Definition of Function

Vocabulary development becomes essential in a mathematics classroom that focuses on the Common Core Standards for Mathematical Practice of attending to precision (SMP.6). In order for math students to communicate precisely to others, they must use clear definitions in their discussion and reasoning. And then subsequently, students can use their vocabulary in constructing arguments (SMP.3).

One strategy for vocabulary development involves the teacher telling a story that involves the new term. Use the Vending Machine Saga to help students determine if the machine is functioning properly for each transaction. (We are working under the assumption that if a product type is unavailable then the machine returns your dollar in exact change; therefore, no transaction has occurred for our review.)

Concrete Function Story Expands to Abstract

Another effective vocabulary strategy is engaging students in an activity that helps students add to their knowledge of the term. Present students with a two-column example/counterexample description. Provide think time for each student to generate facts or characteristics consistent with the term. Have students use the RoundRobin structure to share their pieces of a definition. With each rotation the team forms and refines a definition to present to the class. Once the teams reach consensus, the teacher and class discuss samples to develop a class definition. The final definition, examples, and counterexamples can be recorded in a Frayer Model template. Or the examples and counterexamples can be used as a card sort in an interactive student notebook.

Definition of Function

Although students investigate linear functions in MATH-8, the conceptual definition of a function is most critical for success with using function notation and finding an inverse function in Algebra 1. This investigation highlights Common Core State Standard 8.F.A.1 that is included in MATH-8 and Accelerated Algebra 1.