Dates Topics Core
Content
Program of
Study
Essential
Question
Strategies/Activities Assessment Vocabulary
2 Days 1-1
Patterns and
Inductive
Reasoning
MA-HS-1.3.2 Students will describe and extend sequences.
Can you use
inductive
reasoning to
make
conjectures?
Textbook
Life experiences &
connections
Models
Posters
Bell ringers
Quiz/Test/ORQ
Homework
Class work
Questioning
Common
assessment
• Inductive
reasoning
• Conjecture
• Counterexample
2 Days 1-2
Points, Lines,
and Planes
MA-HS-3.1.1
Students will
analyze and
apply spatial
relationships
(not using
Cartesian
coordinates)
among points,
lines and planes
(e.g.,
betweenness of
points,
midpoint,
segment length,
collinear,
coplanar,
parallel,
Do you
understand the
basic terms of
geometry?
Do you
understand the
basic axioms of
geometry?
• Point
• Space
• Line
• Collinear points
• Plane
• Coplanar
• Postulate
• Axiom
perpendicular,
skew MA-HS-
3.4.1
Students will
identify
definitions,
axioms and
theorems,
explain the
necessity for
them and give
examples of
them.
).DOK 2
2 Days 1-3 Segments,
Rays, Parallel
Lines, and
Planes
MA-HS-3.1.1
Students will
analyze and
apply spatial
relationships
(not using
Cartesian
coordinates)
among points,
lines and planes
(e.g.,
Can you
identify
segments and
rays?
Can you
recognize
parallel lines,
planes, and
skew lines?
• Segment
• Ray
• Opposite Rays
• Parallel Lines
• Skew Lines
• Parallel Planes
betweenness of
points,
midpoint,
segment length,
collinear,
coplanar,
parallel,
perpendicular,
skew).DOK 2
2 Days 1-4
Measuring
Segments and
Angles
MA-HS-3.1.1
Students will
analyze and
apply spatial
relationships
(not using
Cartesian
coordinates)
among points,
lines and planes
(e.g.,
betweenness of
points,
midpoint,
segment length,
collinear,
coplanar,
parallel,
perpendicular,
skew).DOK 2
Can you find
the length of a
line segment?
Can you find
the measure of
an angle?
• Coordinate
• Congruent
segments
• Midpoint
• Angle
• Acute angle
• Right angle
• Obtuse angle
• Straight angle
• Congruent angles
2 Days 1-5
Basic MA-HS-Can you
construct
• Construction
• Straightedge
Constructions 3.4.3
Students will be
able to perform
constructions
such as a line
parallel to a
given line
through a point
not on the line,
the
perpendicular
bisector of a line
segment and the
bisector of an
angle.
congruent
segments or
congruent
angles using a
compass and a
straightedge?
Can you bisect
segments or
angles using a
compass and a
straightedge?
• Compass
• Perpendicular
lines
• Perpendicular
bisector
• Angle bisector
2 Days 1-6
The Coordinate
Plane
MA-HS-3.1.1
Students will
analyze and
apply spatial
relationships
(not using
Cartesian
coordinates)
among points,
lines and planes
(e.g.,
betweenness of
points,
midpoint,
segment length,
collinear,
coplanar,
parallel,
Can you find
the distance
between two
points on the
coordinate
plane?
Can you find
the
coordinates of
the midpoint
of a segment in
the coordinate
plane?
• Distance
• Midpoint
perpendicular,
skew).DOK 2
2 Days 1-7
Perimeter,
Circumf, and
Area
MA-HS-3.1.6
Students will
know the
definitions and
basic properties
of a circle and
will use them to
prove basic
theorems and
solve problems.
MA-HS-2.1.2
Students will
describe how a
change in one
or more
dimensions of a
geometric
figure affects
the perimeter,
area and
volume of the
figure.
DOK 3
Can you find
the perimeter
of a rectangle
or a square?
Can you find
the
circumference
of a circle?
Can you find
the area of a
rectangle or a
circle?
