North Carolina High School Mathematics Alignment to Traditional Text
MATH III
Standard
N.RN.3
Math III Concept (s)



N.Q.1




N.Q.2

N.Q.3
N-CN.1
N.CN.2



N.CN.7

N.CN.9 (+)

A.SSE.1a

A.SSE.1b

09/10/13
Sum or product of two rational numbers
is rational
Sum of rational and irrational numbers
is irrational
Product of a nonzero and irrational
number is irrational
Use units to understand problems and
guide solutions
Choose units appropriately
Interpret units in context
Choose and interpret the scale and the
origin in graphs and data displays
Define appropriate quantities for
descriptive modeling
Chose a level of accuracy within context
Know and represent complex numbers
Add, subtract, and multiply complex
numbers
Solve quadratics that have complex
solutions
Know the Fundamental Theorem of
Algebra and show it’s true for quadratic
polynomials
Interpret parts of an expression
Traditional Alignment
* Supplement
Geo textbook
 Finding perimeter, area, and volume of
geometric figures
* Supplement
*Supplement
*Supplement
Alg II textbook
Alg II textbook
Alg II textbook
Alg II textbook
Alg I textbook
 Only linear and exponential
*Supplement other functions
* Supplement
Interpret the meaning of grouped
together parts of an expression as single
entity
1
A.SSE.2

A.SSE.3b

A.SSE.4


A-APR.1

A.APR.2

A.APR.3


A.APR.4

A.APR.6

A.APR.7 (+)

A.CED.1

A.CED.2

A.CED.3

Alg I and Alg II text
 Foundations in Alg II and advanced
problems in Alg II
Alg I and Alg II textbooks
Produce equivalent forms of
 Foundations in Alg I and advanced
expressions to reveal key features
problems in Alg II
Complete the square to reveal vertex
Derive the formula for a finite geometric Alg II textbook
series and use the formula to solve
problems
Add, subtract, and multiply polynomials Alg I and Alg II textbooks
 Foundations in Alg I and advanced
problems in Alg II
Alg II textbook
Know and apply the Remainder
Theorem
Alg II textbook
Identify zeros of polynomials from
factored forms
 Only factoring to reveal zeros
Use zeros to construct rough graph
* Supplement constructing rough graphs
* Supplement
Prove polynomial identities and use
them to describe numerical
relationships
Rewrite rational expressions using long Alg II textbook
division, synthetic division, or
technology
Alg II textbook
Perform operations with rational
expressions and understand properties
Alg I and Alg II textbooks
Create and solve equations and
 Foundations in Alg 1 and advanced in Alg
inequalities with one variable
II
Create and graph equations with two or Alg I, Alg II, and Geo textbooks
more variables
 Foundations in Alg 1 and advanced in Alg
II, trig in Geo
Alg I and Alg II textbooks
Represent constraints by equations or
 Only linear systems
inequalities and by systems of equations
and/or inequalities
Rewriting expressions by combining
like terms, expanding, and factoring
2
North Carolina High School Mathematics Alignment to Traditional Text
MATH III
A.CED.4
A.REI.1



A.REI.2



A.REI.4.a


A.REI.4.b
A.REI.10


A.REI.11

F.IF.2
F.IF.4



Interpret solutions
Rearrange formulas
Construct an argument for solving
simple equations
Solve rational equations with one
variable
Solve radical equations with one
variable
Show how extraneous solutions may
arise
Complete the square to write quadratics
in vertex form
Derive the quadratic formula by
completing the square
Solve quadratics in all ways
Graph of an equation represents all the
solutions
Solving systems using function notation
Use, evaluate, and interpret statements
written in function notation
Interpret key features of graphs and
tables
Given verbal description, sketch graphs
*Supplement for all other functions
Alg I and Alg II textbooks
Alg I and Alg II textbooks
Alg I and Alg II textbooks
 Foundations to solving are in Alg I and
advanced solving is in Alg II
Alg II textbook
Alg I and Alg II textbooks
Alg I and Alg II textbooks
Alg I and Alg II textbooks
 Concepts
* Must supplement for all types of functions
Alg I and Alg II textbooks
* Supplement interpreting the rules and
numbers
Alg I and Alg II
 Foundations in Alg 1 and advanced in Alg
II
* Supplement identifying key features of a graph
within context
09/10/13
3
F.IF.5

