Function and Algebra Concepts
Elementary School
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 non-linear 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.

Middle School
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.

High School
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.