Course
Number:
1200700
Course
Path:
Section:
Grades
PreK
to
12
Education
Courses
»
Grade
Group:
Grades
9
to
12
and
Adult
Education
Courses
»
Subject:
Mathematics»
SubSubject:
Algebra
»
Course
Title:
Mathematics
for
College
Readiness
Course
Section:
Grades
PreK
to
12
Education
Courses
Abbreviated
Title:
Math
Coll.
Readiness
Number
of
Credits:
1
Course
Length:
Year
Course
Type:
Core
Course
Level:
2
Course
Status:
DRAFT
‐
State
Board
approval
pending
Graduation
Requirements:
Course
Description:
This
course
incorporates
the
Common
Core
Standards
for
Mathematical
Practices
as
well
as
the
following
Common
Core
Standards
for
Mathematical
Content:
an
introduction
to
functions,
linear
equations
and
inequalities,
solving
systems
of
equations,
rational
equations
and
algebraic
fractions,
radicals
and
rational
exponents,
factoring
and
quadratic
equations,
complex
numbers,
and
the
Common
Core
Standards
for
High
School
Modeling.
The
benchmarks
reflect
the
Florida
College
Competencies
necessary
for
entry
‐
level
college
courses.
RELATED
BENCHMARKS:
Scheme
Descriptor
MACC.K12.MP
Mathematical
Practices
MACC.K12.MP.1
Make
sense
of
problems
and
persevere
in
solving
them
MACC.K12.MP.2
Reason
abstractly
and
quantitatively
MACC.K12.MP.3
Construct
viable
arguments
and
critique
the
reasoning
of
others
MACC.K12.MP.4
Model
with
mathematics
MACC.K12.MP.5
Use
appropriate
tools
strategically
MACC.K12.MP.6
Attend
to
precision
MACC.K12.MP.7
Look
for
and
make
use
of
structure
MACC.K12.MP.8
Look
for
and
express
regularity
in
repeated
reasoning
MACC.7.EE
Expressions
and
Equations
MACC.7.EE.1
Use
properties
of
operations
to
generate
equivalent
expressions.
MACC.7.EE.1.1
Apply
properties
of
operations
as
strategies
to
add,
subtract,
factor,
and
expand
linear
expressions
with
rational
coefficients.
MACC.7.EE.2
Solve
real
‐
life
and
mathematical
problems
using
numerical
and
algebraic
expressions
and
equations
MACC.7.EE.2.4
Use
variables
to
represent
quantities
in
a
real
‐
world
or
mathematical
problem,
and
construct
simple
equations
and
inequalities
to
solve
problems
by
reasoning
about
the
quantities.
DRAFT
?
MACC.7.EE.2.4a
Solve
word
problems
leading
to
equations
of
the
form
px
+
q
=
r
and
p(x
+
q)
=
r
,
where
p,
q,
and
r
are
specific
rational
numbers.
Solve
equations
of
these
forms
fluently.
Compare
an
algebraic
solution
to
an
arithmetic
solution,
identifying
the
sequence
of
the
operations
used
in
each
approach.
For
example,
the
perimeter
of
a
rectangle
is
54
cm.
Its
length
is
6
cm.
What
is
its
width?
MACC.7.EE.2.4b
Solve
word
problems
leading
to
inequalities
of
the
form
px
+
q
>
r
or
px
+
q
<
r
,
where
p,
q
,
and
r
are
specific
rational
numbers.
Graph
the
solution
set
of
the
inequality
and
interpret
it
in
the
context
of
the
problem.
For
example,
As
a
salesperson,
you
are
paid
$50
per
week
plus
$3
per
sale.
This
week
you
want
your
pay
to
be
at
least
$100.
Write
an
inequality
for
the
number
of
sales
you
need
to
make,
and
describe
the
solutions.
MACC.8.EE
Expressions
and
Equations
MACC.8.EE.1
Work
with
radicals
and
integer
exponents
MACC.8.EE.1.2
Use
square
root
and
cube
root
symbols
to
represent
solutions
to
equations
of
the
form
x
2
=
p
and
x
3
=
p
,
where
p
is
a
positive
rational
number.
Evaluate
square
roots
of
small
perfect
squares
and
cube
roots
of
small
perfect
cubes.
Know
that
√
2
is
irrational.
