Keansburg School District
Curriculum Management System
Believe, Understand, and Realize Goals
Mathematics: Geometry - College and Career Ready (CCR)
Board Approved:
1
Keansburg School District
Curriculum System
Mathematics
Keansburg Public Schools
Board of Education
Mrs. Judy Ferraro, President
Ms. Kimberly Kelaher-Moran, Vice President
Ms. Delores A. Bartram
Ms. Ann Marie Best
Ms. Christine Blum
Ms. Ann Commarato
Mr. Michael Donaldson
Ms. Patricia Frizell
Mr. Robert Ketch
District Administration
Mr. Gerald North, Superintendent
Dr. Thomas W. Tramaglini, Director of Curriculum, Instruction, & Funding
Ms. Michelle Derpich, Secondary Supervisor of Curriculum & Instruction
Mrs. Donna Glomb, Elementary Supervisor of Curriculum & Instruction
Ms. Michelle Halperin-Krain, Supervisor of Data & Assessment
Dr. Brian Latwis, Supervisor of Pupil Personnel Services
Ms. Corey Lowell, Business Administrator
Jennifer Anderson
Karen Bruno
Gina Cancellieri
Giacinto Dagostino
Karen Egan
Obed Espada
Curriculum Development Committee
Maureen Hooker
Justine Ince
Tara Kukulski
Carrie Mazak
Michelle Meyers
Nicole Miragliotta
Camille Negri
Jennifer O’Keefe
Frank Reash
Roslyn Simek
2
Keansburg School District
Curriculum System
Mathematics
Believe, Understand, and Realize Goals
Non-Negotiables
Graduates
that are
prepared
and
inspired
to make positive
contributions to society
2
Keansburg School District
Curriculum System
Mathematics
Mission/Vision Statement
The mission of the Keansburg School District is to ensure an optimum, safe teaching and learning environment, which sets high
expectations and enables all students to reach their maximum potential. Through a joint community-wide commitment, we will
meet the diverse needs of our students and the challenges of a changing society.
Beliefs
We believe that:

All children can learn.

To meet the challenges of change, risk must be taken.

Every student is entitled to an equal educational opportunity.

It is our responsibility to enable students to succeed and become the best that they can be.

All individuals should be treated with dignity and respect.

The school system should be responsive to the diversity within our total population.

The degree of commitment and level of involvement in the decision-making processes, from the student, community, home
and school, will determine the quality of education.

Decisions should be based on the needs of the students.

Achievement will rise to the level of expectation.

Students should be taught how to learn.

The educational process should be a coordinated system of services and programs.
3
Keansburg School District
Curriculum System
Mathematics
Curriculum Philosophy
The curriculum philosophy of the Keansburg School District is progressive. We embrace the high expectations of our students and
community towards success in the 21st Century and beyond. At the center of this ideal, we believe that all of our students can be successful.
The following are our core beliefs for all curricula:
All district curricula:

Balances policy driven trends of centralization and standardization with research and what we know is good for our students.

Balances the strong emphasis on test success and curriculum standards with how and what our students must know to be successful in
our community.

Embraces the reality that our students differ in the way they learn and perform, and personalizes instruction to meet the needs of each
learner.

Are aligned to be developmentally appropriate.

Provides teachers the support and flexibility to be innovative and creative to meet the needs of our students.
Mathematics Goals
To deliver a curriculum that is:

Pertinent for the success of all of our students and useful for teachers in the 21st Century.

Problem-based, where students understand the importance of mathematical concepts and applications.

Socially, emotionally, and academically driven with regards to statute and code, while focusing on what is best for each of the students
in our school district to achieve successful outcomes.

Significant in the processes of growth and development, and relevant to the students.

Differentiated with regards to our students’ abilities and needs.

Embedded with teaching responsibility, respect, and the value of hard work and self-pride over time.

Designed with both content knowledge and experiences which:
o
Are aligned from one grade level to the next, with scaffolded underpinnings of similar concepts for success.
o
Engage our diverse population for positive outcomes.
o
Build and support the language of mathematics.
o
Develop educational and mathematical independence over time.
4
Keansburg School District
Curriculum System
Mathematics
Geometry Scope and Sequence
Concepts/Big ideas
Year
Concepts/Big ideas
September
Block
September
I.
Lines, Angles, and Planes
September
September
II.
Logical Reasoning and Conditional Statements
October
September
October
III.
Parallel and Perpendicular Lines
November
October
IV.
Congruent Triangles
December
October
November
V.
Right Triangles and Trigonometry
January
November
VI.
Proportions and Similarity
February
November
December
VII.
Triangle Relationships
March
December
VIII.
Quadrilaterals
5
Keansburg School District
Curriculum System
Mathematics
IX.
Transformations
April
December
May
January
X.
Circles
June
January
XI.
Three Dimensional Figures
6
Keansburg School District
Curriculum System
Mathematics
Keansburg School District
Curriculum Management System
Subject/Grade/Level:
Mathematics/Geometry
Timeline:
September (Year)
September (Block)
Topic(s): Lines, Angles, and Planes
Suggested Days of
Instruction
Significance of Learning Goal(s): TBAT find distance and direction. Realize these are the building blocks of
geometric figures.
Content
Standards /
CPI /
Essential
Questions
CPI:
G.CO.12
G.CO.13
G.CO.9
6 days
(Year)
3 days
(Block)
EQ:Is every
baseball field
the same
length?
Is the distance
from each pair
of bases the
same?
Specific Learning Objective(s)
Suggested Activities
Instructional Tools / Materials / Technology /
Resources / Assessments and Assessment Models
The Students Will Be Able To:
Concept(s):
Lines, Angles, and Planes
Meets the Standard (SWBAT):

Identify points, lines, and
planes

Construct and label
points, lines, planes, and angles

Explain special angle
pairs including vertical angles

Construct the mid-point
on a line segment

Discover the distance of a
line segment
Exceeds the Standard (SWBAT):

Justify the different
between points, lines, and planes

Illustrate special angle
pairs

Compute the midpoint,
using the midpoint formula

Calculate distance using
the distance formula
Meets Standard:
1. Draw a map of your town showing
where streets intersect. Label parallel,
perpendicular lines, and types of lines
& angles formed.
(2 days)
2. Telecommunications – A cell phone
tower at point A receives a cell phone
signal from the southeast. A cell
phone tower at point B receives a
signal from the same cell phone from
due west. Create a diagram and find
the location of the cell phone.
Protractor, compass, straight-edge, large post-it paper,
calculators, video-http://phschool.com/webcodes10/
index.cfm?fuseaction=home.gotoWebCode&wcprefix=
aue&wcsuffix=0105#, Khan Academy,
http://www.mathplayground.com/measuringangles.html
Typical Assessment Question(s) or Task(s):
Exceeds Standard:
1. Draw a trapezoid on grid paper
then find the area and perimeter of
the trapezoid.
2. Construct an equilateral triangle
and find its medians.
3. Design a compass to construct
geometric figures
7
Keansburg School District
Curriculum System
Mathematics
Keansburg School District
Curriculum Management System
Subject/Grade/Level:
Mathematics/Geometry
Timeline:
September (Year)
September (Block)
Topic(s): Logical Reasoning and Conditional Statements
Suggested Days of
Instruction
Significance of Learning Goal(s): To determine validity of statements. To complete tasks needing sequence.
10
days
(Year)
5 days
(Block)
Content
Standards /
CPI /
Essential
Questions
CPI:
S.CP.2
S.CP.3
S.CP.4
S.CP.5
S.CP.6
S.CP.7
S.CP.8
S.CP.9
A.SSE.4
F.BF.2
EQ: Where
would you
find an
example of a
conditional
statement
outside
school?
Specific Learning
Objective(s)
Suggested Activities
Instructional Tools / Materials / Technology / Resources /
Assessments and Assessment Models
The Students Will Be
Able To:
Concept(s):
Logical Reasoning and
Conditional Statements
Meets the Standard
(SWBAT):

Recognize
patterns and sequence

Find the next
terms in sequences

Classify the
hypothesis & conclusions
of statements

Compose an
if/then statements and
their converse

Produce
counterexamples

Complete
segment and angle proofs
Exceeds the Standard
(SWBAT):

Generate
Meets Standard:
1. Determine validity of a
conditional statement.(1
day)
2. Look at the circles. What
conjecture can you make
about the numbers of
regions 20 diameters form?
Protractor, straight-edge, calculators, videohttp://phschool.com/webcodes10/
index.cfm?fuseaction=home.gotoWebCode&wcprefix=aue&wcsuffix=0201#
, Khan Academy
Typical Assessment Question(s) or Task(s):
Exceeds Standard:
1. Draw a Venn diagram
using three different
components. Then make
statements about the data
and list the converses too.
2. Using the American Sign
8
Keansburg School District
Curriculum System
Mathematics
patterns and sequence
using a conditional
statement, select its
converse, inverse, &
contrapositive

Create &
compose algebraic,
segment, and angle proofs
Language alphabet, decide
whether the description of
each letter is a good
definition. Explain. If not,
provide a counterexample
by giving another letter
that could fit the
definition.
3. You want to use the
coupon to buy 3 different
pairs of jeans. You have
narrowed your choices to
4 pairs. The costs of the
different pairs are $24.99,
39.99, 40.99, and $50. If
you spend as little as
possible, what is the
average amount per pair
of jeans that you will pay?
Explain and show your
work.
9
Keansburg School District
Curriculum System
Mathematics
Keansburg School District
Curriculum Management System
Subject/Grade/Level:
Mathematics/Geometry
Timeline:
October (Year)
September-October (Block)
Topic(s): Parallel and Perpendicular Lines
Suggested Days of
Instruction
Significance of Learning Goal(s): Use coordinates to prove simple geometric theorems algebraic.
Content
Standards /
CPI /
Essential
Questions
CPI:
G.GPE.4
G.GPE.5
G.GPE.6
G.GPE.7
7 days
(year)
4 days
(block)
EQ: Where are
parallel or
perpendicular
lines used
outside school?
Specific Learning
Objective(s)
Suggested Activities
The Students Will
Be Able To:
Concept(s):
Parallel and
Perpendicular Lines
Meets the Standard
(SWBAT):

