Sharp Math
Functions
Standard
M-F-1
6th Grade
Standard
N/A
7th Grade
Standard
N/A
8th Grade
Standard
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
Teacher Target
Teacher Target
Teacher Target
Student Target
Student Target
Student Target
I can define inspection. (K)
I can identify cases in which a
system of two equations in two
unknowns has no solution. (K)
I can solve a system of two
equations (linear) in two
unknown algebraically. (K)
I can solve simple cases of
systems of two linear equations
in two variables by inspection.
(K)
M-F-2
Standard Demonstrator
Standard Demonstrator
Standard
Standard
I can estimate the point(s) of
intersection for a system of two
equations in two unknowns by
graphing the equations. (R)
Standard Demonstrator
Standard
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.
Teacher Target
Teacher Target
Teacher Target
Student Target
Student Target
Student Target
I can identify functions
algebraically including slope and
y intercept. (K)
I can identify functions using
graphs. (K)
I can identify functions using
tables. (K)
I can identify functions using
verbal descriptions. (K)
I can compare and contrast
functions with different
representations. (R)
I can draw conclusions based on
different representations of
functions. (R)
M-F-3
Standard Demonstrator
Standard Demonstrator
Standard Demonstrator
Standard
Standard
Standard
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 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.
Teacher Target
Teacher Target
Teacher Target
Student Target
Student Target
Student Target
I can determine that a linear
function is graphed as a straight
line. (K)
I can explain that the equation
y=mx+b is the equation of a
function whose graph is a
straight line where m is the
slope and b is the y-intercept.
(K)
I can provide examples of
nonlinear functions using
multiple representations. (K)
M-F-4
I can compare the characteristics
of linear and nonlinear functions
using various representations.
(R)
Standard Demonstrator
Standard Demonstrator
Standard Demonstrator
Standard
Standard
Standard
Construct a function to model a
linear relationship between two
quantities. Determine the rate
of change and initial value of
the function from a description
of a relationship or from two (x,
y) values, including reading
these from a table or from a
graph. Interpret the rate of
change and initial value of a
linear function in terms of the
situation it models, and in terms
of its graph or a table of values.
Teacher Target
Teacher Target
Teacher Target
Student Target
Student Target
Student Target
I can recognize that slope is
determined by the constant rate
of change. (K)
I can recognize that the y
intercept is the initial value
where x=0. (K)
I can determine the rate of
change from two (x,y) values, a
verbal description, values in a
table, or graph. (K)
I can construct a function to
model a linear relationship
between tow quantities. (R)
I can relate the rate of change
and initial value to real world
quantities in a linear function in
terms of the situation modeled
and in terms of its graph or a
table of values. (R)
M-F-5
Standard Demonstrator
Standard Demonstrator
Standard Demonstrator
Standard
Standard
Standard
Describe qualitatively the
functional relationship between
two quantities by analyzing a
graph (e.g., where the function
is increasing or decreasing,
linear or nonlinear). Sketch a
graph that exhibits the
qualitative features of a function
that has been described
verbally.
Teacher Target
Teacher Target
Teacher Target
Student Target
Student Target
Student Target
I can analyze a graph and
describe the functional
relationship between two
quantities using the qualities of
the graph. (K)
I can sketch a graph given a
verbal description of its
qualitative features. (K)
I can interpret the relationship
between x and y values by
analyzing a graph. (R)
Standard Demonstrator
Standard Demonstrator
Standard Demonstrator