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