Recognize
angles formed by
transversals

Generate
angles formed by
transversals

Devise the
slopes of lines and
use slope to identify
parallel and
perpendicular line

Write
equations of lines
parallel or
perpendicular to
given lines or
coordinates
Meets Standard:
1. Model an example (make a collage of parallel and
perpendicular lines shown in magazine)
(3 days)
2. The maze below has 2 intersecting sets of parallel
paths. A mouse makes 5 turns in the maze to get to a
piece of cheese. Follow the mouse’s path through the
maze. What are the number of degrees at each turn?
Explain. (original picture @ Pearson Prentice Hall –
Geometry p.156)
Instructional Tools / Materials / Technology /
Resources / Assessments and Assessment
Models
Protractors, calculators, straight-edge, digital
camera, magazines, glue stick, poster board, videohttp://phschool.com/webcodes10/
index.cfm?fuseaction=home.gotoWebCode&wcprefix
=afe&wcsuffix=0775#, Khan Academy
Typical Assessment Question(s) or Task(s):
10
Keansburg School District
Curriculum System
Mathematics

Justify
parallel and
perpendicular lines
using slope
Exceeds the
Standard
(SWBAT):

Compile
parallel &
perpendicular lines
to draw models

Design floor
plans using parallel
& perpendicular
lines
Exceeds Standard:
Model a train track and road crossing to show parallel &
perpendicular lines. Then make a non-perpendicular
crossing and label all resulting angles on the diagram.
11
Keansburg School District
Curriculum System
Mathematics
Keansburg School District
Curriculum Management System
Subject/Grade/Level:
Mathematics/Geometry
Timeline:
November (Year)
October (Block)
Topic(s): Congruent Triangles
Suggested Days of
Instruction
Significance of Learning Goal(s): To match triangles in different situations. To translate congruent parts in
congruent triangles.
Content
Standards /
CPI /
Essential
Questions
CPI:
G.SRT.2
G.SRT.3
G.SRT.4
G.SRT.5
G.CO.8
7 days
(year)
4 days
(block)
EQ: If the pitch
and length of
the roofs of
two different
houses are the
same; are the
houses the
same?
Specific Learning Objective(s)
Suggested Activities
Instructional Tools / Materials / Technology /
Resources / Assessments and Assessment Models
The Students Will Be Able To:
Concept(s):
Congruent Triangles
Meets the Standard (SWBAT):

Manipulate the angle sum
theorem

Specify and label
corresponding parts of congruent
triangles

Compare corresponding
parts of triangles

Utilize the SSS,SAS,ASA, and
AAS tests for congruence

Produce missing parts of
congruent triangles
Exceeds the Standard (SWBAT):

Construct triangles given
their parts

Justify the angle sum
theorem using real life examples

Manufacture congruent
triangle, using SSS,SAS,ASA, and AAS
Meets Standard:

Create a quilt template to
duplicate triangles. Then cut out
triangles and measure for
congruence.

Cut out six right triangles
of various sizes using 40° and 50°
angles. The triangles of the same
color are congruent. Arrange the
triangles to form one large triangle.
Classify this triangle by its sides.
What are the angle measures of
this triangle? Explain.
Pearson-Prentice HallGeometry
(2011) pg.250

Pearson-Prentice HallGeometry (2011) pg.240 #21
Letter (using geometric
knowledge)
Exceeds Standard:

Use a picture of a moth to
fond the two congruent triangles
needed to create a moth. Write a
Protractor, calculator, moth picture, scissors, videohttp://phschool.com/webcodes10/index.cfm?fuseaction=
home.gotoWebCode&wcprefix=afe&wcsuffix=0775#,
Khan Academy
Typical Assessment Question(s) or Task(s):
12
Keansburg School District
Curriculum System
Mathematics
tests for congruence
two-column proof proving the S.S.S.
theorem.

Siepinski’s triangle is a
famous geometric pattern. To
draw Sierpinkski’s triangle, start
with a single triangle and connect
the midpoints of the sides to draw
a smaller triangle. Repeat the
pattern several times. Are all the
triangles congruent?
13
Keansburg School District
Curriculum System
Mathematics
Keansburg School District
Curriculum Management System
Subject/Grade/Level:
Mathematics/Geometry
Timeline:
December (Year)
October and November (Block)
Topic(s): Right Triangles and Trigonometry
Suggested Days of
Instruction
Significance of Learning Goal(s): To find measurements given right triangles.
Content
Standards /
CPI /
Essential
Questions
CPI:
G.SRT.6
G.SRT.7
G.SRT.8
G.SRT.9
G.SRT.10
G.SRT.11
9 days
(year)
5 days
(block)
EQ: How
would you find
the height of
the school
without using
a ruler?
Specific Learning Objective(s)
Suggested Activities
Instructional Tools / Materials / Technology /
Resources / Assessments and Assessment Models
The Students Will Be Able To:
Concept(s):
Right Triangles and Trigonometry
Meets the Standard (SWBAT):

Identify trigonometry
functions when finding the side of a
right triangle

Retrieve vocabulary to
understand right triangle in
trigonometry

Select & use properties of
45-45-90 & 30-60-90 triangles
Exceeds the Standard (SWBAT):

Model a real life situation
finding a missing angle/side

Develop Law of Sines &
Cosines

Apply Pythagorean
Theorem

Set up Trigonometric ratios
to find the missing parts in right
triangles
Meets Standard:

Using vectors have
students travel south a distance of
5, then west 12 units. Then have
students find shortest distance
between the starting and ending
point.

Dog agility courses often
contain a seesaw obstacle, show
below. To the nearest inch, how far
above the ground are the dog’s
paws when the seesaw is parallel to
the ground?
Pearson-Prentice Hall-Geometry
(2011) pg.493
Calculator, straight-edge, graph paper, videohttp://phschool.com/webcodes10/index.cfm?fuseaction=
home.gotoWebCode&wcprefix=afe&wcsuffix=0775#,
Khan Academy
Typical Assessment Question(s) or Task(s):
Exceeds Standard:

Design an in ground pool,
show the depth of the water
changes-the different additions to
the pool (stairs-slide)

What is the ratio of the
length of the shorter leg to the
14
Keansburg School District
Curriculum System
Mathematics
length of the hypotenuse for each of
triangle ADF, triangle AEG, and
triangle ABC? Make a conjecture
based on your results. PearsonPrentice Hall-Geometry (2011) pg.
507

Problem #2-Using a
Trigonometric Ratio to find
distance. (Picture of Leaning Tower
of Pisa) Pearson-Prentice HallGeometry (2011) pg.508
15
Keansburg School District
Curriculum System
Mathematics
Keansburg School District
Curriculum Management System
Subject/Grade/Level:
Mathematics/Geometry
Timeline:
January (Year)
November (Block)
Topic(s): Proportions and Similarity
Suggested Days of
Instruction
Significance of Learning Goal(s): Compare images dealing with sides and angles.
Content
Standards /
CPI /
Essential
Questions
CPI:
G.SRT.2
G.SRT.3
G.SRT.4
G.SRT.5
7 days
(year)
4 days
(block)
EQ: Which
equation can
you use to find
a missing
equation?
Specific Learning Objective(s)
Suggested Activities
Instructional Tools / Materials / Technology /
Resources / Assessments and Assessment Models
The Students Will Be Able To:
Concept(s):
Proportions and Similarity
Meets the Standard (SWBAT):

Provide examples of
proportions of real life situations

Match up corresponding
sides and angles in similar shapes

Work with lengths &
measures of sides & angles in
similar figures

Recognize and calculate
missing parts of similar triangles
Exceeds the Standard (SWBAT):

Design a model of a real
life proportion
Meets Standard:

Convert dimensions from
drawn images to actual objects and
vice versa.

Finding the distancesetting up proportion. (picture)
Pearson-Prentice Hall-Geometry
(2011) pg. 464, problem #4

A bookcase is 4 ft. tall. A
model of the bookcase is 6 inches
tall. What is the ratio of the height
of the model bookcase to the height
of the real bookcase?
Calculators, protractors, straight-edge, videohttp://phschool.com/webcodes10/index.cfm?fuseaction=
home.gotoWebCode&wcprefix=afe&wcsuffix=0775#,
Khan Academy
Typical Assessment Question(s) or Task(s):
Exceeds Standard:

Use a spreadsheet to create
twenty terms of the Fibonacci
Sequence.

Architecture-Floor Plan for
a Home
Pearson-Prentice Hall-Geometry
(2011)-pg.446, problem #48 A and
B (Picture)
16
Keansburg School District
Curriculum System
Mathematics

Indirect Measurementfinding length in similar triangle.
(picture) Pearson-Prentice Hall –
Geometry (2011) pg.454, problem
#4
17
Keansburg School District
Curriculum System
Mathematics
Keansburg School District
Curriculum Management System
Subject/Grade/Level:
Mathematics/Geometry
Timeline:
February (Year)
November-December (Block)
Topic(s): Triangle Relationships
Suggested Days of
Instruction
Significance of Learning Goal(s): Prove theorems about triangles. Construct triangles.
Content
Standards /
CPI /
Essential
Questions
CPI:
G.CO.10
G.CO.13
EQ: Do all
triangles have
medians?
9 days
(year)
5 days
(block)
What kinds of
triangles are
found in a
house?
Specific Learning Objective(s)
Suggested Activities
Instructional Tools / Materials / Technology /
Resources / Assessments and Assessment Models
The Students Will Be Able To:
Concept(s):
Triangle Relationships
Meets the Standard (SWBAT):

Identify and construct
medians, altitudes, and angle
bisectors in triangles

Classify triangles by sides
& angles

Implement the triangle
inequality theorem

Produce the area of a
triangle
Exceeds the Standard (SWBAT):

Defend the inequality
theorem

Recognize & construct
points of concurrency in triangles
Meets Standard:

Pick two cities on a map.
Find a third city equally distant from
each of those cities.

a) Draw a large triangle,
triangle CDE. Construct the angle
bisectors of each angle.
b) What appears to be true about the
angle bisectors? Make a conjecture.
c) Test your conjecture with another
triangle.