• Perimeter
• Circumference
• Area
2 Days 2-4
Reasoning in
Algebra
MA-HS-1.5.1 Students will identify real number properties (commutative properties of addition and multiplication, associative properties of addition and multiplication, distributive property of multiplication over addition and subtraction, identity properties of addition and multiplication and inverse properties of addition and multiplication) when used to justify a given step in simplifying an expression or solving an equation. MA-HS-1.5.2
Students will
use equivalence
relations
(reflexive,
Can you justify
steps in a
logical
argument?
• Reflexive
Property
• Symmetric
Property
• Transitive
Property
symmetric,
transitive).
2 Days 2-5
Proving Angles
Congruent
MA-HS-3.1.3
Students will
analyze and
apply angle
relationships
(e.g., linear
pairs, vertical,
complementary
,
supplementary,
corresponding
and alternate
interior angles)
in real-world
and
mathematical
problems.
DOK 2
MA-HS-3.1.4
Students will
use angle
relationships to
prove basic
theorems.
Can you
identify angle
pairs?
Can you prove
and apply
theorems
about angles?
• Vertical Angles
• Adjacent Angles
• Complementary
Angles
• Supplementary
Angles
• Theorem
• Paragraph Proof
2 Days 3-1
Properties of
Parallel Lines
MA-HS-3.1.3
Students will
analyze and
apply angle
relationships
(e.g., linear
pairs, vertical,
complementary
,
supplementary,
corresponding
and alternate
interior angles)
in real-world
and
mathematical
problems.
DOK 2
MA-HS-3.1.4
Students will
use angle
relationships to
prove basic
theorems.
Can you
identify the
angles formed
by two lines
and a
transversal?
Can you prove
lines are
parallel by
using theorems
and
properties?
• Transversal
• Alternate interior
angles
• Same-side
interior angles
• Corresponding
angles
• Two-column
proof
2 Days 3-2
Proving Lines
Parallel
MA-HS-3.1.3
Students will
analyze and
apply angle
relationships
(e.g., linear
pairs, vertical,
complementary
,
supplementary,
corresponding
and alternate
interior angles)
in real-world
and
mathematical
problems.
DOK 2
MA-HS-3.1.4
Students will
use angle
relationships to
prove basic
theorems.
Can you prove
lines are
parallel by
using theorems
and
properties?
-none-
2 Days 3-3
Parallel Lines
and the
Triangle Angle-
Sum Theorem
MA-HS-3.1.7
Students will
solve real-world
and
mathematical
problems by
applying
properties of
triangles (e.g.,
Triangle Sum
theorem and
Isosceles
Triangle
theorems).
DOK 2
MA-HS-3.1.8
Students will
use the
properties of
triangles to
prove basic
theorems.
MA-HS-3.1.5
Students will
classify and
apply
properties of
Can you
classify
triangles?
Can you
measure
triangles?
Can you use
exterior angles
of triangles?
• Acute Triangle
• Right triangle
• Obtuse triangle
• Equiangular
triangle
• Equilateral
triangle
• Isosceles triangle
• Scalene triangle
• Exterior angle of
a polygon
• Remote interior
angle
two-
dimensional
geometric
figures (e.g.,
number of
sides, vertices,
length of sides,
sum of interior
and exterior
angle
measures).
DOK 2
2 Days 3-4
The Polygon
Angle-Sum
Theorems
MA-HS-3.1.7
Students will
solve real-world
and
mathematical
problems by
applying
properties of
triangles (e.g.,
Triangle Sum
theorem and
Isosceles
Triangle
theorems).
DOK 2
MA-HS-3.1.8
Can you
classify
polygons?
Can you find
the sums and
measure s of
the interior
and exterior
angles of a
polygon?
• Polygon
• Convex Polygon
• Concave Polygon
• Equilateral
polygon
• Equiangular
polygon
• Regular polygon
Students will
use the
properties of
triangles to
prove basic
theorems.
