Common Core State Standards for Mathematics
Standards for Mathematical Practice
Look for and make use of structure.
Define, evaluate, and compare functions.
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.
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.
Use functions to model relationships between quantities.
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.
Ohio Mathematics Academic Content Standards (2001)
Patterns, Functions and Algebra Standard
Represent, analyze and generalize a variety of patterns and functions with tables, graphs, words and symbolic rules.
Use rules and variables to describe patterns, functions and other relationships
Analyze functional relationships, and explain how a change in one quantity results in a change in the other.
Translate information from one representation (words, table, graph or equation) to another representation of a relation or function.
Describe and interpret rates of change from graphical and numerical data.
Grade Level Indicators (Grade 6)
Use words and symbols to describe numerical and geometric patterns, rules and functions.
Grade Level Indicators (Grade 7)
Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable expressions.
Analyze linear and simple nonlinear relationships to explain how a change in one variable results in the change of another.
Grade Level Indicators (Grade 8)
Relate the various representations of a relationship; i.e., relate a table to graph, description and symbolic form.
Grade Level Indicators (Grade 9)
Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations.
Principles and Standards for School Mathematics
Represent and analyze mathematical situations and structures using algebraic symbols
develop an initial conceptual understanding of different uses of variables;
explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope;
use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships;