Instructional Alignment Chart (8-HS)
Domain: Functions
A. Cluster for Grade/Course
8.IF.A: Define, evaluate, and compare
functions.(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.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.
(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 = s2 giving the
area of a square as a function f 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.
B. Cluster for Grade/Course
C. Cluster for Grade/Course:
F.IF.C Analyze functions using different
representations (Algebra 1 as defined by
PARCC)
F.IF.C Analyze functions using different
representations (Algebra 2 as defined by
PARCC)
7. Graph functions expressed symbolically
and show key features of the graph, by hand
in simple cases and using technology for
more complicated cases. a. Graph linear and
quadratic functions and show intercepts,
maxima, and minima. b. Graph square root,
cube root, and piecewise-defined functions,
including step functions and absolute value
functions.
7. Graph functions expressed symbolically
and show key features of the graph, by hand
in simple cases and using technology for more
complicated cases. c. Graph polynomial
functions, identifying zeros when suitable
factorizations are available, and showing end
behavior. d. (+) Graph rational functions,
identifying zeros and asymptotes when
suitable factorizations are available, and
showing end behavior. (Pre-Calc) e. Graph
exponential and logarithmic functions,
showing intercepts and end behavior, and
trigonometric functions, showing period,
midline, and amplitude.
8. Write a function defined by an expression
in different but equivalent forms to reveal
and explain different properties of the
function. 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.
D.
8. Write a function defined by an expression
in different but equivalent forms to reveal and
explain different properties of the function. b.
Use the properties of exponents to interpret
expressions for exponential functions. For
example, identify percent rate of change in
functions such as y = (1.02)t, y = (0.97)t, y =
(1.01)12t, y = (1.2)t/10, and classify them as
representing exponential growth or decay.
E. Changes
Linear functions-mastery at 8th
Linear, quadratic, exponential-mastery at
Alg 1
Factoring/completing the square at Alg 1
Describe other types of functions in terms of
input, output, context
Graph other functions and manipulate
expressions to describe function behavior
Polynomials, zeros, factorizing, end behaviors
Exponential, trigonometric, and logarithmic—
intercepts, end behaviors, period, midline, and
amplitude
Percent of change
F. Levels of Instruction (Eighth Grade)
Provide Developmental and Reinforcement Activities
Linear functions
G. Implications for Instruction and Assessment (Eighth Grade)
How activities are structured to promote mathematical practices
Tasks need to support conceptual understanding and real world applications
Adapted from A Study of the Common Core State Standards developed by the Charles A. Dana Center at the University of Texas
at Austin
Instructional Alignment Chart (8-HS)
Domain: Functions
A. Cluster for Grade/Course
8.IF.A: Define, evaluate, and compare
functions.(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.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.
(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 = s2 giving the
area of a square as a function f 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.
B. Cluster for Grade/Course
C. Cluster for Grade/Course:
F.IF.C Analyze functions using different
representations (Algebra 1 as defined by
PARCC)
F.IF.C Analyze functions using different
representations (Algebra 2 as defined by
PARCC)
7. Graph functions expressed symbolically
and show key features of the graph, by hand
in simple cases and using technology for
more complicated cases. a. Graph linear and
quadratic functions and show intercepts,
maxima, and minima. b. Graph square root,
cube root, and piecewise-defined functions,
including step functions and absolute value
functions.
7. Graph functions expressed symbolically
and show key features of the graph, by hand
in simple cases and using technology for more
complicated cases. c. Graph polynomial
functions, identifying zeros when suitable
factorizations are available, and showing end
behavior. d. (+) Graph rational functions,
identifying zeros and asymptotes when
suitable factorizations are available, and
showing end behavior. (Pre-Calc) e. Graph
exponential and logarithmic functions,
showing intercepts and end behavior, and
trigonometric functions, showing period,
midline, and amplitude.
8. Write a function defined by an expression
in different but equivalent forms to reveal
and explain different properties of the
function. 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.
D.
8. Write a function defined by an expression
in different but equivalent forms to reveal and
explain different properties of the function. b.
Use the properties of exponents to interpret
expressions for exponential functions. For
example, identify percent rate of change in
functions such as y = (1.02)t, y = (0.97)t, y =
(1.01)12t, y = (1.2)t/10, and classify them as
representing exponential growth or decay.