MA-HS-3.1.5
Students will
classify and
apply
properties of
two-
dimensional
geometric
figures (e.g.,
number of
sides, vertices,
length of sides,
sum of interior
and exterior
angle
measures).
DOK 2
1 Day Slope
(p. 151)
MA-HS-3.3.1
Students will
apply algebraic
concepts and
What does the
slope of a line
measure?
How do you
find the slope
of a line?
• Slope
graphing in the
coordinate
plane to analyze
and solve
problems (e.g.,
finding the final
coordinates for
a specified
polygon,
midpoints,
between-ness
of points,
parallel and
perpendicular
lines, the
distance
between two
points, the
slope of a
segment).
DOK 2
3 Days 3-5
Lines in the
Coordinate
Plane
MA-HS-5.3.1
Students will
model, solve
and graph first
degree, single
variable
equations and
inequalities,
How do you
graph linear
equations?
How do you
find linear
equations?
• Slope-intercept
form
• Standard form of
a linear equation
• Point-slope form
including
absolute value,
based in real-
world and
mathematical
problems and
graph the
solutions on a
number line.
DOK 2
3 Days 3-6
Slopes of
Parallel and
Perpendicular
Lines
MA-HS-3.3.1
Students will
apply algebraic
concepts and
graphing in the
coordinate
plane to analyze
and solve
problems (e.g.,
finding the final
coordinates for
a specified
polygon,
midpoints,
between-ness
of points,
parallel and
perpendicular
lines, the
How do you
find slopes of
parallel and
perpendicular
lines?
How do you
find an
equation of a
line parallel to
or
perpendicular
to another
line?
distance
between two
points, the
slope of a
segment).
DOK 2
MA-HS-3.3.1
Students will
apply algebraic
concepts and
graphing in the
coordinate
plane to analyze
and solve
problems (e.g.,
finding the final
coordinates for
a specified
polygon,
midpoints,
between-ness
of points,
parallel and
perpendicular
lines, the
distance
between two
points, the
slope of a
segment).
DOK 2
2 days 4-1
Congruent
Figures
MA-HS-3.1.12
Students will
apply the
concepts of
congruence and
similarity to
solve real-world
and
mathematical
problems.
DOK 3
MA-HS-3.1.13
Students will
prove triangles
congruent and
similar.
Can you
recognize
congruent
figures and
their
corresponding
parts?
• Congruent
polygons
• Corresponding
parts
2 days 4-2
Triangle
Congruence by
SSS and SAS
MA-HS-3.1.12
Students will
apply the
concepts of
congruence and
similarity to
solve real-world
and
Can you prove
two triangles
are congruent
by using the
SSS and the
SAS
Postulates?
• None
mathematical
problems.
DOK 3
MA-HS-3.1.13
Students will
prove triangles
congruent and
similar.
2 Days 4-3
Triangle
Congruence by
ASA and AAS
MA-HS-3.1.12
Students will
apply the
concepts of
congruence and
similarity to
solve real-world
and
mathematical
problems.
DOK 3
MA-HS-3.1.13
Students will
prove triangles
congruent and
similar.
Can you prove
two triangles
are congruent
using the ASA
Postulate and
the AAS
Theorem?
• None
2 Days 4-4
Using
Congruent
Triangles:
CPCTC
MA-HS-3.1.12
Students will
apply the
Can you use
triangle
congruence
and CPCTC to
prove that
• CPCTC
concepts of
congruence and
similarity to
solve real-world
and
mathematical
problems.
DOK 3
MA-HS-3.1.13
Students will
prove triangles
congruent and
similar.
parts of two
triangles are
congruent?
1 Day Systems of
Linear
Equations
(p. 209)
MA-HS-5.3.4
Students will
model, solve
and graph
systems of two
linear equations
in real-world
and
mathematical
problems.
DOK 3
MA-HS-5.3.5
Students will
write, graph,
and solve
Can you model
and solve
systems of
linear
equations?
• Solution
systems of two
linear
inequalities
based on real-
world or
mathematical
problems and
interpret the
solution.