To identify properties of
medians and altitudes of a triangle
(picture) Pearson-Prentice HallGeometry (2011) pg.314 (paperfolding) problem #29 and 30
Calculator, protractor, straight-edge, compass, ruler,
maps, videohttp://phschool.com/webcodes10/index.cfm?fuseaction=
home.gotoWebCode&wcprefix=afe&wcsuffix=0775#,
Khan Academy
Typical Assessment Question(s) or Task(s):
Exceeds Standard:

Draw the Sierpinski
Triangle; draw the first four stages
illustrating the geometric pattern.

Environmental Scienceusing a mid-segment of a triangle.
Pearson-Prentice Hall-Geometry
18
Keansburg School District
Curriculum System
Mathematics
(2011) pg.287 problem #3 (picture)
19
Keansburg School District
Curriculum System
Mathematics
Keansburg School District
Curriculum Management System
Subject/Grade/Level:
Mathematics/Geometry
Timeline:
March (Year)
December (Block)
Topic(s): Quadrilaterals
Suggested Days of
Instruction
Significance of Learning Goal(s): Recognize four sided figures and their properties. Compare different
properties of special parallelograms.
Content
Standards /
CPI / Essential
Questions
CPI:
G.CO.9
G.CO.10
G.CO.11
G.CO.12
G.CO.13
12
days
(year)
6 days
(block)
EQ: What are
the difficulties
between the
different
parallelograms?
Specific Learning Objective(s)
Suggested Activities
Instructional Tools / Materials / Technology /
Resources / Assessments and Assessment Models
The Students Will Be Able To:
Concept(s):
Quadrilaterals
Meets the Standard (SWBAT):

Identify and label properties
of parallelograms and special
parallelograms

Prove that the quadrilateral
is a parallelogram

Validate tests for
parallelograms

Label and apply the
properties of trapezoids

Draw conclusions involving
the median of trapezoids

Obtain measures of angles
using algebra

Demonstrate knowledge of
differences between quadrilaterals
using characteristics
Exceeds the Standard (SWBAT):

Discover properties of
isosceles trapezoids
Meets Standard:

Draw a rectangle with an
area of 36”. Find all possible
measurements for length and
width.

Sketch a convex
pentagon, hexagon, and heptagon.
For each figure, draw all the
diagonals you can from one
vertex. What conjecture can you
make about the relationship
between the number of sides of a
polygon and the number of
triangles formed by the diagonals
from one vertex?

Angle-Sum Theorem.
Pearson-Prentice Hall-Geometry
(2011) Biology (picture) pg. 354
problem #2
Calculators, ruler, protractor, videohttp://phschool.com/webcodes10/index.cfm?fuseaction=
home.gotoWebCode&wcprefix=afe&wcsuffix=0775#,
Khan Academy, http://www.woodlandsjunior.kent.sch.uk/maths/shape.htm
Typical Assessment Question(s) or Task(s):
Exceeds Standard:

Find the area of a
window of a Smart Car.

Studio lighting
20
Keansburg School District
Curriculum System
Mathematics
(parallelogram) (picture)
Pearson-Prentice Hall-Geometry
(2011) pg. 365 problem #31 A-C

Finding angle measures
in an Isosceles Trapezoids
(picture) Pearson-Prentice HallGeometry (2011) pg. 390 problem
#2
21
Keansburg School District
Curriculum System
Mathematics
Keansburg School District
Curriculum Management System
Subject/Grade/Level:
Mathematics/Geometry
Timeline:
April (Year)
December (Block)
Topic(s): Transformations
Suggested Days of
Instruction
Significance of Learning Goal(s): To change placement, shape and size of objects.
9 days
(year)
5 days
(block)
Content
Standards /
CPI /
Essential
Questions
CPI:
G.SRT.1
G.CO.1
G.CO.2
G.CO.3
G.CO.4
G.CO.5
G.CO.6
G.CO.7
G.CO.9
EQ: How do
you move a
figure or a
point from one
place on a
graph to
another?
Specific Learning Objective(s)
Suggested Activities
Instructional Tools / Materials / Technology /
Resources / Assessments and Assessment Models
The Students Will Be Able To:
Concept(s):
Transformations
Meets the Standard (SWBAT):

Distinguish the four types of
transformations

Graph figures given
coordinates & different
transformations

Construct vectors to find
speed & distance
Exceeds the Standard (SWBAT):

Demonstrate the three
types of transformations and how
they are different from each other

Illustrate change in
coordinates by using matrices
Meets Standard:

Using a map-transform a
“house” from one state to another

Translation Images of
Figures (Picture)-Getting ReadyGeometry Pearson Prentice Hall2011 pg. 544
Exceeds Standard:

Using computers, find a
mosaic tiling from the 13th century.
Describe the transformations found
in the picture. Then use
transformations to create a mosaic
of your own.

Rotation-(Picture)Geometry-Pearson Prentice Hall
(2011) pg. 564 #35-37
Calculator, map, computer, graph paper, ruler, videohttp://phschool.com/webcodes10/index.cfm?fuseaction=
home.gotoWebCode&wcprefix=afe&wcsuffix=0775#,
Khan Academy, http://www.woodlandsjunior.kent.sch.uk/maths/shape.htm
Typical Assessment Question(s) or Task(s):
22
Keansburg School District
Curriculum System
Mathematics
Keansburg School District
Curriculum Management System
Subject/Grade/Level:
Mathematics/Geometry
Timeline:
May (Year)
January (Block)
Topic(s): Circles
Suggested Days of
Instruction
Significance of Learning Goal(s): Understand and apply theorems about circle.
12
days
(year)
6 days
(block)
Content
Standards /
CPI /
Essential
Questions
CPI:
G.C.1
G.C.2
G.C.3
G.C.4
G.C.5
G.GPE.1
G.GPE.2
G.GPE.3
EQ: How do
you find the
area of the hole
in a donut? Can
you fit a
“munchkin”
into the hole of
a donut?
Specific Learning Objective(s)
Suggested Activities
Instructional Tools / Materials / Technology /
Resources / Assessments and Assessment Models
The Students Will Be Able To:
Concept(s):
Circles
Meets the Standard (SWBAT):

Describe and implement
parts of a circle

Generate the area &
circumference of circles

Distinguish between central
& inscribed angles

Acquire chord, angle, & arc
measure

Recognize secants, tangents,
& angles formed by these in and on a
circle
Exceeds the Standard (SWBAT):

Design the circle and their
parts

Identify & develop
concentric & congruent circles
Meets Standard:

Using a picture of a
Conestoga Wagon Wheel, find all
parts of a circle.

Inscribed Angles-Getting
Ready- Geometry Pearson Prentice
Hall (2011), pg.780
Exceeds Standard:

Find a circle graph from a
magazine. Then use the percent’s
to determine what part of the
whole circle (3600) each central
angle contains. Then make a circle
graph from data collected in class.

Using Diameters and
Chords- Geometry Pearson
Prentice Hall-(2011), Problem #3
(picture & diagram) pg. 775
Calculator, protractor, compass, picture of a wagon wheel,
magazines, large poster paper, colored pencils, videohttp://phschool.com/webcodes10/index.cfm?fuseaction=
home.gotoWebCode&wcprefix=afe&wcsuffix=0775#,
Khan Academy
Typical Assessment Question(s) or Task(s):
23
Keansburg School District
Curriculum System
Mathematics
Keansburg School District
Curriculum Management System
Subject/Grade/Level:
Mathematics/Geometry
Timeline:
June (Year)
January (Block)
Topic(s): Three Dimensional Figures
Suggested Days of
Instruction
Significance of Learning Goal(s): Visualize relationships between two-and three-dimensional objects.
Content
Standards /
CPI /
Essential
Questions
CPI:
G.GMD.1
G.GMD.2
G.GMD.3
G.GMD.4
G.MG.1
G.MG.2
G.MG.3
7 days
(year)
4 days
(block)
EQ: Which is a
better to sell
“A round oats
box” or a
rectangular
box of
envelopes?
Specific Learning Objective(s)
Suggested Activities
Instructional Tools / Materials / Technology /
Resources / Assessments and Assessment Models
The Students Will Be Able To:
Concept(s):
Three Dimensional Figures
Meets the Standard (SWBAT):

Recognize different 3Dimensional figures & polygons
(cones, prism)

Label different parts of 3Dimensional figures (faces, bases)

Produce surface area &
volume
Exceeds the Standard (SWBAT):

Draw 3-Dimensional figures

Apply 3-Dimensional figures
to real world situations

Manufacture the area of
conic sections
Meets Standard:

Argue whether a volcano
is a three-dimensional figure
(1 day)

Finding volume of a
composite figure-problem #4
pg.720- Geometry Pearson
Prentice Hall-(2011)
Exceeds Standard:

Draw a net for a
rectangular prism.
Construct a model of a rocket. Find
the surface area of each part.

An ice cream vendor
presses a sphere of frozen yogurt
into a cone. If the yogurt melts
into the cone, will the cone
overflow? Explain. Geometry
Pearson-Prentice Hall (2011)
(picture) #46 pg.739
Calculator, construction paper, ruler, videohttp://phschool.com/webcodes10/index.cfm?fuseaction=
home.gotoWebCode&wcprefix=afe&wcsuffix=0775#,
Khan Academy, http://www.woodlandsjunior.kent.sch.uk/maths/shape.htm
Typical Assessment Question(s) or Task(s):
24
Keansburg School District
Curriculum System
Mathematics
Keansburg School District
Curriculum Management System
Subject/Grade/Level:
Mathematics/Geometry
Timeline:
June (Year)
January (Block)
Topic(s): Polygons
Suggested Days of
Instruction
Significance of Learning Goal(s): Recognize properties of figures other than 4-sided figure. Find area of
regular polygons with more than 4 sides.
Content
Standards /
CPI /
Essential
Questions
CPI:
G-GPE-7
G-MG.1-3
8 days
(year)
4 days
(block)
EQ:
What polygons
are found
outside of
school? Where
are they
found?
Specific Learning Objective(s)
Suggested Activities
Instructional Tools / Materials / Technology /
Resources / Assessments and Assessment Models
The Students Will Be Able To:
Concept(s):
Polygons
Meets the Standard (SWBAT):

Relate polygons by sides

Discover angle measures
using formulas

Detect measures of sides
using coordinates

Name concave, convex, &
regular polygons
Exceeds the Standard (SWBAT):

Model polygons for real
world applications

Construct an object using
polygons
Meets Standard:

Create a net drawing and
prove it is a polygon.
(2 days)

Using Algebra to find
lengths, problem #3 pg.362
(explanation and drawings)
Pearson-Prentice Hall- Geometry
(2011)
Exceeds Standard:

Recreate the “Star” to
make a regular decagon.