E. Changes
Linear functions-mastery at 8th
Linear, quadratic, exponential-mastery at
Alg 1
Factoring/completing the square at Alg 1
Describe other types of functions in terms of
input, output, context
Graph other functions and manipulate
expressions to describe function behavior
Polynomials, zeros, factorizing, end behaviors
Exponential, trigonometric, and logarithmic—
intercepts, end behaviors, period, midline, and
amplitude
Percent of change
F. Levels of Instruction (Algebra 1)
Provide Developmental Activities
Factoring and completing the square
Provide Developmental and Reinforcement Activities
Square root, cube root, piecewise and absolute value
Quadratic Functions
Provide Drill and Practice Activities
Linear functions
G. Implications for Instruction and Assessment (Algebra 1)
Build on existing knowledge of linear functions developed in 8th grade
Use what they know about distributing, factoring, and properties of equality to change forms
How activities are structured to promote mathematical practices
Tasks need to support conceptual understanding and real world applications
Adapted from A Study of the Common Core State Standards developed by the Charles A. Dana Center at the University of Texas
at Austin
Instructional Alignment Chart (8-HS)
Domain: Functions
A. Cluster for Grade/Course
8.IF.A: Define, evaluate, and compare
functions.(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.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.
(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 = s2 giving the
area of a square as a function f 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.
B. Cluster for Grade/Course
C. Cluster for Grade/Course:
F.IF.C Analyze functions using different
representations (Algebra 1 as defined by
PARCC)
F.IF.C Analyze functions using different
representations (Algebra 2 as defined by
PARCC)
7. Graph functions expressed symbolically
and show key features of the graph, by hand
in simple cases and using technology for
more complicated cases. a. Graph linear and
quadratic functions and show intercepts,
maxima, and minima. b. Graph square root,
cube root, and piecewise-defined functions,
including step functions and absolute value
functions.
7. Graph functions expressed symbolically
and show key features of the graph, by hand
in simple cases and using technology for more
complicated cases. c. Graph polynomial
functions, identifying zeros when suitable
factorizations are available, and showing end
behavior. d. (+) Graph rational functions,
identifying zeros and asymptotes when
suitable factorizations are available, and
showing end behavior. (Pre-Calc) e. Graph
exponential and logarithmic functions,
showing intercepts and end behavior, and
trigonometric functions, showing period,
midline, and amplitude.
8. Write a function defined by an expression
in different but equivalent forms to reveal
and explain different properties of the
function. 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.
D.
8. Write a function defined by an expression
in different but equivalent forms to reveal and
explain different properties of the function. b.
Use the properties of exponents to interpret
expressions for exponential functions. For
example, identify percent rate of change in
functions such as y = (1.02)t, y = (0.97)t, y =
(1.01)12t, y = (1.2)t/10, and classify them as
representing exponential growth or decay.
E. Changes
Linear functions-mastery at 8th
Linear, quadratic, exponential-mastery at
Alg 1
Factoring/completing the square at Alg 1
Describe other types of functions in terms of
input, output, context
Graph other functions and manipulate
expressions to describe function behavior
Polynomials, zeros, factorizing, end behaviors
Exponential, trigonometric, and logarithmic—
intercepts, end behaviors, period, midline, and
amplitude
Percent of change
F. Levels of Instruction (Algebra 2)
Provide Developmental Activities
Polynomial, exponential logarithmic, and trigonometric functions
Provide Developmental and Reinforcement Activities
Square root, cube root, piecewise and absolute value
Quadratic Functions
Provide Drill and Practice Activities
Linear and Quadratic functions
G. Implications for Instruction and Assessment (Algebra 2)
Build on existing knowledge of linear functions developed in 8th grade
Use what they know about distributing, factoring, and properties of equality to change forms
How activities are structured to promote mathematical practices
Tasks need to support conceptual understanding and real world applications
Adapted from A Study of the Common Core State Standards developed by the Charles A. Dana Center at the University of Texas
at Austin
Instructional Alignment Chart (8-HS)
Adapted from A Study of the Common Core State Standards developed by the Charles A. Dana Center at the University of Texas
at Austin