Download State, ACT, and Common Core Standards Alignment

State, ACT, and Common Core Standards Alignment
Standards to Use for Common Benchmark Assessment Development
Tennessee Standards
ACT Standards
Common Core Standards
Tennessee Standards
Standard 1 –
Mathematical
Processes
Course Level Expectations:
CLE 3102.1.1 Use mathematical
language, symbols, definitions,
proofs and counterexamples
correctly
and precisely in mathematical
reasoning.
CLE 3102.1.2 Apply and adapt a
variety of
appropriate
strategies to problem solving,
including testing
cases, estimation, and then
checking induced errors and the
reasonableness of the
solution.
CLE 3102.1.3 Develop inductive
and deductive reasoning to
independently make and evaluate
mathematical arguments and
construct appropriate proofs;
include various types of
reasoning, logic, and intuition.
CLE 3102.1.4 Move flexibly
between
multiple
representations (contextual,
physical, written, verbal,
iconic/pictorial, graphical, tabular,
and symbolic), to solve problems,
to model
mathematical ideas, and to
communicate solution strategies.
CLE 3102.1.5 Recognize and use
mathematical ideas and processes
that arise in different settings, with
an emphasis on formulating a
problem in mathematical terms,
interpreting the solutions,
mathematical ideas, and
communication of solution
strategies.
CLE 3102.1.6 Employ reading and
writing to recognize the major
themes of mathematical processes,
the historical development of
mathematics, and the connections
ACT Standards
Common Core Standards
Draw conclusions
based on number
concepts, algebraic
properties, and/or
relationships

between
expressions and
numbers.
Perform
straightforward
word-to-symbol
translations

Students who score
in the 1–12 range
are most likely
beginning to
develop the
knowledge and
skills
assessed in the 
other score ranges.
Draw conclusions

based on number
concepts, algebraic
properties, and/or
o
relationships
between
expressions and
numbers
Interpret and use
information from o
figures, tables, and
graphs
Understand solving
equations as a
process of reasoning
and explain the
reasoning.
A-REI.1. 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.
A-REI.2. Solve
simple rational and radical
equations in one variable,
and give examples showing
how extraneous solutions
may arise.
Solve equations and
inequalities in one
variable.
A-REI.3. Solve linear
equations and inequalities in
one variable, including
equations with coefficients
represented by letters.
A-REI.4. Solve
quadratic equations in one
variable.
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.
Solve
quadratic equations by
inspection (e.g., for x2 = 49),
taking square roots,
completing the square, the
quadratic formula and
factoring, as appropriate to
the initial form of the
Tennessee Standards
Standard 2 – Number
& Operations
Grade Level Expectations:
CLE 3102.2.1 Understand
computational results and
operations involving real numbers
in multiple
representations.
CLE 3102.2.2 Understand
properties of and relationships
between subsets and elements of
the real
number system.
ACT Standards
Common Core Standards
Find and use the 
least common
multiple
■ Order fractions
■ Work with
numerical factors
■ Work with
scientific notation 
■ Work with
squares and square
roots of numbers
■ Work problems
involving positive
integer
exponents*

■ Work with cubes
and cube roots
of numbers*
■ Determine when
an expression is
undefined*
■ Exhibit some
knowledge of the
complex
numbers†
A-CED.1. 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.
Evaluate algebraic
expressions by
substituting
integers for
unknown quantities
■ Add and subtract
simple algebraic
expressions
■ Solve routine
first-degree
equations
■ Perform
straightforward
word-toSymbol
translations
■ Multiply two
binomials*
A-CED.4. 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.
A-CED.2. Create
equations in two or more
variables to represent
relationships between
quantities; graph equations
on coordinate axes with
labels and scales.
A-CED.3. Represent
constraints by equations or
inequalities, and by systems
of equations and/or
inequalities, and interpret
solutions as viable or
nonviable options in a
modeling context. For
example, represent
inequalities describing
nutritional and cost
constraints on combinations
of different foods.
Tennessee Standards
ACT Standards
Common Core Standards
Draw conclusions
the structure of
Standard 3 – Algebra based on number Interpret
expressions.
concepts, algebraic
Grade Level Expectations:
properties, and/or
CLE 3102.3.1 Use algebraic