Finding Angle Measures in
Isosceles Trapezoids, problem #2
pg. 390, Pearson-Prentice HallGeometry (2011)

Activity-Quadrilaterals in
Quadrilaterals, Construct and
Investigate pg.413, PearsonPrentice Hall-Geometry (2011)
Calculators, graph paper, construction paper, ruler, videohttp://www.khanacademy.org/math/geometry/polygonsquads-parallelograms/v/sum-of-interior-angles-of-apolygon, http://www.woodlandsjunior.kent.sch.uk/maths/shape.htm
Typical Assessment Question(s) or Task(s):
25
Keansburg School District
Curriculum System
Mathematics
Alignment Matrices of Common Core State Standards
Common Core State Standards Vocabulary
Addition and subtraction within 5, 10, 20, 100, or 1000. Addition or subtraction of two whole numbers with whole number answers, and
with sum or minuend in the range 0-5, 0-10, 0-20, or 0-100, respectively. Example: 8 + 2 = 10 is an addition within 10, 14 – 5 = 9 is a
subtraction within 20, and 55 – 18 = 37 is a subtraction within 100.
Additive inverses. Two numbers whose sum is 0 are additive inverses of one another. Example: 3/4 and – 3/4 are additive inverses of one
another because 3/4 + (– 3/4) = (– 3/4) + 3/4 = 0.
Associative property of addition. See Table 3 in this Glossary.
Associative property of multiplication. See Table 3 in this Glossary.
Bivariate data. Pairs of linked numerical observations. Example: a list of heights and weights for each player on a football team.
Box plot. A method of visually displaying a distribution of data values by using the median, quartiles, and extremes of the data set. A box
shows the middle 50% of the data.1
Commutative property. See Table 3 in this Glossary.
Complex fraction. A fraction A/B where A and/or B are fractions (B nonzero).
Computation algorithm. A set of predefined steps applicable to a class of problems that gives the correct result in every case when the steps
are carried out correctly. See also: computation strategy.
Computation strategy. Purposeful manipulations that may be chosen for specific problems, may not have a fixed order, and may be aimed at
converting one problem into another. See also: computation algorithm.
Congruent. Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations,
reflections, and translations).
Counting on. A strategy for finding the number of objects in a group without having to count every member of the group. For example, if a
stack of books is known to have 8 books and 3 more books are added to the top, it is not necessary to count the stack all over again. One can
find the total by counting on—pointing to the top book and saying “eight,” following this with “nine, ten, eleven. There are eleven books now.”
26
Keansburg School District
Curriculum System
Mathematics
Dot plot. See: line plot.
Dilation. A transformation that moves each point along the ray through the point emanating from a fixed center, and multiplies distances from
the center by a common scale factor.
Expanded form. A multi-digit number is expressed in expanded form when it is written as a sum of single-digit multiples of powers of ten. For
example, 643 = 600 + 40 + 3.
Expected value. For a random variable, the weighted average of its possible values, with weights given by their respective probabilities.
First quartile. For a data set with median M, the first quartile is the median of the data values less than M. Example: For the data set {1, 3, 6, 7,
10, 12, 14, 15, 22, 120}, the first quartile is 6.2 See also: median, third quartile, interquartile range.
Fraction. A number expressible in the form a/b where a is a whole number and b is a positive whole number. (The word fraction in these
standards always refers to a non-negative number.) See also: rational number.
Identity property of 0. See Table 3 in this Glossary.
Independently combined probability models. Two probability models are said to be combined independently if the probability of each
ordered pair in the combined model equals the product of the original probabilities of the two individual outcomes in the ordered pair.
Integer. A number expressible in the form a or –a for some whole number a.
Interquartile Range. A measure of variation in a set of numerical data, the interquartile range is the distance between the first and third
quartiles of the data set. Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the interquartile range is 15 – 6 = 9. See also: first quartile,
third quartile.
Line plot. A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line.
Also known as a dot plot.3
Mean. A measure of center in a set of numerical data, computed by adding the values in a list and then dividing by the number of values in the
list.4 Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean is 21.
Mean absolute deviation. A measure of variation in a set of numerical data, computed by adding the distances between each data value and
the mean, then dividing by the number of data values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean absolute deviation
is 20.
27
Keansburg School District
Curriculum System
Mathematics
Median. A measure of center in a set of numerical data. The median of a list of values is the value appearing at the center of a sorted version of
the list—or the mean of the two central values, if the list contains an even number of values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15,
22, 90}, the median is 11.
Midline. In the graph of a trigonometric function, the horizontal line halfway between its maximum and minimum values.
Multiplication and division within 100. Multiplication or division of two whole numbers with whole number answers, and with product or
dividend in the range 0-100. Example: 72 ÷ 8 = 9.
Multiplicative inverses. Two numbers whose product is 1 are multiplicative inverses of one another. Example: 3/4 and 4/3 are multiplicative
inverses of one another because 3/4 × 4/3 = 4/3 × 3/4 = 1.
Number line diagram. A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram
for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.
Percent rate of change. A rate of change expressed as a percent. Example: if a population grows from 50 to 55 in a year, it grows by 5/50 =
10% per year.
Probability distribution. The set of possible values of a random variable with a probability assigned to each.
Properties of operations. See Table 3 in this Glossary.
Properties of equality. See Table 4 in this Glossary.
Properties of inequality. See Table 5 in this Glossary.
Properties of operations. See Table 3 in this Glossary.
Probability. A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin,
selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).
Probability model. A probability model is used to assign probabilities to outcomes of a chance process by examining the nature of the
process. The set of all outcomes is called the sample space, and their probabilities sum to 1. See also: uniform probability model.
Random variable. An assignment of a numerical value to each outcome in a sample space.
28
Keansburg School District
Curriculum System
Mathematics
Rational expression. A quotient of two polynomials with a non-zero denominator.
Rational number. A number expressible in the form a/b or – a/b for some fraction a/b. The rational numbers include the integers.
Rectilinear figure. A polygon all angles of which are right angles.
Rigid motion. A transformation of points in space consisting of a sequence of one or more translations, reflections, and/or rotations. Rigid
motions are here assumed to preserve distances and angle measures.
Repeating decimal. The decimal form of a rational number. See also: terminating decimal.
Sample space. In a probability model for a random process, a list of the individual outcomes that are to be considered.
Scatter plot. A graph in the coordinate plane representing a set of bivariate data. For example, the heights and weights of a group of people
could be displayed on a scatter plot.5
Similarity transformation. A rigid motion followed by a dilation.
Tape diagram. A drawing that looks like a segment of tape, used to illustrate number relationships. Also known as a strip diagram, bar model,
fraction strip, or length model.
Terminating decimal. A decimal is called terminating if its repeating digit is 0.
Third quartile. For a data set with median M, the third quartile is the median of the data values greater than M. Example: For the data set {2, 3,
6, 7, 10, 12, 14, 15, 22, 120}, the third quartile is 15. See also: median, first quartile, interquartile range.
Transitivity principle for indirect measurement. If the length of object A is greater than the length of object B, and the length of object B is
greater than the length of object C, then the length of object A is greater than the length of object C. This principle applies to measurement of
other quantities as well.
Uniform probability model. A probability model which assigns equal probability to all outcomes. See also: probability model.
Vector. A quantity with magnitude and direction in the plane or in space, defined by an ordered pair or triple of real numbers.
Visual fraction model. A tape diagram, number line diagram, or area model.
Whole numbers. The numbers 0, 1, 2, 3, ….5
29
Keansburg School District
Curriculum System
Mathematics
9-12
N
RN.1
9-12
N
RN.2
9-12
N
RN.3
9-12
N
Q.1
9-12
N
Q.2
9-12
N
Q.3
9-12
N
CN.1
9-12
N
CN.2
9-12
N
CN.3
9-12
N
CN.4
Standard
CC.9-12.N.RN.1 Extend the properties of exponents to rational exponents. Explain how the
definition of the meaning of rational exponents follows from extending the properties of
integer exponents to those values, allowing for a notation for radicals in terms of rational
exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want
[5^(1/3)]^3 = 5^[(1/3) x 3] to hold, so [5^(1/3)]^3 must equal 5.
CC.9-12.N.RN.2 Extend the properties of exponents to rational exponents. Rewrite
expressions involving radicals and rational exponents using the properties of exponents.
CC.9-12.N.RN.3 Use properties of rational and irrational numbers. Explain why the sum or
product of rational numbers is rational; that the sum of a rational number and an
irrational number is irrational; and that the product of a nonzero rational number and an
irrational number is irrational.
CC.9-12.N.Q.1 Reason quantitatively and use units to solve problems. Use units as a way to
understand problems and to guide the solution of multi-step problems; choose and
interpret units consistently in formulas; choose and interpret the scale and the origin in
graphs and data displays.*
CC.9-12.N.Q.2 Reason quantitatively and use units to solve problems. Define appropriate
quantities for the purpose of descriptive modeling.*
CC.9-12.N.Q.3 Reason quantitatively and use units to solve problems. Choose a level of
accuracy appropriate to limitations on measurement when reporting quantities.*
CC.9-12.N.CN.1 Perform arithmetic operations with complex numbers. Know there is a
complex number i such that i^2 = −1, and every complex number has the form a + bi with a
