Instructional Setting/Audience

The instructional setting included six ninth grade algebra classrooms in a small rural high school in West Virginia. The population is just over 60% low socioeconomic, with 99.9% of the population being Caucasian. Class sizes range from 8 students for support classes to 19 for honors instruction. Class periods are 50 minutes, except for the support classes which are block scheduled. Students are sectioned into classes based on their performance on the previous year’s summative assessment and year-end grade point averages.

Performance Objectives

Task 1.0 – Understand the Concept of a Function
  • 1.1 – Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range.
  • 1.2 – Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
Performance Objective 1:   Given a graph, Algebra 1 students will be able to describe a function in terms of its name, domain and range, with 80% accuracy.
Task 2.0 – Interpret functions that arise in applications in terms of the context.
  • 2.1 – For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
  • 2.2 - Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
  • 2.3 - Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Performance Objective 2:  Given various representations of functions (graphs, tables, equations or word problems), Algebra 1 students will be able to represent the domain of various functions with 80% accuracy.
 
Task 3.0 - Analyze functions using different representations.
  • 3.1 - Graph functions expressed symbolically and show key features of the graph either by hand or with the use of a graphing calculator.
  • 3.2 - Write a function defined by an expression in different but equivalent forms.
  • 3.3 - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
 Performance Objective 3:  Given various representations of functions (graphs, tables, number lines, verbal descriptions and symbols), Algebra 1 students will be able to compare properties of two linear functions when given in two different forms with 80% accuracy.