DCA Erie 1 BOCES
Mathematics: 2012 - 2013
Updated on: 3/1/2013
CCLS Algebra
Module 5: Quadratic Functions
Essential Questions:
Common Core Standards
N-RN.3. Explain why the sum or
product of two 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.
Content
Skills
(10%)
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Rational and irrational numbers
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Rigorous Sample Tasks
Vocabulary
I can define the properties
of rational numbers.
I can define the properties
of irrational numbers.
I can explain why adding
or multiplying two rational
numbers results in a
solution that is rational
(closure property).
I can explain why adding
or multiplying a rational
and irrational number
results in a solution that is
irrational (closure
property).
I can solve real-world
problems requiring
operations with rational
and irrational numbers
(Calculate the perimeter of
a square with an area of
2).
Resources
Rational
Irrational
Closure with
rational and
irrational
numbers
Properties of
operations
Scaffolded sample tasks
DCA Erie 1 BOCES
Mathematics: 2012 - 2013
Updated on: 3/1/2013
CCLS Algebra
Identify the following numbers as rational or
irrational:
a) 5
b) 𝜋
−1
c) 2
d) √3
Find the sum of the following:
a) 5 + -5
1
b) 2 + 2
c) 0 + √2
d) π + 5
e) -√2 + √2
Find the product of the following:
a) 5 + -5
1
b) 2 + 2
c) 0 + √2
d) π + 5
e) -√2 + √2
** The focus is on properties, not operations.**
F-IF.4. For a function that models a
relationship between two quantities,
interpret key features of graphs and
tables in terms of the quantities, and
sketch graphs showing key features
(70%)
Key features of graphs
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I can identify the slope and
y-intercept of a linear
function.
I can identify the domain
for a step function.
Step function
Piece-wise
function
Absolute value
function
DCA Erie 1 BOCES
Mathematics: 2012 - 2013
given a verbal description of the
relationship. Key features include:
intercepts; intervals where the
function is increasing, decreasing,
positive, or negative; relative
maximums and minimums;
symmetries; end behavior; and
periodicity.
CCLS Algebra
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I can identify the range for
a step function.
I can identify minimums
and maximums of a
function (linear,
exponential, and
quadratic).
I can identify intervals
where a function is
increasing or decreasing
(linear, exponential, and
quadratic).
I can identify the roots of a
graph (linear, exponential,
and quadratic).
I can identify the x and y
intercepts (linear,
exponential, and
quadratic).
I can identify symmetries
and end behaviors for
graphs (linear,
exponential, and
quadratic).
I can sketch the key
features of a function
(linear, exponential, and
quadratic).
I can describe the key
features of a function
(linear, exponential, and
quadratic).
**Also include square
root, cube root, piece-
Updated on: 3/1/2013
Square root
function
Cube root
function
DCA Erie 1 BOCES
Mathematics: 2012 - 2013
Updated on: 3/1/2013
CCLS Algebra
wise, step, and absolute
value functions when
describing key features.
Rigorous Sample Tasks
Scaffolded sample tasks
Find the minimum/ maximum (turning point,
vertex) of the parabola whose equation is 𝑦 =
3𝑥 2 + 6𝑥 − 1
What is the equation for the axis of symmetry for
this parabola?
What is the maximum point?
Solve the following equation by factoring:
𝑦 = 𝑥 2 +3x – 10
Solve the following equation using the quadratic
formula:
𝑦 = 6𝑥 2 + 5𝑥 − 4
DCA Erie 1 BOCES
Mathematics: 2012 - 2013
F-IF.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.
(70%)

Domain
Rigorous Sample Tasks
Updated on: 3/1/2013
CCLS Algebra

I can write the correct
domain for a function
(linear, exponential, and
quadratic).
I can identify the
appropriated domain for a
function within the
context of a word problem
(e.g. when to accept/reject
negative solutions, when
fractional solutions are not
appropriate).
Scaffolded sample tasks
DCA Erie 1 BOCES
Mathematics: 2012 - 2013
F-IF.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.
(70%)
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Rate of change
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I can calculate the rate of
change from an equation.
I can calculate the rate of
change from a graph.
I can calculate the rate of
change from a table of
values.
I can calculate the rate of
change of an exponential
function using percent
growth/decay (the r value
found in geometric
sequence).
I can calculate the rate of
change for a given interval.
I can estimate the rate of
change from a graph.
I can describe the rate of
change in terms of the
context of the situation.
**Include linear,
quadratic, square root,
cube root, piece-wise,
step, absolute, and
exponential functions with
domains in the integers.
Rigorous Sample Tasks
F-IF.7. Graph functions expressed
symbolically and show key features
(20%)
Updated on: 3/1/2013
CCLS Algebra
Scaffolded sample tasks