MACC.8.EE.2
Understand
the
connections
between
proportional
relationships,
lines,
and
linear
equations
MACC.8.EE.2.5
Graph
proportional
relationships,
interpreting
the
unit
rate
as
the
slope
of
the
graph.
Compare
two
different
proportional
relationships
represented
in
different
ways.
For
example,
compare
a
distance
‐
time
graph
to
a
distance
‐
time
equation
to
determine
which
of
two
moving
objects
has
greater
speed.
MACC.8.EE.2.6
Use
similar
triangles
to
explain
why
the
slope
m
is
the
same
between
any
two
distinct
points
on
a
non
‐
vertical
line
in
the
coordinate
plane;
derive
the
equation
y
=
mx
for
a
line
through
the
origin
and
the
equation
y
=
mx
+
b
for
a
line
intercepting
the
vertical
axis
at
b
.
MACC.8.EE.3
Analyze
and
solve
linear
equations
and
pairs
of
simultaneous
linear
equations
MACC.8.EE.3.7
Solve
linear
equations
in
one
variable.
MACC.8.EE.3.7a
Give
examples
of
linear
equations
in
one
variable
with
one
solution,
infinitely
many
solutions,
or
no
solutions.
Show
which
of
these
possibilities
is
the
case
by
successively
transforming
the
given
equation
into
simpler
forms,
until
an
equivalent
equation
of
the
form
x
=
a,
a
=
a,
or
a
=
b
results
(where
a
and
b
are
different
numbers).
MACC.8.EE.3.7b
Solve
linear
equations
with
rational
number
coefficients,
including
equations
whose
solutions
require
expanding
expressions
using
the
distributive
property
and
collecting
like
terms.
MACC.8.EE.3.8
Analyze
and
solve
linear
equations
and
pairs
of
simultaneous
linear
equations.
DRAFT
?
MACC.8.EE.3.8a
Understand
that
solutions
to
a
system
of
two
linear
equations
in
two
variables
correspond
to
points
of
intersection
of
their
graphs,
because
points
of
intersection
satisfy
both
equations
simultaneously.
MACC.8.EE.3.8b
Solve
systems
of
two
linear
equations
in
two
variables
algebraically,
and
estimate
solutions
by
graphing
the
equations.
Solve
simple
cases
by
inspection.
For
example,
3x
+
2y
=
5
and
3x
+
2y
=
6
have
no
solution
because
3x
+
2y
cannot
simultaneously
be
5
and
6.
MACC.8.EE.3.8c
Solve
real
‐
world
and
mathematical
problems
leading
to
two
linear
equations
in
two
variables.
For
example,
given
coordinates
for
two
pairs
of
points,
determine
whether
the
line
through
the
first
pair
of
points
intersects
the
line
through
the
second
pair
.
MACC.8.F
Functions
MACC.8.F.1
Define,
evaluate,
and
compare
functions
MACC.8.F.1.2
Compare
properties
of
two
functions
each
represented
in
a
different
way
(algebraically,
graphically,
numerically
in
tables,
or
by
verbal
descriptions).
For
example,
given
a
linear
function
represented
by
a
table
of
values
and
a
linear
function
represented
by
an
algebraic
expression,
determine
which
function
has
the
greater
rate
of
change.
MACC.8.F.1.3
Interpret
the
equation
y
=
mx
+
b
as
defining
a
linear
function,
whose
graph
is
a
straight
line;
give
examples
of
functions
that
are
not
linear.
For
example,
the
function
A
=
s
2
giving
the
area
of
a
square
as
a
function
of
its
side
length
is
not
linear
because
its
graph
contains
the
points
(1,1),
(2,4)
and
(3,9),
which
are
not
on
a
straight
line.
MACC.8.F.2
Use
functions
to
model
relationships
between
quantities
MACC.8.F.2.4
Construct
a
function
to
model
a
linear
relationship
between
two
quantities.
Determine
the
rate
of
change
and
initial
value
of
the
function
from
a
description
of
a
relationship
or
from
two
(x,
y)
values,
including
reading
these
from
a
table
or
from
a
graph.
Interpret
the
rate
of
change
and
initial
value
of
a
linear
function
in
terms
of
the
situation
it
models,
and
in
terms
of
its
graph
or
a
table
of
values.