F.IF.7c

F.IF.7e

F.IF.8a

F.IF.9

F.BF.1a

F.BF.1b

F.BF.2

F.BF.3

F.BF.4a

F.LE.3

F.LE.4

F.TF.1

F.TF.2

F.TF.5

Relate the domain of a function to its
graph
Graph polynomial functions, identifying
zeros and showing end behavior
Graph functions expressed symbolically
and show key features
Use factoring and completing the square
to show key features
Compare properties of two functions
expressed in different ways
Given context, write a function using an
explicit expression, a recursive process,
or showing steps for calculations
Combine standard functions using
arithmetic operation
Model situations to write arithmetic and
geometric sequences both recursively
and explicitly
Identify the effects of algebraic
transformations to include translations,
reflections, and dilations
Solve for f(x) = c and find the inverse of
the function
Understanding that a quantity
increasing exponentially will eventually
exceed all others
For exponential models, express as a
logarithm and evaluate
Understand radian measure of an angle
as the length of the arc on the unit circle
Explain how the unit circle enables the
extension of trig functions, interpreted
as radian measures of angles
Choose trig functions to model periodic
phenomena with specified amplitude,
Alg I and Alg II textbook
* Supplement
Alg I and Alg II textbook
Alg I and Alg II textbook
* Supplement comparison of different forms
Geo and Alg II textbooks
*Supplement recursive process
Alg II textbook
Geo and Alg II textbooks
*Supplement for informal recursive
Alg II textbook
Alg II textbook
*Supplement
Alg II textbook
Alg II textbook
Alg II textbook
* Supplement radian measures
Alg II textbook
4
North Carolina High School Mathematics Alignment to Traditional Text
MATH III
F.TF.8

G.CO.1

G.CO.9
G.CO.10
G.CO.11
G.CO.12




G.SRT.2


G.SRT.3

G.SRT.4
G.SRT.5


G.C.1
G.C.2


G.C.3


G.C.5


09/10/13
frequency, and midline
Prove the Pythagorean identity sin2(θ) +
cos2(θ) =1 and use it to find trig ratios
Define angle, circle, perpendicular line,
parallel line, and line segment
Prove theorems about lines and angles
Prove theorems about triangles
Prove theorems about parallelograms
Make formal geometric constructions
with a variety of tools and methods
Define similarity by using geometric
transformations
Explain using similarity transformations
the meaning of similarity for triangles
Establish the AA criterion for two
triangles to be similar
Prove theorems about triangles
Use congruence and similarity criteria
for triangles to solve problems and to
prove relationships
Prove all circles are similar
Relationships among inscribed angles,
radii, and chords
Construct the inscribed and
circumscribed circles of a triangle
Prove properties of angles for a
quadrilateral inscribed in a circle
Derive using similarity that the length of
the arc intercepted is proportional to
the radius
Define the radian measure of the angle
* Supplement
Alg I and Geo textooks
Geo textbook
Geo textbook
Geo textbook
*Supplement
Geo textbook
Geo textbook
Geo textbook
Geo textbook
* Supplement
Geo textbook
* Supplement
Geo textbook
*Supplement deriving on their own and defining
radian measure
5

G.GPE.1


G.GPE.2

G.MG.3

S.ID.4

S.IC.1


S.IC.3

S.IC.4

S.IC.5



S.IC.6
S.MD.6 (+)
S.MD.7 (+)



as the constant of proportionality
Derive the formula for the area of a
sector
Derive equation of a circle from
Pythagorean Theorem
Complete the square to find the center
and radius of circle
Derive the equation of a parabola give a
focus and directrix
Apply geometric methods to solve
design problems
Use mean and standard deviation to
analyze and estimate
Estimate areas under the normal curves
Process for make inferences about
populations based on random samples
Purposes of and differences among
sample surveys, experiments, and
observational studies and explain how
randomization relates to each
Use data from a sample survey to
estimate a population mean or
proportion
Develop a margin of error
Use data from a randomized experiment
to compare
Use simulations to decide if differences
are significant
Evaluate reports based on data
Use probabilities to make fair decisions
Analyze decisions and strategies using
probability concepts
Alg II textbook
 Only completing the square
* Supplement deriving equation of circle
* Supplement
* Supplement
* Supplement
* Supplement
* Supplement
* Supplement
* Supplement
* Supplement
* Supplement
* Supplement
6