I can graph a linear
function and identify the
DCA Erie 1 BOCES
Mathematics: 2012 - 2013
of the graph, by hand in simple cases
and using technology for more
complicated cases.
F-IF.7.a. Graph linear and quadratic
functions and show intercepts,
maxima, and minima.
Graphing linear and quadratic
functions
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
Rigorous Sample Tasks
F-IF.7.b. Graph square root, cube
root, and piecewise-defined
functions, including step functions
and absolute value functions.
Updated on: 3/1/2013
CCLS Algebra
intercepts, domain, range,
and rate of change.
I can graph a quadratic
function and identify the
roots (x intercepts), y
intercepts, domain, range,
minimum, and/or
maximum.
I can compare the rate of
change of two linear
functions.
Scaffolded sample tasks
(20%)

Graphing square root, cube
root, piece-wise, step, and
absolute functions
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I can graph square root
functions and highlight
issues with domain and
range.
I can graph cube root
functions and highlight
issues with domain and
range.
I can graph piece-wise
defined functions and
highlight issues with
domain and range.
I can graph step functions
and highlight issues with
domain and range.
I can graph absolute value
functions and highlight
DCA Erie 1 BOCES
Mathematics: 2012 - 2013

Rigorous Sample Tasks
F-IF.8. Write a function defined by an
expression in different but
equivalent forms to reveal and
explain different properties of the
function.
F-IF.8.a. 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.
(20%)
Properties of quadratics
Rigorous Sample Tasks
Updated on: 3/1/2013
CCLS Algebra
issues with domain and
range.
I can compare and
contrast piece-wise
defined functions, step
functions, and absolute
value functions with
linear, exponential, and
quadratic functions.
Scaffolded sample tasks
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I can complete the square
to solve a quadratic
equation.
I can factor a quadratic
equation.
I can rewrite quadratic
functions into different
forms to explain different
properties of the function.
I can find the roots,
minimum/maximum
(turning point), symmetry
(axis of symmetry) for a
graph and explain what
the purpose of these
features are to the context
of the problem.
Turning point
Axis of symmetry
Critical points
Scaffolded sample tasks
DCA Erie 1 BOCES
Mathematics: 2012 - 2013
F-IF.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.
(20%)
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Characteristics of functions
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
Rigorous Sample Tasks
F-BF.1. Write a function that
describes a relationship between
two quantities.
F-BF.1.a. Determine an explicit
expression, a recursive process, or
steps for calculation from a context.
Updated on: 3/1/2013
CCLS Algebra
I can compare
characteristics of two
different functions (linear,
quadratic, and
exponential) represented
in two different forms (e.g.
table of values vs.
algebraic representation).
I can identify parts of a
function (linear, quadratic,
and exponential)
algebraically, graphically,
and verbally (max/min of
graphs, roots/solutions).
**Also include square
root, cube root, piecewise, step, and absolute
value functions.
Scaffolded sample tasks
(20%)

Explicit and recursive forms of
functions
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I can explain the steps to
set up a linear, quadratic,
or exponential function.
I can construct an
exponential function
explicitly from a word
problem.
I can construct an
exponential function
DCA Erie 1 BOCES
Mathematics: 2012 - 2013
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
Rigorous Sample Tasks
F-BF.3. Identify the effect on the
graph of replacing f(x) by f(x) + k, k
f(x), f(kx), and f(x + k) for specific
values of k (both positive and
negative); find the value of k given
the graphs. Experiment with cases
and illustrate an explanation of the
effects on the graph using
technology. Include recognizing even
and odd functions from their graphs
and algebraic expressions for them.
(10%)
Updated on: 3/1/2013
CCLS Algebra
recursively from a word
problem.
I can construct a linear
function explicitly from a
word problem.
I can construct a linear
function recursively from a
word problem.
I can construct a quadratic
function explicitly from a
word problem.
I can construct a quadratic
function recursively from a
word problem.
Scaffolded sample tasks
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Shifts of graphs
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I can identify the parent
function of a linear,
quadratic, absolute value,
or exponential function.
I can identify the shift of
the graph of a linear,
quadratic, absolute value
or exponential function.
I can graph the shift of a
function as a translation of
the parent function.
I can create the equation
for the graph after its
translation.
I can identify the vertex
DCA Erie 1 BOCES
Mathematics: 2012 - 2013
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Rigorous Sample Tasks
F-LE.3. Observe using graphs and
tables that a quantity increasing
exponentially eventually exceeds a
quantity increasing linearly,
quadratically, or (more generally) as
a polynomial function.
(20%)
Updated on: 3/1/2013
CCLS Algebra
point of a function (if
applicable).
I can explain the effects of
the shifts of graphs using
my calculator. This
includes square root, cube
root, piece-wise, step, and
absolute value functions.
I can compare the parent
function to the function
that has been shifted.
I can identify the
translation of a function
from the graph and write
the function algebraically.
Scaffolded sample tasks
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Comparing growth of functions
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I can compare and
contrast linear growth to
exponential growth to
quadratic growth from a
graph.
I can compare and
contrast linear growth to
exponential growth to
quadratic growth from a
table.
I can explain why
exponential models
continue to grow/decay
more rapidly than linear or
DCA Erie 1 BOCES
Mathematics: 2012 - 2013
CCLS Algebra
Updated on: 3/1/2013
quadratic models.
Rigorous Sample Tasks
Scaffolded sample tasks