MACC.8.F.2.5
Describe
qualitatively
the
functional
relationship
between
two
quantities
by
analyzing
a
graph
(e.g.,
where
the
function
is
increasing
or
decreasing,
linear
or
nonlinear).
Sketch
a
graph
that
exhibits
the
qualitative
features
of
a
function
that
has
been
described
verbally.
MACC.8.NS
The
Number
System
MACC.8.NS.1
Know
that
there
are
numbers
that
are
not
rational,
and
approximate
them
by
rational
numbers
MACC.8.NS.1.1
Know
that
numbers
that
are
not
rational
are
called
irrational.
Understand
informally
that
every
number
has
a
decimal
expansion;
for
rational
numbers
show
that
the
decimal
expansion
repeats
eventually,
and
convert
a
decimal
expansion
which
repeats
eventually
into
a
rational
number.
DRAFT
?
MACC.8.NS.1.2
Use
rational
approximations
of
irrational
numbers
to
compare
the
size
of
irrational
numbers,
locate
them
approximately
on
a
number
line
diagram,
and
estimate
the
value
of
expressions
(e.g.,
π
2
).
For
example,
by
truncating
the
decimal
expansion
of
√
2
(square
root
of
2),
show
that
√
2
is
between
1
and
2,
then
between
1.4
and
1.5,
and
explain
how
to
continue
on
to
get
better
approximations.
MACC.912.A
‐
APR
Arithmetic
with
Polynomials
and
Rational
Expressions
MACC.912.A
‐
APR.1
Perform
arithmetic
operations
on
polynomials
MACC.912.A
‐
APR.1.1
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.
MACC.912.A
‐
APR.4
Rewrite
rational
expressions.
MACC.912.A
‐
APR.4.6
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.
MACC.912.A
‐
APR.4.7
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.
MACC.912.A
‐
CED
Creating
Equations
MACC.912.A
‐
CED.1
Create
equations
that
describe
numbers
or
relationships
MACC.912.A
‐
CED.1.1
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.*
MACC.912.A
‐
CED.1.2
Create
equations
in
two
or
more
variables
to
represent
relationships
between
quantities;
graph
equations
on
coordinate
axes
with
labels
and
scales.*
MACC.912.A
‐
CED.1.3
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.*
MACC.912.A
‐
CED.1.4
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.*
MACC.912.A
‐
REI
Reasoning
with
Equations
and
Inequalities
MACC.912.A
‐
REI.1
Understand
solving
equations
as
a
process
of
reasoning
and
explain
the
reasoning
MACC.912.A
‐
REI.1.1
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.
DRAFT
?
MACC.912.A
‐
REI.1.2
Solve
simple
rational
and
radical
equations
in
one
variable,
and
give
examples
showing
how
extraneous
solutions
may
arise.
MACC.912.A
‐
REI.2
Solve
equations
and
inequalities
in
one
variable
MACC.912.A
‐
REI.2.3
Solve
linear
equations
and
inequalities
in
one
variable,
including
equations
with
coefficients
represented
by
letters.
MACC.912.A
‐
REI.2.4
Solve
quadratic
equations
in
one
variable.
MACC.912.A
‐
REI.2.4a
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.
MACC.912.A
‐
REI.2.4b
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
.
MACC.912.A
‐
REI.3
Solve
systems
of
equations
MACC.912.A
‐
REI.3.5
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.
MACC.912.A
‐
REI.3.6
Solve
systems
of
linear
equations
exactly
and
approximately
(e.g.,
with
graphs),
focusing
on
pairs
of
linear
equations
in
two
variables.
MACC.912.A
‐
REI.4
Represent
and
solve
equations
and
inequalities
graphically
MACC.912.A
‐
REI.4.10
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).
MACC.912.A
‐
REI.4.11
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.*
MACC.912.A
‐
REI.4.12
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.
MACC.912.A
‐
SSE
Seeing
Structure
in
Expressions
MACC.912.A
‐
SSE.1
Interpret
the
structure
of
expressions
MACC.912.A
‐
SSE.1.1
Interpret
expressions
that
represent
a
quantity
in
terms
of
its
context.*
MACC.912.A
‐
SSE.1.1a
Interpret
parts
of
an
expression,
such
as
terms,
factors,
and
coefficients.*
MACC.912.A
‐
SSE.1.1b
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.*
DRAFT
?
