Ohio's Academic Content Standards in Mathematics

Patterns, Functions and Algebra Standard
Students use patterns, relations and functions to model, represent and analyze problem situations that involve variable quantities. Students analyze, model and solve problems using various representations such as tables, graphs and equations.

By the end of the K - 2 program:

A.  Sort, classify and order objects by size, number and other properties, and describe the attributes used. (ORC Resources) B.  Extend sequences of sounds and shapes or simple number patterns, and create and record similar patterns. (ORC Resources) C.  Create and extend patterns, and describe the rule in words. (ORC Resources) D.  Model problem situations, using objects, pictures, numbers and other symbols. (ORC Resources) E.  Solve open sentences and explain strategies. (ORC Resources) F.  Represent an unknown quantity as a variable using a symbol, such as , , . (ORC Resources) G.  Describe and compare qualitative and quantitative changes. (ORC Resources)

By the end of the 3 - 4 program:

A.  Analyze and extend patterns, and describe the rule in words. (ORC Resources) B.  Use patterns to make predictions, identify relationships, and solve problems. (ORC Resources) C.  Write and solve open sentences and explain strategies. (ORC Resources) D.  Represent an unknown quantity as a variable using a symbol, including letters. (ORC Resources) E.  Use variables to create and solve equations representing problem situations. (ORC Resources) F.  Construct and use a table of values to solve problems associated with mathematical relationships. (ORC Resources) G.  Describe how a change in one variable affects the value of a related variable. (ORC Resources)

By the end of the 5 - 7 program:

A.  Describe, extend and determine the rule for patterns and relationships occurring in numeric patterns, computation, geometry, graphs and other applications. (ORC Resources) B.  Represent, analyze and generalize a variety of patterns and functions with tables, graphs, words and symbolic rules. (ORC Resources) C.  Use variables to create and solve equations and inequalities representing problem situations. (ORC Resources) D.  Use symbolic algebra to represent and explain mathematical relationships. (ORC Resources) E.  Use rules and variables to describe patterns, functions and other relationships (ORC Resources) F.  Use representations, such as tables, graphs and equations, to model situations and to solve problems, especially those that involve linear relationships. (ORC Resources) G.  Write, simplify and evaluate algebraic expressions. (ORC Resources) H.  Solve linear equations and inequalities symbolically, graphically and numerically. (ORC Resources) I.  Explain how inverse operations are used to solve linear equations. (ORC Resources) J.  Use formulas in problem-solving situations. (ORC Resources) K.  Graph linear equations and inequalities. (ORC Resources) L.  Analyze functional relationships, and explain how a change in one quantity results in a change in the other. (ORC Resources) M.  Approximate and interpret rates of change from graphical and numerical data. (ORC Resources)

By the end of the 8 - 10 program:

A.  Generalize and explain patterns and sequences in order to find the next term and the nth term. (ORC Resources) B.  Identify and classify functions as linear or nonlinear, and contrast their properties using tables, graphs or equations. (ORC Resources) C.  Translate information from one representation (words, table, graph or equation) to another representation of a relation or function. (ORC Resources) D.  Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations. (ORC Resources) E.  Analyze and compare functions and their graphs using attributes, such as rates of change, intercepts and zeros. (ORC Resources) F.  Solve and graph linear equations and inequalities. (ORC Resources) G.  Solve quadratic equations with real roots by graphing, formula and factoring. (ORC Resources) H.  Solve systems of linear equations involving two variables graphically and symbolically. (ORC Resources) I.  Model and solve problem situations involving direct and inverse variation. (ORC Resources) J.  Describe and interpret rates of change from graphical and numerical data. (ORC Resources)

By the end of the 11 - 12 program:

A.  Analyze functions by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior. (ORC Resources) B.  Use the quadratic formula to solve quadratic equations that have complex roots. (ORC Resources) C.  Use recursive functions to model and solve problems; e.g., home mortgages, annuities. (ORC Resources) D.  Apply algebraic methods to represent and generalize problem situations involving vectors and matrices. (ORC Resources)