Connecticut Common Core State Standards
Mathematics
Vertical Alignment, Grades 6-12
2013-2014
Connecticut State Defined Units of study grades 6-12
Ratio and Proportion
6th
 Ratios and Rates
The Number System


Operating with Positive
and Rational Numbers
Understanding Integers
7th

Proportional
Relationships

Add, Subtract, Multiply
and Divide with
Rational numbers
8th
 Algebraic Connections

Algebra 1




Using Expressions and
Equations
Algebraic Reasoning


Operating with Rational
Numbers
Algebraic Reasoning



Introduction to
Exponential Functions
Quadratic Functions
and Equations
 Linear Equations and
Inequalities
 Systems of Linear
Equations
 Introduction to
Exponential Functions
 Quadratic Functions and
Equations

Applications of
Geometry

2 and 3 dimensional
Geometry



Pythagorean Theorem
Congruence and
Similarity
Volume



Statistics and Distribution


Functions
Inferences about
Populations
Probability

Functions and Inverse
Functions
Polynomial Functions
Rational Expressions and
Functions
Trigonometric Functions
Exponential and Logarithmic
Functions




Polynomial Functions




Statistics and Probability

Real Numbers
Linear Relationships
Systems of Linear
Relationships
Algebra
Geometry
Algebra 2
Real Numbers
Number and Quantity
Expressions and Equations
Geometry

Patterns in Data

Scatterplots and Trend
lines

Systems of Linear
Relationships




Patterns
Functions
Linear Functions
Scatterplots and Trend
lines
Introduction to
Exponential Functions
Quadratic Functions
and Equations



Transformations in the
coordinate plane
Congruence, Proof and
Constructions
Polygons
Similarity, Proof and
Trigonometry
Circles and Other Conic
Sections
Extend to Three
Dimensions
Applications of
Probability

Inferential Statistics

Functions and Inverse
Functions
Polynomial Functions
Rational Expressions and
Functions
Trigonometric Functions
Exponential and Logarithmic
Functions




The Number System
Darien’s Math Benchmarks for 6-12
based on Connecticut Common Core State Standards
6th
o division of fractions
o multi-digit decimals
o problems
o models
o equations
o standard algorithm
o rational numbers
o integers
o opposites
o absolute value
o absolute value as
magnitude
o order for rational
numbers in realworld contexts
o number line
diagrams
o relative position of
two numbers on a
number line
diagram
o distance from 0 on
the number line
o coordinate plane
o quadrants
o ordered
pairs/coordinates
o reflections
7th
o Operations, begin with
integers and extend to
rational number
o Number Line
o Equivalent Forms of
numbers and expresions
o Distributive Property
o Additive Inverses
o Absolute Value
o Properties of Operations
o Mental Computation
Strategies
o Estimation Strategies
o Terminating and
Repeating decimals
8th
o
o
o
o
o
o
o
o
o
Rational number
Irrational number
Decimal expansion
Integer power of 10
o Scientific notation
Properties of integer
exponents
Square root
Perfect square
Cube root
Perfect cube
Algebra 1
o Laws of Exponents
o Sequences and patterns
o Radicals and rational
exponents
Geometry
Algebra 2
o Complex numbers
o Properties of exponents
Ratios and Proportional Relationships
6th
o ratios and rates
o tables of
equivalent ratios
o missing values in
tables
o tape diagrams
o double number line
diagrams
o equations
o pairs of values on a
coordinate plane
o unit rate
o unit pricing
o constant speed
o percent
o a quantity as a rate
per 100
o finding the whole,
given a part and
the percent
o measurement units
7th
 Proportional relationships
 Equivalent ratios
o In a table
o Straight line
through the origin
when graphing
on a coordinate
plane
o Equation
 Constant of
proportionality (unit rate)
o Tables
o Graphs
o Equations
o Diagrams
o Verbal
descriptions
 Point (x,y) in terms of
situation
o (0, 0)
o (1, r) where r is the
unit rate
 Multi-step problems
o Ratio
o Percent
 Scale drawings
o Scale
o Actual lengths
and areas
8th




