Livingston County Schools
Algebra I Unit 4
Expressions and Equations
Unit Overview
Students will extend the laws of exponents to rational exponents.
Students will see structure in and create quadratic and exponential expressions.
Students will compare characteristics of linear, quadratic and exponential functions to model phenomena.
Length of unit: 7 weeks
KY Core Academic Standard
Learning Target
K
A.SSE.1a Interpret
expressions that represent
a quantity in terms of its
context.★
a. Interpret parts of an
expression, such as terms,
factors, and coefficients.
I can identify and define parts of an
expression.
X
A.SSE.1b Interpret
expressions that represent
a quantity in terms of its
context.* (Modeling
standard)
b. 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.
I can define and recognize parts of
an expression in a contextual
quantity.
I can interpret parts of an
expression in terms of context.
I can interpret complicated
expressions in terms of context.
R
X
X
X
S
P
Critical
Vocabulary
expression
term
factor
coefficients
quadratic
expression
exponential
expression
rational
exponents
square root
cube root
Texts/Resources/Activities
A.SSE.2 Use the structure of
an expression to identify
ways to rewrite
it. For example, see x4 – y4
as (x2)2 – (y2)2, thus
recognizing it as a
difference of squares that
can be factored as (x2 –
y2)(x2 + y2).
I can identify ways to rewrite
expressions.
I can identify various structures of
expressions.
X
X
I can use the structure of an
expression to identify ways to
rewrite it.
X
I can classify expressions by
structure.
X
A.SSE.3a Choose and
produce an equivalent form
of an expression
to reveal and explain
properties of the quantity
represented by the
expression.★
a. Factor a quadratic
expression to reveal the
zeros of the function
it defines.
I can factor a quadratic expression.
X
I can explain the connection
between the factored form and the
zeros of the function.
X
I can explain the properties of the
quantity represented by the
quadratic expression.
X
A.SSE.3b Choose and
produce an equivalent form
of an expression to reveal
and explain properties of
the quantity represented by
I can complete the square.
quadratic
expression
zeros
X
I can choose and produce an
equivalent form of a quadratic
expression.
I can explain the connection
between the completed square
form and the maximum or
difference of
squares
factoring
regrouping
scalar
X
complete the
square
X
maximum
the expression.* (Modeling
standard)
b. Complete the square in a
quadratic expression to
reveal the maximum or
minimum value of the
function it defines.
minimum value.
A.SSE.3c Choose and
produce an equivalent form
of an expression to reveal
and explain properties of
the quantity represented by
the expression.*
(*Modeling standard)
c. Use the properties of
exponents to transform
expressions for exponential
functions. For example the
expression 1.15t can be
rewritten as (1.151/12)12t
≈ 1.01212t to reveal the
approximate equivalent
monthly interest rate if the
annual rate is 15%.
I can complete the square.
X
I can explain the connection
between the completed square
form and the maximum or
minimum value.
X
I can explain the properties of the
quantity represented by the
expression.
X
A.APR.1 Understand that
polynomials form a system
analogous to the
integers, namely, they are
closed under the operations
I can identify that the sum,
difference or product of two
polynomials will always be a
polynomial.
minimum
I can explain the properties of the
quantity represented by the
expression.
X
I can choose and produce an
equivalent form of a quadratic
expression.
X
complete the
square
maximum
I can choose and produce an
equivalent form of a quadratic
expression.
minimum
X
X
polynomial
closure
of addition,
subtraction, and
multiplication; add,
subtract, and multiply
polynomials.
I can define "closure."
X
I can apply arithmetic operations to
polynomials.
X
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.
I can solve one variable linear and
exponential equations.
X
quadratic
equations
I can solve one variable
inequalities.
X
solve
I can solve quadratic equations.
X
I can describe and express the
relationships between the
quantities in the problem.
X
A.CED.2 Create equations in
two or more variables to
represent
I can create and use equations and
inequalities in one variable to solve
problems.
X
I can create equations and
inequalities in one variable to
model real-world situations.
X
I can compare/contrast problems
that can be solved by different
types of equations.
X
I can identify and describe the
quantities represented by distinct
variables in real-world situations.
X
distinct
variables
dependent
relationships between
quantities; graph equations
on coordinate axes
with labels and scales.
independent
I can graph one or more equation
on a coordinate axes.
X
I can create at least two equations
in two or more variables to
represent relationships.
X
I can justify which quantities in a
real-world situation are dependent
and independent.
X
I can determine appropriate units
for the labels/scale of a graph.
X
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.
I can define a quantity of interest.
A.REI.4a Solve quadratic
equations in one variable.
a. 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.
I can complete the square to
transform any quadratic equation.
X
X
I can solve a formula for a given
variable.
I can solve quadratic equations in
one variable.
quantity of
interest
literal
equations
X
complete the
square
X
complex
number
I can derive the quadratic formula.
X
I can solve quadratic equations.
X
quadratic
Derive the quadratic
formula from this form.
b. 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 equation.
Recognize when the
quadratic formula gives
complex solutions and write
them as a ± bi for real
numbers a and b.
A.REI.7 Solve a simple
system consisting of a linear
equation and a
quadratic equation in two
variables algebraically and
graphically. For
example, find the points of
intersection between the
line y = –3x and the
circle x2 + y2 = 3.
Spiraled Standards:
formula
X
I can express complex solutions.
square roots
I can determine appropriate
strategies to solve quadratic
equations.
X
factoring
I can recognize when the quadratic
formula gives complex solutions.
I can transform a simple system
consisting of a linear equation and
a quadratic equation in 2 variables
so that a solution can be found
algebraically and graphically.
I can explain the correspondence
between the algebraic and
graphical solutions.
X
X
complex
solution
linear
equation
quadratic
equation
X
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