A-SSE.1. Interpret
thinking to analyze and generalize relationships
expressions that represent a
between
patterns.
quantity in terms of its
expressions and
CLE 3102.3.2 Understand and
context.★
numbers
apply properties in order to
o
Interpret
perform operations with, evaluate, ■ Exhibit
parts
of
an
expression,
such
knowledge of
simplify,
as terms, factors, and
logarithms
and factor expressions and
coefficients.
and geometric
polynomials.
o
Interpret
sequences
CLE 3102.3.3 Understand and
complicated
expressions
by
■ Apply properties
apply operations with rational
viewing one or more of their
of complex
expressions and equations.
parts as a single entity. For
numbers
example, interpret P(1+r)n as
CLE 3102.3.4 Solve problems
■
Solve
real-world
the product of P and a factor
involving linear equations and
problems
using
not depending on P.
linear inequalities.
first
degree
CLE 3102.3.5 Manipulate

A-SSE.2. Use the
equations
formulas and solve literal
structure of an expression to
■ Write
identify ways to rewrite it. For
equations.
expressions,
example, see x4 – y4 as (x2)2
CLE 3102.3.6 Understand and use
– (y2)2, thus recognizing it as
equations, or
relations and functions in various
a difference of squares that
Inequalities with
representations to solve contextual
can be factored as (x2 –
a single variable
problems.
y2)(x2 + y2).
for common preCLE 3102.3.7 Construct and solve
algebra settings
systems of
linear equations
Write expressions in
(e.g., rate and
equivalent forms to solve
and inequalities in two variables
distance
problems
problems.
by
and
problems
various methods.
that can be solved 
A-SSE.3. Choose
CLE 3102.3.8 Solve and
and
produce
an equivalent
by using
understand solutions
of
form
of
an
expression
to
quadratic equations with real roots. proportions)
reveal and explain properties
CLE 3102.3.9 Understand and use ■ Identify solutions of the quantity represented
to simple
exponential functions to
by the expression.★
Quadratic
solve contextual problems.
o
a. Factor a
equations
quadratic
expression
to
■ Add, subtract,
reveal the zeros of the
and multiply
function it defines.
polynomials*
b. Complete
■ Factor simple o
the
square
in
a
quadratic
quadratics (e.g.,
expression to reveal the
the difference of
maximum or minimum value
squares and
of the function it defines.
perfect square
c. Use the properties of
trinomials)*
■ Solve first-degreeexponents to transform
expressions for exponential
inequalities that functions. For example the
do not require expression 1.15t can be rewritten
reversing the
as (1.151/12)12t ≈ 1.01212t to reveal
Tennessee Standards
Standard 4 –
Geometry &
Measurement
Grade Level Expectations:
CLE 3102.4.1 Use algebraic
reasoning in applications involving
geometric formulas and contextual
problems.
CLE 3102.4.2 Apply appropriate
units of
measu
re and convert measures in
problem solving situations.
ACT Standards
■ Apply properties
of 30°- 60°-90°,
45°-45°-90°,
similar, and
congruent
triangles
■ Use the
Pythagorean
theorem
■ Evaluate
composite functions
at
integer values†
■ Apply basic
trigonometric ratios
to
solve righttriangle problems†
■ Use relationships
involving area,
perimeter, and
volume of
geometric figures
to compute
another measure
Perform oneoperation
computation
with whole numbers
and decimals
■ Solve problems in
one or two
Steps using
whole numbers
■ Perform common
conversions
(e.g., inches to
feet or hours to
minutes)
Common Core Standards
Tennessee Standards
Standard 5 – Data
Analysis, Statistics, &
Probability
Grade Level Expectations:
CLE 3102.5.1 Describe and
interpret quantitative information.
CLE 3102.5.2 Use statistical
thinking to draw conclusions and
make predictions.
CLE 3102.5.3 Understand basic
counting procedures and
concepts of probability.
ACT Standards
■ Calculate or use
a weighted
average
■ Interpret and use
information from
figures, tables,
and graphs
■ Apply counting
techniques
■ Compute a
probability when
the
event and/or
sample space are
not given or
obvious
Compute
straightforward
probabilities for
common situations
■ Distinguish
between mean,
median, and
mode for a list of
numbers
■ Analyze and draw
conclusions
based on
information from
figures, tables,
and graphs
■ Exhibit
knowledge of
conditional
and joint
probability
■ Draw conclusions
based on
Common Core Standards