FUNCTIONS: RATE OF CHANGE
Grade 7
INTERPRETING FUNCTIONS
Interpret functions in applications
Relationship
Describe the rate of change in one variable as
between variables another variable increases/decreases for linear
functions including unit rate.
Grade 8
Algebra
Beyond
Describe the rate of change in one variable as
another variable increases/decreases for
exponential, quadratic and inverse variation
functions and relationships over an interval.
Describe the rate of change in one variable as
another variable increases/decreases for
polynomial (cubic) and root functions and
relationships over an interval.
Identify and interpret the key
features of a function from it’s
graph or it’s equation(s).
Find and interpret the average rate
of change of a function over a given
interval.
a. Understand, estimate, calculate, and
interpret rate of change for horizontal,
vertical, and perpendicular lines as
represented in and among tables, graphs,
equations, and related contexts
(mathematical and real world).
Understand which transformations
preserve rate of change and which do
not.
INTERPRETING FUNCTIONS
Analyze functions with different representations
Multiple
a. Understand, estimate, calculate, and
representations &
interpret rate of change (constant) in linear
Connections
patterns as represented in and among tables
(points), graphs, equations (recursive
and/or explicit), and related mathematical
and real world contexts (e.g., ratios and
rates) described in words.
b. Understand that when the first differences
of consecutive y values are constant the
function is linear.
c. Make sense of first differences (linear
relationship) as seen in both recursive and
explicit representations and make
connections between the two
representations.
BUILDING FUNCTIONS
Building a function that models a relationship between two quantities
Modeling
Create and use a table, graph, words and/or
equation (recursive and/or explicit) to analyze
linear functions given the rate of change and/or
pairs of values for various contexts
(mathematical and real world) and the reverse
(i.e., given the graph identify a context, rate of
change, etc.)
FUNCTIONS: Rate of Change w/Quadratic
Version 3.0 March 7, 2011
a. Understand, estimate, calculate, and
interpret rate of change for parallel,
overlapping, and intersecting lines as
represented in and among tables, graphs,
equations (recursive and explicit), and
related contexts (mathematical and real
world) with respect to systems of equations
described in words.
b. Understand that when the second
differences of consecutive y values are
constant (non-zero) a function is quadratic.
b. Understand that finding the point where
the differences of consecutive values of
f(x) are constant (non-zero) determines
the degree of a polynomial.
c. Make sense of a constant factor
(exponential relationships) as seen in both
recursive and explicit representations and
make connections between the two
representations.
Recognize the rate of change features in linear
and other basic functions (e.g., circumference
and area of a circle or volume of sphere) in
problem context and represent them using
tables, graphs, words, and formulas.
Interpret the slope of a linear regression line.
BUILDING FUNCTIONS
Building a function that models a relationship between two quantities
Proportionality
Understand and recognize directly proportional
relationships as a special case of linear
relationships and as it relates to rate of change
and y-intercept and, how graphs, tables,
equations and related contexts (mathematical
and real world) described in words reflect these
differences.
Recognize and understand the characteristics of
inversely proportional relationships as they
appear in contextual, graphic, numeric, and
symbolic representations.
LINEAR AND EXPONENTIAL MODELS
Construct and compare linear and exponential models and solve problems
Relationship
Compare and contrast the rate of change among Compare and contrast the rate of change in
between and
various linear functions and with other nonlinear functions with exponential, quadratic,
among functions
linear functions and relations (e.g., y=k/x or
inverse variation functions and relations as
change in area vs. perimeter) as represented in
tables, graphs, equations (recursive and/or
explicit) and related contexts (mathematical and
real world) described in words.
FUNCTIONS: Rate of Change w/Quadratic
Version 3.0 March 7, 2011
represented in tables, graphs, equations
(recursive and/or explicit) and related contexts
(mathematical and real world) described in
words.
Compare and contrast estimated rate
of change/slope over specific
intervals for nonlinear functions using
linear approximations.