2 days 4-5
Isosceles and
Equilateral
Triangles
MA-HS-3.1.12
Students will
apply the
concepts of
congruence and
similarity to
solve real-world
and
mathematical
problems.
DOK 3
MA-HS-3.1.7
Students will
solve real-world
and
mathematical
problems by
applying
Can you use
and apply
properties of
isosceles
triangles?
• Legs of an
isosceles triangle
• Base of an
isosceles triangle
• Vertex angle of
an isosceles
triangle
• Base angles of an
isosceles triangle
• Corollary
properties of
triangles (e.g.,
Triangle Sum
theorem and
Isosceles
Triangle
theorems).
MA-HS-3.1.8
Students will
use the
properties of
triangles to
prove basic
theorems.
DOK 2
2 Days 4-6
Congruence in
Right Triangles
MA-HS-3.1.12
Students will
apply the
concepts of
congruence and
similarity to
solve real-world
and
mathematical
problems.
DOK 3
Can you prove
two triangles
are congruent
by using the HL
Theorem?
• Hypotenuse
• Legs of a right
triangle
MA-HS-3.1.7
Students will
solve real-world
and
mathematical
problems by
applying
properties of
triangles (e.g.,
Triangle Sum
theorem and
Isosceles
Triangle
theorems).
MA-HS-3.1.8
Students will
use the
properties of
triangles to
prove basic
theorems.
DOK 2
2 Days 4-7
Using CPCTC
MA-HS-3.1.12
Students will
apply the
concepts of
Can you
identify
congruent
overlapping
triangles?
• None
congruence and
similarity to
solve real-world
and
mathematical
problems.
DOK 3
MA-HS-3.1.8
Students will
use the
properties of
triangles to
prove basic
theorems.
DOK 2
Can you prove
two triangles
are congruent
by first proving
two other
triangles are
congruent?
2 Days 6-1
Classifying
Quadrilaterals
MA-HS-3.1.5
Students will
classify and
apply
properties of
two-
dimensional
geometric
figures (e.g.,
number of
sides, vertices,
length of sides,
Can you define
and classify
special types of
quadrilaterals?
• Parallelogram
• Rhombus
• Rectangle
• Square
• Kite
• Trapezoid
• Isosceles
trapezoid
sum of interior
and exterior
angle
measures).
DOK 2
2 Days 6-2
Properties of
Parallelograms
MA-HS-3.1.5
Students will
classify and
apply
properties of
two-
dimensional
geometric
figures (e.g.,
number of
sides, vertices,
length of sides,
sum of interior
and exterior
angle
measures).
DOK 2
Can you use
relationships of
parallelograms
to prove that
two
parallelograms
are congruent?
• None
2 Days 6-3
Proving that a
Quadrilateral is
a
Parallelogram
MA-HS-3.1.5
Students will
classify and
apply
Can you
determine
whether a
quadrilateral is
a
• None
properties of
two-
dimensional
geometric
figures (e.g.,
number of
sides, vertices,
length of sides,
sum of interior
and exterior
angle
measures).
DOK 2
parallelogram?
2 Days 6-4
Special
Parallelograms
MA-HS-3.1.5
Students will
classify and
apply
properties of
two-
dimensional
geometric
figures (e.g.,
number of
sides, vertices,
length of sides,
sum of interior
and exterior
angle
Can you use
the properties
of diagonals of
rhombuses and
rectangles?
Can you
determine
whether a
parallelogram
is a rhombus or
a rectangle?
• None
measures).
DOK 2
2 Days 6-5
Trapezoids and
Kites
MA-HS-3.1.5
Students will
classify and
apply
properties of
two-
dimensional
geometric
figures (e.g.,
number of
sides, vertices,
length of sides,
sum of interior
and exterior
angle
measures).
DOK 2
Can you verify
and use
properties of
trapezoids and
kites?
• Base angles of a
trapezoid
2 days 7-1
Areas of
Parallelograms
and Triangles
MA-HS-3.1.5
Students will
classify and
apply
properties of
two-
dimensional
Can you find
the area of a
parallelogram?
