Course
Number:
1200410
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
Success
Course
Section:
Grades
PreK
to
12
Education
Courses
Abbreviated
Title:
Math
Coll.
Success
Number
of
Credits:
.5
Course
Length:
Semester
Course
Type:
Elective
Course
Level:
2
Course
Status:
DRAFT
‐
State
Board
approval
pending
Graduation
Requirements:
Course
Description:
This
course
is
targeted
for
grade
12
students,
whose
test
scores
on
the
Postsecondary
Educational
Readiness
Test
are
below
the
established
cut
scores
for
mathematics,
indicating
that
they
are
not
yet
“college
ready”
in
mathematics.
This
course
incorporates
the
Common
Core
Standards
for
Mathematical
Practices
as
well
as
the
following
Common
Core
Standards
for
Mathematical
Content:
Ratios
and
Proportional
Relationships,
Number
and
Quantities,
Algebra,
Functions,
Expressions
and
Equations,
Geometry,
Statistics,
Real
Number
Systems,
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.1.2
Understand
that
rewriting
an
expression
in
different
forms
in
a
problem
context
can
shed
light
on
the
problem
and
how
the
quantities
in
it
are
related.
For
example,
a
+
0.05a
=
1.05a
means
that
“increase
by
5%”
is
the
same
as
“multiply
by
1.05.”
DRAFT
?
MACC.7.EE.2
Solve
real
‐
life
and
mathematical
problems
using
numerical
and
algebraic
expressions
and
equations.
MACC.7.EE.2.3
Solve
multi
‐
step
real
‐
life
and
mathematical
problems
posed
with
positive
and
negative
rational
numbers
in
any
form
(whole
numbers,
fractions,
and
decimals),
using
tools
strategically.
Apply
properties
of
operations
as
strategies
to
calculate
with
numbers
in
any
form;
convert
between
forms
as
appropriate;
and
assess
the
reasonableness
of
answers
using
mental
computation
and
estimation
strategies.
For
example:
If
a
woman
making
$25
an
hour
gets
a
10%
raise,
she
will
make
an
additional
1/10
of
her
salary
an
hour,
or
$2.50,
for
a
new
salary
of
$27.50.
If
you
want
to
place
a
towel
bar
9
3/4
inches
long
in
the
center
of
a
door
that
is
27
1/2
inches
wide,
you
will
need
to
place
the
bar
about
9
inches
from
each
edge;
this
estimate
can
be
used
as
a
check
on
the
exact
computation.
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.
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.7.G
Geometry
MACC.7.G.1
Draw,
construct,
and
describe
geometrical
figures
and
describe
the
relationships
between
them.
MACC.7.G.1.6
Solve
real
‐
world
and
mathematical
problems
involving
area,
volume
and
surface
area
of
two
‐
and
three
‐
dimensional
objects
composed
of
triangles,
quadrilaterals,
polygons,
cubes,
and
right
prisms.
MACC.7.RP
Ratios
and
Proportional
Relationships
MACC.7.RP.1
Analyze
proportional
relationships
and
use
them
to
solve
real
‐
world
and
mathematical
problems.
MACC.7.RP.1.1
Compute
unit
rates
associated
with
ratios
of
fractions,
including
ratios
of
lengths,
areas
and
other
quantities
measured
in
like
or
different
units.
For
example,
if
a
person
walks
1/2
mile
in
each
1/4
hour,
compute
the
unit
rate
as
the
complex
fraction
(1/2)/(1/4)
miles
per
hour,
equivalently
2
miles
per
hour.
DRAFT
?
MACC.7.RP.1.2
Recognize
and
represent
proportional
relationships
between
quantities.
MACC.7.RP.1.2a
Decide
whether
two
quantities
are
in
a
proportional
relationship,
e.g.,
by
testing
for
equivalent
ratios
in
a
table
or
graphing
on
a
coordinate
plane
and
observing
whether
the
graph
is
a
straight
line
through
the
origin.
MACC.7.RP.1.2b
Identify
the
constant
of
proportionality
(unit
rate)
in
tables,
graphs,
equations,
diagrams,
and
verbal
descriptions
of
proportional
relationships.
MACC.7.RP.1.2c
Represent
proportional
relationships
by
equations.