and b real.
CC.9-12.N.CN.2 Perform arithmetic operations with complex numbers. Use the relation i2
= –1 and the commutative, associative, and distributive properties to add, subtract, and
multiply complex numbers.
CC.9-12.N.CN.3 (+) Perform arithmetic operations with complex numbers. Find the
conjugate of a complex number; use conjugates to find moduli and quotients of complex
numbers.
CC.9-12.N.CN.4 (+) Represent complex numbers and their operations on the complex
Other
Standard #
Geometry
Strand
Geometry
Grade
Geometry
Common Core Standards for Mathematics
Common Core State Standards for Mathematics (Grades 9-12)
X
X
X
X
X
X
X
x
X
30
Keansburg School District
Curriculum System
Mathematics
9-12
N
CN.5
9-12
N
CN.6
9-12
N
CN.7
9-12
N
CN.8
9-12
N
CN.9
9-12
N
VM.1
9-12
N
VM.2
9-12
N
VM.3
9-12
N
VM.4
9-12
N
VM.4a
9-12
N
VM.4b
9-12
N
VM.4c
9-12
9-12
N
N
VM.5
VM.5a
plane. Represent complex numbers on the complex plane in rectangular and polar form
(including real and imaginary numbers), and explain why the rectangular and polar forms
of a given complex number represent the same number.
CC.9-12.N.CN.5 (+) Represent complex numbers and their operations on the complex
plane. Represent addition, subtraction, multiplication, and conjugation of complex
numbers geometrically on the complex plane; use properties of this representation for
computation. For example, (-1 + √3i)^3 = 8 because (-1 + √3i) has modulus 2 and
argument 120°.
CC.9-12.N.CN.6 (+) Represent complex numbers and their operations on the complex
plane. Calculate the distance between numbers in the complex plane as the modulus of the
difference, and the midpoint of a segment as the average of the numbers at its endpoints.
CC.9-12.N.CN.7 Use complex numbers in polynomial identities and equations. Solve
quadratic equations with real coefficients that have complex solutions.
CC.9-12.N.CN.8 (+) Use complex numbers in polynomial identities and equations. Extend
polynomial identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x –
2i).
CC.9-12.N.CN.9 (+) Use complex numbers in polynomial identities and equations. Know
the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
CC.9-12.N.VM.1 (+) Represent and model with vector quantities. Recognize vector
quantities as having both magnitude and direction. Represent vector quantities by
directed line segments, and use appropriate symbols for vectors and their magnitudes
(e.g., v (bold), |v|, ||v||, v (not bold)).
CC.9-12.N.VM.2 (+) Represent and model with vector quantities. Find the components of a
vector by subtracting the coordinates of an initial point from the coordinates of a terminal
point.
CC.9-12.N.VM.3 (+) Represent and model with vector quantities. Solve problems involving
velocity and other quantities that can be represented by vectors.
CC.9-12.N.VM.4 (+) Perform operations on vectors. Add and subtract vectors.
CC.9-12.N.VM.4a (+) Add vectors end-to-end, component-wise, and by the parallelogram
rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the
magnitudes.
CC.9-12.N.VM.4b (+) Given two vectors in magnitude and direction form, determine the
magnitude and direction of their sum.
CC.9-12.N.VM.4c (+) Understand vector subtraction v – w as v + (–w), where (–w) is the
additive inverse of w, with the same magnitude as w and pointing in the opposite
direction. Represent vector subtraction graphically by connecting the tips in the
appropriate order, and perform vector subtraction component-wise.
CC.9-12.N.VM.5 (+) Perform operations on vectors. Multiply a vector by a scalar.
CC.9-12.N.VM.5a (+) Represent scalar multiplication graphically by scaling vectors and
X
X
31
Keansburg School District
Curriculum System
Mathematics
9-12
N
VM.5b
9-12
N
VM.6
9-12
N
VM.7
9-12
N
VM.8
9-12
N
VM.9
9-12
N
VM.10
9-12
N
VM.11
9-12
N
VM.12
9-12
A
SSE.1
9-12
A
SSE.1a
9-12
A
SSE.1b
9-12
A
SSE.2
9-12
A
SSE.3
possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c
(v (sub x), v (sub y)) = (cv (sub x), cv (sub y)).
CC.9-12.N.VM.5b (+) Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v.
Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along
v (for c > 0) or against v (for c < 0).
CC.9-12.N.VM.6 (+) Perform operations on matrices and use matrices in applications. Use
matrices to represent and manipulate data, e.g., to represent payoffs or incidence
relationships in a network.
CC.9-12.N.VM.7 (+) Perform operations on matrices and use matrices in applications.
Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a
game are doubled.
CC.9-12.N.VM.8 (+) Perform operations on matrices and use matrices in applications. Add,
subtract, and multiply matrices of appropriate dimensions.
CC.9-12.N.VM.9 (+) Perform operations on matrices and use matrices in applications.
Understand that, unlike multiplication of numbers, matrix multiplication for square
matrices is not a commutative operation, but still satisfies the associative and distributive
properties.
CC.9-12.N.VM.10 (+) Perform operations on matrices and use matrices in applications.
Understand that the zero and identity matrices play a role in matrix addition and
multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a
square matrix is nonzero if and only if the matrix has a multiplicative inverse.
CC.9-12.N.VM.11 (+) Perform operations on matrices and use matrices in applications.
Multiply a vector (regarded as a matrix with one column) by a matrix of suitable
dimensions to produce another vector. Work with matrices as transformations of vectors.
CC.9-12.N.VM.12 (+) Perform operations on matrices and use matrices in applications.
Work with 2 X 2 matrices as transformations of the plane, and interpret the absolute value
of the determinant in terms of area.
CC.9-12.A.SSE.1 Interpret the structure of expressions. Interpret expressions that
represent a quantity in terms of its context.*
CC.9-12.A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients.*
CC.9-12.A.SSE.1b Interpret complicated expressions by viewing one or more of their parts
as a single entity. For example, interpret P(1+r)^n as the product of P and a factor not
depending on P.*
CC.9-12.A.SSE.2 Interpret the structure of expressions. Use the structure of an expression
to identify ways to rewrite it. For example, see x^4 – y^4 as (x^2)^2 – (y^2)^2, thus
recognizing it as a difference of squares that can be factored as (x^2 – y^2)(x^2 + y^2).
CC.9-12.A.SSE.3 Write expressions in equivalent forms to solve problems. Choose and
produce an equivalent form of an expression to reveal and explain properties of the
quantity represented by the expression.*
X
X
X
X
X
X
X
32
Keansburg School District
Curriculum System
Mathematics
9-12
A
SSE.3a
9-12
A
SSE.3b
9-12
A
SSE.3c
9-12
A
SSE.4
9-12
A
APR.1
9-12
A
APR.2
9-12
A
APR.3
9-12
A
APR.4
9-12
A
APR.5
9-12
A
APR.6
9-12
A
APR.7
9-12
A
CED.1
9-12
A
CED.2
CC.9-12.A.SSE.3a Factor a quadratic expression to reveal the zeros of the function it
defines.*
CC.9-12.A.SSE.3b Complete the square in a quadratic expression to reveal the maximum or
minimum value of the function it defines.*
CC.9-12.A.SSE.3c Use the properties of exponents to transform expressions for exponential
functions. For example the expression 1.15^t can be rewritten as [1.15^(1/12)]^(12t) ≈
1.012^(12t) to reveal the approximate equivalent monthly interest rate if the annual rate
is 15%.*
CC.9-12.A.SSE.4 Write expressions in equivalent forms to solve problems. Derive the
formula for the sum of a finite geometric series (when the common ratio is not 1), and use
the formula to solve problems. For example, calculate mortgage payments.*
CC.9-12.A.APR.1 Perform arithmetic operations on polynomials. Understand that
polynomials form a system analogous to the integers, namely, they are closed under the
operations of addition, subtraction, and multiplication; add, subtract, and multiply
polynomials.
CC.9-12.A.APR.2 Understand the relationship between zeros and factors of polynomial.
Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the
remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).
CC.9-12.A.APR.3 Understand the relationship between zeros and factors of polynomials.
Identify zeros of polynomials when suitable factorizations are available, and use the zeros
to construct a rough graph of the function defined by the polynomial.
CC.9-12.A.APR.4 Use polynomial identities to solve problems. Prove polynomial identities
and use them to describe numerical relationships. For example, the polynomial identity
(x^2 + y^2)^2 = (x^2 – y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples.
CC.9-12.A.APR.5 (+) Know and apply the Binomial Theorem for the expansion of (x + y)n in
powers of x and y for a positive integer n, where x and y are any numbers, with coefficients
determined for example by Pascal’s Triangle.1
CC.9-12.A.APR.6 Rewrite rational expressions. Rewrite simple rational expressions in
different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and
r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection,
long division, or, for the more complicated examples, a computer algebra system.
CC.9-12.A.APR.7 (+) Rewrite rational expressions. Understand that rational expressions
form a system analogous to the rational numbers, closed under addition, subtraction,
multiplication, and division by a nonzero rational expression; add, subtract, multiply, and
divide rational expressions.
CC.9-12.A.CED.1 Create equations that describe numbers or relationship. Create equations
and inequalities in one variable and use them to solve problems. Include equations arising
from linear and quadratic functions, and simple rational and exponential functions.*
CC.9-12.A.CED.2 Create equations that describe numbers or relationship. Create equations
X
x
X
X
X
X
X
X
X
X
X
X
33
Keansburg School District
Curriculum System
Mathematics
9-12
A
CED.3
9-12
A
CED.4
9-12
A
REI.1
9-12
A
REI.2
9-12
A
REI.3
9-12
A
REI.4
9-12
A
REI.4a
9-12
A
REI.4b
9-12
A
REI.5
9-12
A
REI.6
9-12
A
REI.7
9-12
A
REI.8
in two or more variables to represent relationships between quantities; graph equations
on coordinate axes with labels and scales.*
CC.9-12.A.CED.3 Create equations that describe numbers or relationship. Represent
constraints by equations or inequalities, and by systems of equations and/or inequalities,
and interpret solutions as viable or non-viable options in a modeling context. For example,
represent inequalities describing nutritional and cost constraints on combinations of
different foods.*
CC.9-12.A.CED.4 Create equations that describe numbers or relationship. Rearrange
formulas to highlight a quantity of interest, using the same reasoning as in solving
equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.*
CC.9-12.A.REI.1 Understand solving equations as a process of reasoning and explain the
reasoning. 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.
CC.9-12.A.REI.2 Understand solving equations as a process of reasoning and explain the