Can you find
the area of a
triangle?
• Base of a
parallelogram
• Altitude of a
parallelogram
• Height of a
parallelogram
• Base of a triangle
• Height of a
geometric
figures (e.g.,
number of
sides, vertices,
length of sides,
sum of interior
and exterior
angle
measures).
DOK 2
MA-HS-2.1.2
Students will
describe how a
change in one
or more
dimensions of a
geometric
figure affects
the perimeter,
area and
volume of the
figure.
DOK 3
triangle
1 Day Simplifying
Radicals
(p. 355)
MA-HS-1.3.1 Students will solve real-world and
Can you
simplify
radicals?
• None
mathematical problems to specified accuracy levels by simplifying expressions with real numbers involving addition, subtraction, multiplication, division, absolute value, integer exponents, roots (square, cube) and factorials.
DOK 2
2 Days 7-2
The
Pythagorean
Theorem and
Its Converse
MA-HS-2.1.3
Students will
apply
definitions and
properties of
right triangle
relationships
(right triangle
trigonometry
and the
Pythagorean
theorem) to
determine
length and
Can you use
the
Pythagorean
Theorem?
Can you use
the Converse
of the
Pythagorean
Theorem?
• Pythagorean
triple
angle measures
to solve real-
world and
mathematical
problems.
DOK 3
MA-HS-2.1.4
Students will
apply special
right triangles
and the
converse of the
Pythagorean
theorem to
solve real-world
problems.
2 Days 7-3
Special Right
Triangles
MA-HS-2.1.3
Students will
apply
definitions and
properties of
right triangle
relationships
(right triangle
trigonometry
and the
Pythagorean
theorem) to
determine
Can you use
the properties
of the special
triangles to
find unknown
parts?
• None
length and
angle measures
to solve real-
world and
mathematical
problems.
DOK 3
MA-HS-2.1.4
Students will
apply special
right triangles
and the
converse of the
Pythagorean
theorem to
solve real-world
problems.
2 Days 7-4
Areas of
Trapezoids,
Rhombuses,
and Kites
MA-HS-3.1.5
Students will
classify and
apply
properties of
two-
dimensional
geometric
figures (e.g.,
number of
sides, vertices,
length of sides,
Can you find
the area of a
trapezoid?
Can you find
the area of a
rhombus?
• Height of a
trapezoid
sum of interior
and exterior
angle
measures).
DOK 2
MA-HS-2.1.2
Students will
describe how a
change in one
or more
dimensions of a
geometric
figure affects
the perimeter,
area and
volume of the
figure.
DOK 3
2 Days 7-5
Areas of
Regular
Polygons
MA-HS-3.1.5
Students will
classify and
apply
properties of
two-
dimensional
Can you find
the area of a
regular
polygon?
• Center of a
regular polygon
• Radius of a
regular polygon
• Apothem of a
regular polygon
geometric
figures (e.g.,
number of
sides, vertices,
length of sides,
sum of interior
and exterior
angle
measures).
DOK 2
MA-HS-2.1.2
Students will
describe how a
change in one
or more
dimensions of a
geometric
figure affects
the perimeter,
area and
volume of the
figure.
DOK 3
2 Days 7-6
Circles and
Arcs
MA-HS-3.1.6
Students will
Can you find
the measures
of central
• Circle
• Center
• Radius
know the
definitions and
basic properties
of a circle and
will use them to
prove basic
theorems and
solve problems.
angles and
arcs?
Can you find
the
circumference
and arc length
of a circle?
• Congruent circles
• Diameter
• Central angles
• Semicircle
• Minor arc
• Major arc
• Adjacent arcs
• Circumference
• Pi
• Concentric circles
• Arc length
• Congruent arcs
2 Days 7-7
Areas of Circles
and Sectors
MA-HS-3.1.6
Students will
know the
definitions and
basic properties
of a circle and
will use them to
prove basic
theorems and
solve problems.
Can you find
areas of circles,
sectors, and
segments of
circles?