For
example,
if
total
cost
t
is
proportional
to
the
number
n
of
items
purchased
at
a
constant
price
p,
the
relationship
between
the
total
cost
and
the
number
of
items
can
be
expressed
as
t
=
pn.
MACC.7.RP.1.2d
Explain
what
a
point
(x,
y)
on
the
graph
of
a
proportional
relationship
means
in
terms
of
the
situation,
with
special
attention
to
the
points
(0,
0)
and
(1,
r
)
where
r
is
the
unit
rate.
MACC.7.RP.1.3
Use
proportional
relationships
to
solve
multistep
ratio
and
percent
problems.
Examples:
simple
interest,
tax,
markups
and
markdowns,
gratuities
and
commissions,
fees,
percent
increase
and
decrease,
percent
error.
MACC.8.EE
Expressions
and
Equations
MACC.8.EE.1
Work
with
radicals
and
integer
exponents.
MACC.8.EE.1.1
Know
and
apply
the
properties
of
integer
exponents
to
generate
equivalent
numerical
expressions.
For
example,
3
2
×
3
‐
5
=
3
‐
3
=
1/(3
3
)
=
1/27.
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.1.3
Use
numbers
expressed
in
the
form
of
a
single
digit
times
an
integer
power
of
10
to
estimate
very
large
or
very
small
quantities,
and
to
express
how
many
times
as
much
one
is
than
the
other.
For
example,
estimate
the
population
of
the
United
States
as
3
×
10
8
and
the
population
of
the
world
as
7
×
10
9
,
and
determine
that
the
world
population
is
more
than
20
times
larger.
MACC.8.EE.1.4
Perform
operations
with
numbers
expressed
in
scientific
notation,
including
problems
where
both
decimal
and
scientific
notation
are
used.
Use
scientific
notation
and
choose
units
of
appropriate
size
for
measurements
of
very
large
or
very
small
quantities
(e.g.,
use
millimeters
per
year
for
seafloor
spreading).
Interpret
scientific
notation
that
has
been
generated
by
technology.
MACC.8.EE.2
Understand
the
connections
between
proportional
relationships,
lines,
and
linear
equations.
DRAFT
?
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.F
Functions
MACC.8.F.1
Define,
evaluate,
and
compare
functions.
MACC.8.F.1.1
Understand
that
a
function
is
a
rule
that
assigns
to
each
input
exactly
one
output.
The
graph
of
a
function
is
the
set
of
ordered
pairs
consisting
of
an
input
and
the
corresponding
output.
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.G
Geometry
MACC.8.G.2
Understand
and
apply
the
Pythagorean
Theorem
MACC.8.G.2.6
Explain
a
proof
of
the
Pythagorean
Theorem
and
its
converse.
MACC.8.G.2.7
Apply
the
Pythagorean
Theorem
to
determine
unknown
side
lengths
in
right
triangles
in
real
‐
world
and
mathematical
problems
in
two
and
three
dimensions.
MACC.8.G.2.8
Apply
the
Pythagorean
Theorem
to
find
the
distance
between
two
points
in
a
coordinate
system.
DRAFT
?
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.
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.
DRAFT
?
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
‐
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.*
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.F
‐
IF
Interpreting
Functions
MACC.912.F
‐
IF.3
Analyze
functions
using
different
representations
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
‐
LE
Linear,
Quadratic,
and
Exponential
Models*
MACC.912.F
‐
LE.1
Construct
and
compare
linear,
quadratic,
and
exponential
models
and
solve
problems*
MACC.912.F
‐
LE.1.1b
Recognize
situations
in
which
one
quantity
changes
at
a
constant
rate
per
unit
interval
relative
to
another.*
MACC.912.N
‐
Q
Quantities*
MACC.912.N
‐
Q.1
Reason
quantitatively
and
use
units
to
solve
problems.
MACC.912.N
‐
Q.1.1
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.*
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.
DRAFT
?
MACC.912.N
‐
RN.1.2
Rewrite
expressions
involving
radicals
and
rational
exponents
using
the
properties
of
exponents.
MACC.912.N
‐
RN.1.3
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.*
MACC.912.S
‐
ID.3.8
Compute
(using
technology)
and
interpret
the
correlation
coefficient
of
a
linear
fit.*
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
?