events
MAFS.912.G.CP.8
Instructional
Time Frame
1 Day
Additional Resources
2 Days
Permutations and
Combinations
1 Day
Permutations and
Combinations
1 Day
2 Days
Compound
Independent Events
Compound
Independent and
Dependent Events