• Sector of a circle
• Segment of a
circle
2 Days 7-8
Geometric
Probability
MA-HS-4.4.3
Students will
represent
probabilities in
Can you use
segment and
area models to
find the
probabilities of
events?
• Geometric
Probability
multiple ways,
such as
fractions,
decimals,
percentages and
geometric area
models.
8-1
Ratios and
Proportions
MA-HS-3.1.12
Students will
apply the
concepts of
congruence and
similarity to
solve real-world
and
mathematical
problems.
DOK 3
MA-HS-3.1.13
Students will prove triangles congruent and similar. MA-HS-1.4.1 Students will apply ratios, percents and proportional
reasoning to solve real-world problems (e.g., those involving slope and rate, percent of increase and decrease) and will explain how slope determines a rate of change in linear functions representing real-world problems.
DOK 2
8-2
Similar
Polygons
MA-HS-3.1.12
Students will
apply the
concepts of
congruence and
similarity to
solve real-world
and
mathematical
problems.
DOK 3
MA-HS-3.1.13
Students will
prove triangles
congruent and
similar.
MA-HS-3.1.5
Students will
classify and
apply
properties of
two-
dimensional
geometric
figures (e.g.,
number of
sides, vertices,
length of sides,
sum of interior
and exterior
angle
measures).
DOK 2
8-3
Proving
Triangles
Similar
MA-HS-3.1.12
Students will
apply the
concepts of
congruence and
similarity to
solve real-world
and
mathematical
problems.
DOK 3
MA-HS-3.1.13
Students will
prove triangles
congruent and
similar.
MA-HS-3.1.5
Students will
classify and
apply
properties of
two-
dimensional
geometric
figures (e.g.,
number of
sides, vertices,
length of sides,
sum of interior
and exterior
angle
measures).
DOK 2
8-4
Similarity in
Right Triangles
MA-HS-3.1.12
Students will
apply the
concepts of
congruence and
similarity to
solve real-world
and
mathematical
problems.
DOK 3
MA-HS-3.1.13
Students will
prove triangles
congruent and
similar.
MA-HS-3.1.5
Students will
classify and
apply
properties of
two-
dimensional
geometric
figures (e.g.,
number of
sides, vertices,
length of sides,
sum of interior
and exterior
angle
measures).
DOK 2
8-5
Proportions in
Triangles
MA-HS-3.1.12
Students will
apply the
concepts of
congruence and
similarity to
solve real-world
and
mathematical
problems.
DOK 3
MA-HS-3.1.13
Students will
prove triangles
congruent and
similar.
MA-HS-3.1.5
Students will
classify and
apply
properties of
two-
dimensional
geometric
figures (e.g.,
number of
sides, vertices,
length of sides,
sum of interior
and exterior
angle
measures).
DOK 2
8-6
Perimeters and
Areas of
Similar Figures
MA-HS-3.1.12
Students will
apply the
concepts of
congruence and
similarity to
solve real-world
and
mathematical
problems.
DOK 3
MA-HS-3.1.13
Students will
prove triangles
congruent and
similar.
MA-HS-3.1.5
Students will
classify and
apply
properties of
two-
dimensional
geometric
figures (e.g.,
number of
sides, vertices,
length of sides,
sum of interior
and exterior
angle
measures).
9-1
The Tangent
Ratio
9-2
Sine and
Cosine Ratios
9-3
Angles of
Elevation and
Depression
10-1
Space Figures
and Nets
10-2
Space Figures
and Drawings
10-3
Surface Area of
Prisms and
Cylinders
10-4
Surface Area of
Pyramids and
Cones
10-5
Volumes of
Prisms and
Cylinders
10-6
Volumes of
Pyramids and
Cones
10-7
Surface Areas
and Volumes
of Spheres
10-8
Areas and
Volumes of
Similar Solids
11-1
Tangent Lines
11-2
Chords and
Arcs
11-3
Inscribed
Angles
11-4
Angle
Measures and
Segment
Lengths
11-5
Circles in the
Coordinate
Plane