The student produces evidence that demonstrates
understanding of function and algebra concepts; that is, the student:
a
Uses linear patterns to solve problems; that
is: 
• 
shows how one quantity determines another in a linear
(“repeating”) pattern, i.e., describes, extends, and recognizes
the linear pattern by its rule, such as, the total number of legs
on a given number of horses can be calculated by counting by fours; 
• 
shows how one quantity determines another quantity in a functional
relationship based on a linear pattern, e.g., for the “number
of people and total number of eyes,” figure out how many eyes
100 people have all together. 
b
Builds iterations of simple nonlinear patterns,
including multiplicative and squaring patterns (e.g., “growing”
patterns) with concrete materials, and recognizes that these patterns
are not linear.
c
Uses the understanding that an equality relationship
between two quantities remains the same as long as the same change is
made to both quantities.
d
Uses letters, boxes, or other symbols to stand
for any number, measured quantity, or object in simple situations with
concrete materials, i.e., demonstrates understanding and use of a beginning
concept of a variable.
The student produces evidence that demonstrates
understanding of function and algebra concepts; that is, the student:
a
Discovers, describes, and generalizes patterns,
including linear, exponential, and simple quadratic relationships, i.e.,
those of the form f(n)=n2 or f(n)=cn2, for constant c, including A=r2,
and represents them with variables and expressions.
b
Represents relationships with tables, graphs in
the coordinate plane, and verbal or symbolic rules.
c
Analyzes tables, graphs, and rules to determine
functional relationships.
d
Finds solutions for unknown quantities in linear
equations and in simple equations and inequalities.
The student produces evidence that demonstrates
understanding of function and algebra concepts; that is, the student:
a
Models given situations with formulas and functions,
and interprets given formulas and functions in terms of situations.
b
Describes, generalizes, and uses basic types of
functions: linear, exponential, power, rational, square and square root,
and cube and cube root.
c
Utilizes the concepts of slope, evaluation, and
inverse in working with functions.
d
Works with rates of many kinds, expressed numerically,
symbolically, and graphically.
e
Represents constant rates as the slope of a straight
line graph, and interprets slope as the amount of one quantity (y) per
unit amount of another (x).
f
Understands and uses linear functions as a mathematical
representation of proportional relationships.
g
Uses arithmetic sequences and geometric sequences
and their sums, and sees these as the discrete forms of linear and exponential
functions, respectively.
h
Defines, uses, and manipulates expressions involving
variables, parameters, constants, and unknowns in work with formulas,
functions, equations, and inequalities.
i
Represents functional relationships in formulas,
tables, and graphs, and translates between pairs of these.
j
Solves equations symbolically, graphically, and
numerically, especially linear, quadratic, and exponential equations;
and knows how to use the quadratic formula for solving quadratic equations.
k
Makes predictions by interpolating or extrapolating
from given data or a given graph.
l
Understands the basic algebraic structure of number
systems.
m
Uses equations to represent curves such as lines,
circles, and parabolas.
n
Uses technology such as graphics calculators to
represent and analyze functions and their graphs.
o
Uses functions to analyze patterns and represent
their structure.