reasoning. Solve simple rational and radical equations in one variable, and give examples
showing how extraneous solutions may arise.
CC.9-12.A.REI.3 Solve equations and inequalities in one variable. Solve linear equations
and inequalities in one variable, including equations with coefficients represented by
letters.
CC.9-12.A.REI.4 Solve equations and inequalities in one variable. Solve quadratic equations
in one variable.
CC.9-12.A.REI.4a Use the method of completing the square to transform any quadratic
equation in x into an equation of the form (x – p)^2 = q that has the same solutions. Derive
the quadratic formula from this form.
CC.9-12.A.REI.4b Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square
roots, completing the square, the quadratic formula and factoring, as appropriate to the
initial form of the equation. Recognize when the quadratic formula gives complex
solutions and write them as a ± bi for real numbers a and b.
CC.9-12.A.REI.5 Solve systems of equations. Prove that, given a system of two equations in
two variables, replacing one equation by the sum of that equation and a multiple of the
other produces a system with the same solutions.
CC.9-12.A.REI.6 Solve systems of equations. Solve systems of linear equations exactly and
approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
CC.9-12.A.REI.7 Solve systems of equations. Solve a simple system consisting of a linear
equation and a quadratic equation in two variables algebraically and graphically. For
example, find the points of intersection between the line y = –3x and the circle x^2 + y^2 =
3.
CC.9-12.A.REI.8 (+) Solve systems of equations. Represent a system of linear equations as a
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
34
Keansburg School District
Curriculum System
Mathematics
9-12
A
REI.9
9-12
A
REI.10
9-12
A
REI.11
9-12
A
REI.12
9-12
F
IF.1
9-12
F
IF.2
9-12
F
IF.3
9-12
F
IF.4
9-12
F
IF.5
single matrix equation in a vector variable.
CC.9-12.A.REI.9 (+) Solve systems of equations. Find the inverse of a matrix if it exists and
use it to solve systems of linear equations (using technology for matrices of dimension 3 ×
3 or greater).
CC.9-12.A.REI.10 Represent and solve equations and inequalities graphically. Understand
that the graph of an equation in two variables is the set of all its solutions plotted in the
coordinate plane, often forming a curve (which could be a line).
CC.9-12.A.REI.11 Represent and solve equations and inequalities graphically. Explain why
the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x)
intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g.,
using technology to graph the functions, make tables of values, or find successive
approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational,
absolute value, exponential, and logarithmic functions.*
CC.9-12.A.REI.12 Represent and solve equations and inequalities graphically. Graph the
solutions to a linear inequality in two variables as a half-plane (excluding the boundary in
the case of a strict inequality), and graph the solution set to a system of linear inequalities
in two variables as the intersection of the corresponding half-planes.
CC.9-12.F.IF.1 Understand the concept of a function and use function notation. Understand
that a function from one set (called the domain) to another set (called the range) assigns to
each element of the domain exactly one element of the range. If f is a function and x is an
element of its domain, then f(x) denotes the output of f corresponding to the input x. The
graph of f is the graph of the equation y = f(x).
CC.9-12.F.IF.2 Understand the concept of a function and use function notation. Use
function notation, evaluate functions for inputs in their domains, and interpret statements
that use function notation in terms of a context.
CC.9-12.F.IF.3 Understand the concept of a function and use function notation. Recognize
that sequences are functions, sometimes defined recursively, whose domain is a subset of
the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1,
f(n+1) = f(n) + f(n-1) for n ≥ 1 (n is greater than or equal to 1).
CC.9-12.F.IF.4 Interpret functions that arise in applications in terms of the context. For a
function that models a relationship between two quantities, interpret key features of
graphs and tables in terms of the quantities, and sketch graphs showing key features given
a verbal description of the relationship. Key features include: intercepts; intervals where
the function is increasing, decreasing, positive, or negative; relative maximums and
minimums; symmetries; end behavior; and periodicity.*
CC.9-12.F.IF.5 Interpret functions that arise in applications in terms of the context. Relate
the domain of a function to its graph and, where applicable, to the quantitative
relationship it describes. For example, if the function h(n) gives the number of personhours it takes to assemble n engines in a factory, then the positive integers would be an
X
X
X
X
X
X
X
x
X
X
X
35
Keansburg School District
Curriculum System
Mathematics
9-12
F
IF.6
9-12
F
IF.7
9-12
F
IF.7a
9-12
F
IF.7b
9-12
F
IF.7c
9-12
F
IF.7d
9-12
F
IF.7e
9-12
F
IF.8
9-12
F
IF.8a
9-12
F
IF.8b
9-12
F
IF.9
9-12
F
BF.1
9-12
F
BF.1a
9-12
F
BF.1b
9-12
F
BF.1c
appropriate domain for the function.*
CC.9-12.F.IF.6 Interpret functions that arise in applications in terms of the context.
Calculate and interpret the average rate of change of a function (presented symbolically or
as a table) over a specified interval. Estimate the rate of change from a graph.*
CC.9-12.F.IF.7 Analyze functions using different representations. Graph functions
expressed symbolically and show key features of the graph, by hand in simple cases and
using technology for more complicated cases.*
CC.9-12.F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and
minima.*
CC.9-12.F.IF.7b Graph square root, cube root, and piecewise-defined functions, including
step functions and absolute value functions.*
CC.9-12.F.IF.7c Graph polynomial functions, identifying zeros when suitable factorizations
are available, and showing end behavior.*
CC.9-12.F.IF.7d (+) Graph rational functions, identifying zeros and asymptotes when
suitable factorizations are available, and showing end behavior.*
CC.9-12.F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end
behavior, and trigonometric functions, showing period, midline, and amplitude.*
CC.9-12.F.IF.8 Analyze functions using different representations. Write a function defined
by an expression in different but equivalent forms to reveal and explain different
properties of the function.
CC.9-12.F.IF.8a Use the process of factoring and completing the square in a quadratic
function to show zeros, extreme values, and symmetry of the graph, and interpret these in
terms of a context.
CC.9-12.F.IF.8b Use the properties of exponents to interpret expressions for exponential
functions. For example, identify percent rate of change in functions such as y = (1.02)^t, y
= (0.97)^t, y = (1.01)^(12t), y = (1.2)^(t/10), and classify them as representing
exponential growth and decay.
CC.9-12.F.IF.9 Analyze functions using different representations. Compare properties of
two functions each represented in a different way (algebraically, graphically, numerically
in tables, or by verbal descriptions). For example, given a graph of one quadratic function
and an algebraic expression for another, say which has the larger maximum.
CC.9-12.F.BF.1 Build a function that models a relationship between two quantities. Write a
function that describes a relationship between two quantities.*
CC.9-12.F.BF.1a Determine an explicit expression, a recursive process, or steps for
calculation from a context.
CC.9-12.F.BF.1b Combine standard function types using arithmetic operations. For
example, build a function that models the temperature of a cooling body by adding a
constant function to a decaying exponential, and relate these functions to the model.
CC.9-12.F.BF.1c (+) Compose functions. For example, if T(y) is the temperature in the
X
X
x
X
X
x
X
X
X
X
X
X
36
Keansburg School District
Curriculum System
Mathematics
9-12
F
BF.2
9-12
F
BF.3
9-12
F
BF.4
9-12
F
BF.4a
9-12
F
BF.4b
9-12
F
BF.4c
9-12
F
BF.4d
9-12
F
BF.5
9-12
F
LE.1
9-12
F
LE.1a
9-12
F
LE.1b
9-12
F
LE.1c
9-12
F
LE.2
9-12
F
LE.3
atmosphere as a function of height, and h(t) is the height of a weather balloon as a function
of time, then T(h(t)) is the temperature at the location of the weather balloon as a function
of time.
CC.9-12.F.BF.2 Build a function that models a relationship between two quantities. Write
arithmetic and geometric sequences both recursively and with an explicit formula, use
them to model situations, and translate between the two forms.*
CC.9-12.F.BF.3 Build new functions from existing functions. Identify the effect on the graph
of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive
and negative); find the value of k given the graphs. Experiment with cases and illustrate an
explanation of the effects on the graph using technology. Include recognizing even and odd
functions from their graphs and algebraic expressions for them.
CC.9-12.F.BF.4 Build new functions from existing functions. Find inverse functions.
CC.9-12.F.BF.4a Solve an equation of the form f(x) = c for a simple function f that has an
inverse and write an expression for the inverse. For example, f(x) =2(x^3) or f(x) =
(x+1)/(x-1) for x ≠ 1 (x not equal to 1).
CC.9-12.F.BF.4b (+) Verify by composition that one function is the inverse of another.
CC.9-12.F.BF.4c (+) Read values of an inverse function from a graph or a table, given that
the function has an inverse.
CC.9-12.F.BF.4d (+) Produce an invertible function from a non-invertible function by
restricting the domain.
CC.9-12.F.BF.5 (+) Build new functions from existing functions. Understand the inverse
relationship between exponents and logarithms and use this relationship to solve
problems involving logarithms and exponents.
CC.9-12.F.LE.1 Construct and compare linear, quadratic, and exponential models and solve
problems. Distinguish between situations that can be modeled with linear functions and
with exponential functions.*
CC.9-12.F.LE.1a Prove that linear functions grow by equal differences over equal intervals
and that exponential functions grow by equal factors over equal intervals.*
CC.9-12.F.LE.1b. Recognize situations in which one quantity changes at a constant rate per
unit interval relative to another.*
CC.9-12.F.LE.1c Recognize situations in which a quantity grows or decays by a constant
percent rate per unit interval relative to another.*
CC.9-12.F.LE.2 Construct and compare linear, quadratic, and exponential models and solve
problems. Construct linear and exponential functions, including arithmetic and geometric
sequences, given a graph, a description of a relationship, or two input-output pairs
(include reading these from a table).*
CC.9-12.F.LE.3 Construct and compare linear, quadratic, and exponential models and solve