MACC.912.A
‐
SSE.1.2
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
).
MACC.912.A
‐
SSE.2
Write
expressions
in
equivalent
forms
to
solve
problems
MACC.912.A
‐
SSE.2.3
Choose
and
produce
an
equivalent
form
of
an
expression
to
reveal
and
explain
properties
of
the
quantity
represented
by
the
expression.*
MACC.912.A
‐
SSE.2.3a
Factor
a
quadratic
expression
to
reveal
the
zeros
of
the
function
it
defines.*
MACC.912.A
‐
SSE.2.3b
Complete
the
square
in
a
quadratic
expression
to
reveal
the
maximum
or
minimum
value
of
the
function
it
defines.*
MACC.912.A
‐
SSE.2.3c
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%.*
MACC.912.F
‐
IF
Interpreting
Functions
MACC.912.F
‐
IF.1
Understand
the
concept
of
a
function
and
use
function
notation
MACC.912.F
‐
IF.1.1
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).
MACC.912.F
‐
IF.1.2
Use
function
notation,
evaluate
functions
for
inputs
in
their
domains,
and
interpret
statements
that
use
function
notation
in
terms
of
a
context.
MACC.912.F
‐
IF.2
Interpret
functions
that
arise
in
applications
in
terms
of
the
context
MACC.912.F
‐
IF.2.5
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
person
‐
hours
it
takes
to
assemble
n
engines
in
a
factory,
then
the
positive
integers
would
be
an
appropriate
domain
for
the
function.
*
MACC.912.F
‐
IF.2.6
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.*
MACC.912.F
‐
IF.3.7
Graph
functions
expressed
symbolically
and
show
key
features
of
the
graph,
by
hand
in
simple
cases
and
using
technology
for
more
complicated
cases.*
MACC.912.F
‐
IF.3.7a
Graph
linear
and
quadratic
functions
and
show
intercepts,
maxima,
and
minima.*
MACC.912.F
‐
IF.3.7b
Graph
square
root,
cube
root,
and
piecewise
‐
defined
functions,
including
step
functions
and
absolute
value
functions.*
MACC.912.F
‐
IF.3.8a
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.
DRAFT
?
MACC.912.F
‐
IF.3.9
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
MACC.912.F
‐
IF
‐
3
Analyze
functions
using
different
representations
MACC.912.N
‐
CN
The
Complex
Number
System
MACC.912.N
‐
CN.1
Perform
arithmetic
operations
with
complex
numbers
MACC.912.N
‐
CN.1.1
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.
MACC.912.N
‐
CN.1.2
Use
the
relation
i
2
=
–1
and
the
commutative,
associative,
and
distributive
properties
to
add,
subtract,
and
multiply
complex
numbers.
MACC.912.N
‐
CN.1.3
Find
the
conjugate
of
a
complex
number;
use
conjugates
to
find
moduli
and
quotients
of
complex
numbers.
MACC.912.N
‐
CN.3
Use
complex
numbers
in
polynomial
identities
and
equations
MACC.912.N
‐
CN.3.7
Solve
quadratic
equations
with
real
coefficients
that
have
complex
solutions.
MACC.912.N
‐
RN
The
Real
Number
System
MACC.912.N
‐
RN.1
Extend
the
properties
of
exponents
to
rational
exponents
MACC.912.N
‐
RN.1.1
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.
MACC.912.N
‐
RN.1.2
Rewrite
expressions
involving
radicals
and
rational
exponents
using
the
properties
of
exponents.
MACC.912.N
‐
RN.2
Use
Properties
of
rational
and
irrational
numbers
MACC.912.N
‐
RN.2.3
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.
MACC.912.S
‐
ID
Interpreting
Categorical
and
Quantitative
Data
MACC.912.S
‐
ID.3
Interpret
linear
models
MACC.912.S
‐
ID.3.7
Interpret
the
slope
(rate
of
change)
and
the
intercept
(constant
term)
of
a
linear
model
in
the
context
of
the
data.*
Modeling
standards
Modeling
is
best
interpreted
not
as
a
collection
of
isolated
topics
but
rather
in
relation
to
other
standards.
Making
mathematical
models
is
a
Standard
for
Mathematical
Practice,
and
specific
modeling
standards
appear
throughout
the
high
school
standards
indicated
by
a
star
symbol
(*).
DRAFT
?