Proportional relationships
Unit rate
Slope (m)
Algebraic connections
Algebra 1
o Rate of change
o Constant additive
change
o Slope
o Graphs and Table
Geometry
o Segment ratios
o Slopes of ∥ 𝑎𝑛𝑑 ⊥ lines
o Trigonometric ratios
Algebra 2
o Trigonometric ratios
Statistics and Probability
6th
o Measure of center
o Median
o Mean
o Measure of
variation
o Range
o Interquartile
range
o Mean
absolute
deviation
o Numerical data
sets
o Observation
s
o Attributes
o Overall
pattern
o Deviations from
o Choice of
measures of center
and variability
o Shape of the data
distribution
o Center
o Spread
o Variability
o Statistical question
o Numerical data
displays
o Number line
o Dot plot
o Histogram
o Box plot
7th
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
statistics
population
representative
sample
representative/valid
random
measures of center
measures of variability
inferences
informal comparative
data
variation
data distribution
variability
center
mean absolute deviation
Probability model
o Uniform/not
uniform
probabilities
events
o compound
frequencies
outcomes
data
chance
process
event
Probability of a chance
event
Relative frequency
Organized list
Tables
Tree diagram
Simulation
Sample space
8th
o Frequencies
o Two-way table
o Scatter Plots
 Clustering
 Outliers
 Equation of Linear
Model
 Line of best fit
 Linear pattern
 Nonlinear pattern
Algebra 1
o Measures of central
tendency (mean,
median, mode)
o Measures of spread
(range, interquartile
range, standard
deviation)
o Shape of distribution
o Outlier
o Histogram
o Box plot
o Scatter plot
o Trend line
o Line of best fit
o Correlation
o Correlation coefficient
o Causation
o Interpolation
o Extrapolation
*Use of technology,
calculators, tables, graphs
Geometry
o events
o subsets
o sample space
o unions
o intersections
o complements
o conditional probability
o independent events
o conditional probability
o Frequency table
Algebra 2
o Mean and standard
deviation
o Normal distribution
o Population percentages
o Normal Approximation
o Area under normal curve
o Inference
o Population parameters
o Random samples
o Sample survey data
o Population mean /
proportion
o Margin of error
o Simulation models
o Random sampling
o Randomized experiment
data
o Two treatments
o Simulations
o Significant differences in
parameters
*Use of technology,
calculators, spreadsheets,
tables, graphs
Geometry
6th
o Volume of
rectangular prisms
o Area of triangles
o Area of
quadrilaterals
o Area of compound
shapes
o Nets and Surface
area
o Area of polygons
o triangles
o special
quadrilater
als
o Problems
o with and without
context
o FIND/DETERMINE
area of polygons
o COMPOSE (into
rectangles)
o DECOMPOSE (into
triangles and other
shapes)
7th
 Area of circle
 Circumference of circle
 Geometric conditions
(points, line segments,
angles, parallelism,
congruence, and
perpendicularity.)
 Plane sections of threedimensional figures
 Angle relationships
o Supplementary
o Complementary
o Vertical
o Adjacent
 Area
o Triangles
o Quadrilaterals
o Polygons
 Volume
o Cubes
o Right prisms
 Surface Area
o Cubes
o Right prisms
 Pythagorean Theorem
 Proof of and its converse
 Right triangles
 Coordinate system
 DETERMINE (unknown
side lengths in right
triangles)
 FIND (distance between
two points in a
coordinate system)
 Transformations
 Congruence
 Similarity (AA)
 Informal proof
 Triangle int/ext angle sum
 Parallel lines cut by a
transversal
8th
o
o
o
o
o
Algebra 1
Formulas (volume)
Cones
Cylinders
Spheres
Similar Triangles
Geometry
o Similarity and
Congruence
o Transformations
o Triangle Theorems
o Quadrilateral Theorems
o Pythagorean Theorem
 Eq of a circle
o Circle Geometry
 equation of circle
● length of the arc
intercepted by an
angle is proportional
to the radius
● the radian measure
of the angle
 area of a sector
 Area/Circumference
o Area &Perimeter
o Distance, midpoint
o Geometric Constructions
o Centers of triangles
o Volume
 Cylinders
 Pyramids
 Cones
 Spheres
*Use of technology, and nontechnology…use tools