problems. Observe using graphs and tables that a quantity increasing exponentially
eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a
X
X
X
X
X
X
X
37
Keansburg School District
Curriculum System
Mathematics
9-12
F
LE.4
9-12
F
LE.5
9-12
F
TF.1
9-12
F
TF.2
9-12
F
TF.3
9-12
F
TF.4
9-12
F
TF.5
9-12
F
TF.6
9-12
F
TF.7
9-12
F
TF.8
9-12
F
TF.9
9-12
G
CO.1
9-12
G
CO.2
polynomial function.*
CC.9-12.F.LE.4 Construct and compare linear, quadratic, and exponential models and solve
problems. For exponential models, express as a logarithm the solution to ab^(ct) = d
where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using
technology.*
CC.9-12.F.LE.5 Interpret expressions for functions in terms of the situation they
model. Interpret the parameters in a linear or exponential function in terms of a context.*
CC.9-12.F.TF.1 Extend the domain of trigonometric functions using the unit circle.
Understand radian measure of an angle as the length of the arc on the unit circle
subtended by the angle.
CC.9-12.F.TF.2 Extend the domain of trigonometric functions using the unit circle. Explain
how the unit circle in the coordinate plane enables the extension of trigonometric
functions to all real numbers, interpreted as radian measures of angles traversed
counterclockwise around the unit circle.
CC.9-12.F.TF.3 (+) Extend the domain of trigonometric functions using the unit circle. Use
special triangles to determine geometrically the values of sine, cosine, tangent for ð/3, ð/4
and ð/6, and use the unit circle to express the values of sine, cosine, and tangent for ð - x, ð
+ x, and 2ð - x in terms of their values for x, where x is any real number.
CC.9-12.F.TF.4 (+) Extend the domain of trigonometric functions using the unit circle. Use
the unit circle to explain symmetry (odd and even) and periodicity of trigonometric
functions.
CC.9-12.F.TF.5 Model periodic phenomena with trigonometric functions. Choose
trigonometric functions to model periodic phenomena with specified amplitude,
frequency, and midline.*
CC.9-12.F.TF.6 (+) Model periodic phenomena with trigonometric functions. Understand
that restricting a trigonometric function to a domain on which it is always increasing or
always decreasing allows its inverse to be constructed.
CC.9-12.F.TF.7 (+) Model periodic phenomena with trigonometric functions. Use inverse
functions to solve trigonometric equations that arise in modeling contexts; evaluate the
solutions using technology, and interpret them in terms of the context.*
CC.9-12.F.TF.8 Prove and apply trigonometric identities. Prove the Pythagorean identity
(sin A)^2 + (cos A)^2 = 1 and use it to find sin A, cos A, or tan A, given sin A, cos A, or tan A,
and the quadrant of the angle.
CC.9-12.F.TF.9 (+) Prove and apply trigonometric identities. Prove the addition and
subtraction formulas for sine, cosine, and tangent and use them to solve problems.
CC.9-12.G.CO.1 Experiment with transformations in the plane. 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 circular arc.
CC.9-12.G.CO.2 Experiment with transformations in the plane. Represent transformations
X
x
X
38
Keansburg School District
Curriculum System
Mathematics
9-12
G
CO.3
9-12
G
CO.4
9-12
G
CO.5
9-12
G
CO.6
9-12
G
CO.7
9-12
G
CO.8
9-12
G
CO.9
9-12
G
CO.10
9-12
G
CO.11
9-12
G
CO.12
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).
CC.9-12.G.CO.3 Experiment with transformations in the plane. Given a rectangle,
parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that
carry it onto itself.
CC.9-12.G.CO.4 Experiment with transformations in the plane. Develop definitions of
rotations, reflections, and translations in terms of angles, circles, perpendicular lines,
parallel lines, and line segments.
CC.9-12.G.CO.5 Experiment with transformations in the plane. 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.
CC.9-12.G.CO.6 Understand congruence in terms of rigid motions. 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.
CC.9-12.G.CO.7 Understand congruence in terms of rigid motions. 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.
CC.9-12.G.CO.8 Understand congruence in terms of rigid motions. Explain how the criteria
for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in
terms of rigid motions.
CC.9-12.G.CO.9 Prove geometric theorems. Prove theorems about lines and angles.
Theorems include: vertical angles are congruent; when a transversal crosses parallel lines,
alternate interior angles are congruent and corresponding angles are congruent; points on
a perpendicular bisector of a line segment are exactly those equidistant from the
segment’s endpoints.
CC.9-12.G.CO.10 Prove geometric theorems. Prove theorems about triangles. Theorems
include: measures of interior angles of a triangle sum to 180 degrees; base angles of
isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle
is parallel to the third side and half the length; the medians of a triangle meet at a point.
CC.9-12.G.CO.11 Prove geometric theorems. Prove theorems about parallelograms.
Theorems include: opposite sides are congruent, opposite angles are congruent, the
diagonals of a parallelogram bisect each other, and conversely, rectangles are
parallelograms with congruent diagonals.
CC.9-12.G.CO.12 Make geometric constructions. Make formal geometric constructions with
a variety of tools and methods (compass and straightedge, string, reflective devices, paper
X
X
X
X
X
X
x
X
X
X
39
Keansburg School District
Curriculum System
Mathematics
9-12
G
CO.13
9-12
G
SRT.1
9-12
G
SRT.2
9-12
G
SRT.3
9-12
G
SRT.4
9-12
G
SRT.5
9-12
G
SRT.6
9-12
G
SRT.7
9-12
G
SRT.8
9-12
G
SRT.9
9-12
G
SRT.10
9-12
G
SRT.11
folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting
a segment; bisecting an angle; constructing perpendicular lines, including the
perpendicular bisector of a line segment; and constructing a line parallel to a given line
through a point not on the line.
CC.9-12.G.CO.13 Make geometric constructions. Construct an equilateral triangle, a
square, and a regular hexagon inscribed in a circle.
CC.9-12.G.SRT.1 Understand similarity in terms of similarity transformations. 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.
CC.9-12.G.SRT.2 Understand similarity in terms of similarity transformations. 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.
CC.9-12.G.SRT.3 Understand similarity in terms of similarity transformations. Use the
properties of similarity transformations to establish the AA criterion for two triangles to
be similar.
CC.9-12.G.SRT.4 Prove theorems involving similarity. Prove theorems about triangles.
Theorems include: a line parallel to one side of a triangle divides the other two
proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
CC.9-12.G.SRT.5 Prove theorems involving similarity. Use congruence and similarity
criteria for triangles to solve problems and to prove relationships in geometric figures.
CC.9-12.G.SRT.6 Define trigonometric ratios and solve problems involving 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.
CC.9-12.G.SRT.7 Define trigonometric ratios and solve problems involving right triangles.
Explain and use the relationship between the sine and cosine of complementary angles.
CC.9-12.G.SRT.8 Define trigonometric ratios and solve problems involving right triangles.
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied
problems.
CC.9-12.G.SRT.9 (+) Apply trigonometry to general triangles. Derive the formula A =
(1/2)ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex
perpendicular to the opposite side.
CC.9-12.G.SRT.10 (+) Apply trigonometry to general triangles. Prove the Laws of Sines and
Cosines and use them to solve problems.
CC.9-12.G.SRT.11 (+) Apply trigonometry to general triangles. Understand and apply the
X
X
X
X
X
X
X
X
X
X
X
40
Keansburg School District
Curriculum System
Mathematics
9-12
G
C.1
9-12
G
C.2
9-12
G
C.3
9-12
G
C.4
9-12
G
C.5
9-12
G
GPE.1
9-12
G
GPE.2
9-12
G
GPE.3
9-12
G
GPE.4
9-12
G
GPE.5
9-12
G
GPE.6
9-12
G
GPE.7
Law of Sines and the Law of Cosines to find unknown measurements in right and non-right
triangles (e.g., surveying problems, resultant forces).
CC.9-12.G.C.1 Understand and apply theorems about circles. Prove that all circles are
similar.
CC.9-12.G.C.2 Understand and apply theorems about circles. Identify and describe
relationships among inscribed angles, radii, and chords. Include the relationship between
central, inscribed, and circumscribed angles; inscribed angles on a diameter are right
angles; the radius of a circle is perpendicular to the tangent where the radius intersects
the circle.
CC.9-12.G.C.3 Understand and apply theorems about circles. Construct the inscribed and
circumscribed circles of a triangle, and prove properties of angles for a quadrilateral
inscribed in a circle.
CC.9-12.G.C.4 (+) Understand and apply theorems about circles. Construct a tangent line
from a point outside a given circle to the circle.
CC.9-12.G.C.5 Find arc lengths and areas of sectors of circles. 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.
CC.9-12.G.GPE.1 Translate between the geometric description and the equation for a conic
section. 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.
CC.9-12.G.GPE.2 Translate between the geometric description and the equation for a conic
section. Derive the equation of a parabola given a focus and directrix.
CC.9-12.G.GPE.3 (+) Translate between the geometric description and the equation for a
conic section. Derive the equations of ellipses and hyperbolas given the foci, using the fact
that the sum or difference of distances from the foci is constant.
CC.9-12.G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. For
example, prove or disprove that a figure defined by four given points in the coordinate
plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at
the origin and containing the point (0, 2).
CC.9-12.G.GPE.5 Use coordinates to prove simple geometric theorems algebraically. 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).
CC.9-12.G.GPE.6 Use coordinates to prove simple geometric theorems algebraically. Find
the point on a directed line segment between two given points that partitions the segment
in a given ratio.
CC.9-12.G.GPE.7 Use coordinates to prove simple geometric theorems algebraically. Use
X
X
X
X
X
X
X
X
X
X
X
X
41
Keansburg School District
Curriculum System
Mathematics
9-12
G
GMD.1
9-12
G
GMD.2
9-12
G
GMD.3
9-12
G
GMD.4
9-12
G
MG.1
9-12
G
MG.2
9-12
G
MG.3
9-12
S
ID.1
9-12
S
ID.2
9-12
S
ID.3
9-12
S
ID.4
coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g.,
using the distance formula.*
CC.9-12.G.GMD.1 Explain volume formulas and use them to solve problems. Give an
informal argument for the formulas for the circumference of a circle, area of a circle,
volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle,
and informal limit arguments.
CC.9-12.G.GMD.2 (+) Explain volume formulas and use them to solve problems. Give an
