Connecting Representations of Functions

In this lesson, the study of functions focuses on relationships in meaningful contexts and is presented through multiple methods of representations examining these relationships. An emphasis is placed on connecting representations of functions (tables, patterns and sequences, student-drawn scatter plots and line graphs, technology-assisted graphs, functions as equations) so that each can provide a different picture of the relationship.

Background

Seven periods of instruction; each period is based on 45 minutes.

Rationale

The concept of function is one of the big ideas in all of mathematics. In the past, a study of functions was relegated to Algebra I courses. Algebra I is typically offered in Grade 8 or 9, and not all students take it. In today's world, it is important that all students develop algebraic reasoning, especially with regard to functions. Principles and Standards for School Mathematics (NCTM) suggests that function concepts should be integrated throughout the middle school program rather than relegated to an algebra course.

The study of functions should focus on relationships in meaningful contexts and be presented through multiple methods of representing and examining these relationships. An emphasis should be placed on connecting representations of functions (tables, patterns and sequences, student-drawn scatter plots and line graphs, technology-assisted graphs, functions as equations) so that each can provide a different picture of the relationship. Technology can aid in this.

Reference

Van de Walle, John A. (2001). Elementary and Middle School Mathematics: Teaching Developmentally (4th ed.). Addison Wesley.

Standards (Grades 6-8)

Patterns, Functions and Algebra Standard

  • Represent, analyze and generalize a variety of patterns and functions with tables, graphs, words and symbolic rules.
  • Relate and compare different forms of representation for a relationship.
  • Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations.
  • Use mathematical models to represent and understand quantitative relationships.
  • Model and solve contextualized problems using various representations, such as graphs, tables, and equations.

Tools/Resources

  • Calculator Based Ranger (CBR)
  • TI-82 or TI-83 Graphing Calculator (http://mason.gmu.edu/~mmankus/ti83/inform.htm)
  • Projection device
  • Presentation computer connected to projection device
  • Spreadsheet software, presentation software, word processing software
  • Internet connectivity for a minimum of four student workstations, one instructor station