strategically
Algebra 2
o Special right Triangles
 Trig ratios
o Pythagorean Identity
o Transformations of
Functions f(x)+k, f(x+h)…
6th
Expressions and Equations/Algebra
o
o
o
o
o
o
o
o
o
o
o
o
o
Expressions
mathematical
terms
o sum
o term
o product
o factor
o quotient
o coefficient
Order of
Operations
properties of
operations
equivalent
expressions
problems
equations
Variable
Two quantities that
change in
relationship to one
another
o Dependent
variable
o Independe
nt variable
Expression
Equation
Graph
Table
7th
8th
Variables
Simple equations
o form px + q = r
and p(x + q) = r,
where p, q, and r
are specific
rational numbers
o Simple Inequalities
o form px + q > r or
px + q < r, where
p, q, and r are
specific rational
numbers.
o Algebraic solution
o Arithmetic solution
o Solution set of an
inequality
o Properties of operations
o Linear expressions
o Rational coefficients
o Expressions in different
forms
Quantities in a problem are
related
o
o
o
o
Algebra 1
Linear Equations
(Simultaneous/system of)
 Rational Number
Coefficients
 One variable
 One solution
 Many solutions
 No solutions
Simplify equations and
expressions
 Expanding
 Distributive Property
 Combining Like Terms
 Factor
o
o
o
o
o
o
o
o
o
o
o
o
o
o
Order of operations
Expression vs. equation
Inequality
Associative property
Commutative property
Distributive property
Inverse operation
Systems of linear
equations
Quadratic Equation
Quadratic Formula
Square Root Property
Zero Product Property
Completing the Square
Literal equations Rate of
change
Geometry
o
o
Complete the Square
Derive formula for
Parabola
 Focus
 Directrix
**Include algebra
throughout curriculum
Algebra 2
o Solve quadratic
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
equations and
inequalities
Complex solutions
Real solutions
Discriminant
Complete the square
Quadratic Formula
Rational equations (leads
to linear or quadratic
equation)
Extraneous solution
examples
Polynomial functions
Zeros of polynomials
Factoring
Equivalent forms of
expression
Binomial Expansion
Exponential and
logarithmic equations
Sum of finite geometric
series
Systems of non-linear
equations
Inverse functions
Trigonometry
 Unit Circle, radian
measure
 Extension of trig
functions to all Reals
 Radian measure;
counterclockwise
motion about unit
circle
Functions
6th
7th
8th
 Y-intercept (b)
 Linear equations (y = mx
and y = mx + b)
o One variable
 One solution
 Infinitely many
solutions
 No solutions
 Functions
o Properties
 Linear
 Non-linear
o Input/Output
o Ordered pairs
 Linear/functional
relationship
 rate of change
 initial value (function)
 table
 graph
o Rate of change
o Initial value (of a linear
function)
o Representation
 Algebraically
 Graphically
 Numerically in table s
 Verbal description
Algebra 1
o Sequence and patterns
 Recursive rule
 Explicit rule
 Arithmetic
 Geometric
 Rate of change
o Independent variable
o Dependent variable
o Function notation
o Domain & Range
o Vertical Line test
o Linear Functions
o slope-intercept
form
o point-slope form
o standard form
o System of Eq
o Piecewise linear function
o Graph square and cube
root
o Exponential Function
 Growth/ Decay
 Asymptote
o Quadratic Function
o Parabola
o Factored form
o Vertex form
o Standard form
o Vertex
o Line of Symmetry
● Key Features
o Intercepts
o Intervals
o inc/dec,pos/neg
*Rule of 4: Represent graph,
table, context, algebra
Use of technology,
calculators, tables, graphs
Geometry
Algebra 2
o Graph functions
 Square and cube
root
 Piecewise-defined
(includes step and
absolute value)
 Polynomial
 y = 1/x, y = 1/x2
 Trig (sin, cos, tan)
 Exponential
 Logarithmic
 Inverse Function
o Composition of functions
● Key Features
o Intercepts
o intervals
 increasing or
decreasing,
 positive or
negative
o relative maximums
and minimums
o symmetries
o end behavior /
endpoints
o periodicity
o midline
o amplitude
*Rule of 4: Represent graph,
table, context, algebra
Use of technology,
calculators, tables, graphs