informal argument using Cavalieri’s principle for the formulas for the volume of a sphere
and other solid figures.
CC.9-12.G.GMD.3 Explain volume formulas and use them to solve problems. Use volume
formulas for cylinders, pyramids, cones, and spheres to solve problems.*
CC.9-12.G.GMD.4 Visualize relationships between two-dimensional and three-dimensional
objects. Identify the shapes of two-dimensional cross-sections of three-dimensional
objects, and identify three-dimensional objects generated by rotations of two-dimensional
objects.
CC.9-12.G.MG.1 Apply geometric concepts in modeling situations. Use geometric shapes,
their measures, and their properties to describe objects (e.g., modeling a tree trunk or a
human torso as a cylinder).*
CC.9-12.G.MG.2 Apply geometric concepts in modeling situations. Apply concepts of
density based on area and volume in modeling situations (e.g., persons per square mile,
BTUs per cubic foot).*
CC.9-12.G.MG.3 Apply geometric concepts in modeling situations. Apply geometric
methods to solve design problems (e.g., designing an object or structure to satisfy physical
constraints or minimize cost; working with typographic grid systems based on ratios).*
CC.9-12.S.ID.1 Summarize, represent, and interpret data on a single count or measurement
variable. Represent data with plots on the real number line (dot plots, histograms, and box
plots).*
CC.9-12.S.ID.2 Summarize, represent, and interpret data on a single count or measurement
variable. Use statistics appropriate to the shape of the data distribution to compare center
(median, mean) and spread (interquartile range, standard deviation) of two or more
different data sets.*
CC.9-12.S.ID.3 Summarize, represent, and interpret data on a single count or measurement
variable. Interpret differences in shape, center, and spread in the context of the data sets,
accounting for possible effects of extreme data points (outliers).*
CC.9-12.S.ID.4 Summarize, represent, and interpret data on a single count or measurement
variable. Use the mean and standard deviation of a data set to fit it to a normal distribution
and to estimate population percentages. Recognize that there are data sets for which such
a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas
under the normal curve.*
X
X
X
X
X
X
X
42
Keansburg School District
Curriculum System
Mathematics
9-12
S
ID.5
9-12
S
ID.6
9-12
S
ID.6a
9-12
9-12
S
S
ID.6b
ID.6c
9-12
S
ID.7
9-12
S
ID.8
9-12
S
ID.9
9-12
S
IC.1
9-12
S
IC.2
9-12
S
IC.3
9-12
S
IC.4
9-12
S
IC.5
9-12
S
IC.6
CC.9-12.S.ID.5 Summarize, represent, and interpret data on two categorical and
quantitative variables. Summarize categorical data for two categories in two-way
frequency tables. Interpret relative frequencies in the context of the data (including joint,
marginal, and conditional relative frequencies). Recognize possible associations and
trends in the data.*
CC.9-12.S.ID.6 Summarize, represent, and interpret data on two categorical and
quantitative variables. Represent data on two quantitative variables on a scatter plot, and
describe how the variables are related.*
CC.9-12.S.ID.6a Fit a function to the data; use functions fitted to data to solve problems in
the context of the data. Use given functions or choose a function suggested by the context.
Emphasize linear, quadratic, and exponential models.*
CC.9-12.S.ID.6b Informally assess the fit of a function by plotting and analyzing residuals.*
CC.9-12.S.ID.6c Fit a linear function for a scatter plot that suggests a linear association.*
CC.9-12.S.ID.7 Interpret linear models. Interpret the slope (rate of change) and the
intercept (constant term) of a linear model in the context of the data.*
CC.9-12.S.ID.8 Interpret linear models. Compute (using technology) and interpret the
correlation coefficient of a linear fit.*
CC.9-12.S.ID.9 Interpret linear models. Distinguish between correlation and causation.*
CC.9-12.S.IC.1 Understand and evaluate random processes underlying statistical
experiments. Understand statistics as a process for making inferences about population
parameters based on a random sample from that population.*
CC.9-12.S.IC.2 Understand and evaluate random processes underlying statistical
experiments. Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. For example, a model says a spinning coin falls
heads up with probability 0. 5. Would a result of 5 tails in a row cause you to question the
model?*
CC.9-12.S.IC.3 Make inferences and justify conclusions from sample surveys, experiments,
and observational studies. Recognize the purposes of and differences among sample
surveys, experiments, and observational studies; explain how randomization relates to
each.*
CC.9-12.S.IC.4 Make inferences and justify conclusions from sample surveys, experiments,
and observational studies. Use data from a sample survey to estimate a population mean
or proportion; develop a margin of error through the use of simulation models for random
sampling.*
CC.9-12.S.IC.5 Make inferences and justify conclusions from sample surveys, experiments,
and observational studies. Use data from a randomized experiment to compare two
treatments; use simulations to decide if differences between parameters are significant.*
CC.9-12.S.IC.6 Make inferences and justify conclusions from sample surveys, experiments,
and observational studies. Evaluate reports based on data.*
X
43
Keansburg School District
Curriculum System
Mathematics
9-12
S
X
CP.1
9-12
S
CP.2
9-12
S
CP.3
9-12
S
CP.4
9-12
S
CP.5
9-12
S
CP.6
9-12
S
CP.7
9-12
S
CP.8
9-12
S
CP.9
9-12
S
MD.1
CC.9-12.S.CP.2 Understand independence and conditional probability and use them to
interpret data. Understand that two events A and B are independent if the probability of A
and B occurring together is the product of their probabilities, and use this characterization
to determine if they are independent.*
CC.9-12.S.CP.3 Understand independence and conditional probability and use them to
interpret data. Understand the conditional probability of A given B as P(A and B)/P(B),
and interpret independence of A and B as saying that the conditional probability of A given
B is the same as the probability of A, and the conditional probability of B given A is the
same as the probability of B.*
CC.9-12.S.CP.4 Understand independence and conditional probability and use them to
interpret data. Construct and interpret two-way frequency tables of data when two
categories are associated with each object being classified. Use the two-way table as a
sample space to decide if events are independent and to approximate conditional
probabilities. For example, collect data from a random sample of students in your school
on their favorite subject among math, science, and English. Estimate the probability that a
randomly selected student from your school will favor science given that the student is in
tenth grade. Do the same for other subjects and compare the results.*
CC.9-12.S.CP.5 Understand independence and conditional probability and use them to
interpret data. Recognize and explain the concepts of conditional probability and
independence in everyday language and everyday situations. For example, compare the
chance of having lung cancer if you are a smoker with the chance of being a smoker if you
have lung cancer.*
CC.9-12.S.CP.6 Use the rules of probability to compute probabilities of compound events in
a uniform probability model. Find the conditional probability of A given B as the fraction of
B’s outcomes that also belong to A, and interpret the answer in terms of the model.*
CC.9-12.S.CP.7 Use the rules of probability to compute probabilities of compound events in
a uniform probability model. 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.*
CC.9-12.S.CP.8 (+) Use the rules of probability to compute probabilities of compound
events in a uniform probability model. Apply the general Multiplication Rule in a uniform
probability model, P(A and B) = [P(A)]x[P(B|A)] =[P(B)]x[P(A|B)], and interpret the
answer in terms of the model.*
CC.9-12.S.CP.9 (+) Use the rules of probability to compute probabilities of compound
events in a uniform probability model. Use permutations and combinations to compute
probabilities of compound events and solve problems.*
CC.9-12.S.MD.1 (+) Calculate expected values and use them to solve problems. Define a
random variable for a quantity of interest by assigning a numerical value to each event in a
sample space; graph the corresponding probability distribution using the same graphical
X
X
X
x
X
X
X
X
X
X
X
X
X
X
44
Keansburg School District
Curriculum System
Mathematics
9-12
S
MD.2
9-12
S
MD.3
9-12
S
MD.4
9-12
S
MD.5
9-12
S
MD.5a
9-12
S
MD.5b
9-12
S
MD.6
9-12
S
MD.7
displays as for data distributions.*
CC.9-12.S.MD.2 (+) Calculate expected values and use them to solve problems. Calculate
the expected value of a random variable; interpret it as the mean of the probability
distribution.*
CC.9-12.S.MD.3 (+) Calculate expected values and use them to solve problems. Develop a
probability distribution for a random variable defined for a sample space in which
theoretical probabilities can be calculated; find the expected value. For example, find the
theoretical probability distribution for the number of correct answers obtained by
guessing on all five questions of a multiple-choice test where each question has four
choices, and find the expected grade under various grading schemes.*
CC.9-12.S.MD.4 (+) Calculate expected values and use them to solve problems. Develop a
probability distribution for a random variable defined for a sample space in which
probabilities are assigned empirically; find the expected value. For example, find a current
data distribution on the number of TV sets per household in the United States, and
calculate the expected number of sets per household. How many TV sets would you expect
to find in 100 randomly selected households?*
CC.9-12.S.MD.5 (+) Use probability to evaluate outcomes of decisions. Weigh the possible
outcomes of a decision by assigning probabilities to payoff values and finding expected
values.*
CC.9-12.S.MD.5a (+) Find the expected payoff for a game of chance. For example, find the
expected winnings from a state lottery ticket or a game at a fast-food restaurant.*
CC.9-12.S.MD.5b (+) Evaluate and compare strategies on the basis of expected values. For
example, compare a high-deductible versus a low-deductible automobile insurance policy
using various, but reasonable, chances of having a minor or a major accident.*
CC.9-12.S.MD.6 (+) Use probability to evaluate outcomes of decisions. Use probabilities to
make fair decisions (e.g., drawing by lots, using a random number generator).*
CC.9-12.S.MD.7 (+) Use probability to evaluate outcomes of decisions. Analyze decisions
and strategies using probability concepts (e.g., product testing, medical testing, pulling a
hockey goalie at the end of a game).*
45
Keansburg School District
Curriculum System
Mathematics
46