Step Functions

Topic: Step Functions

Objectives & Outcomes

• learners will be able to define step functions and describe their properties, including the fact that they are discontinuous, monotonic, and increasing or decreasing depending on the values of their arguments.

Materials

• whiteboard and markers
• handouts with examples of step functions

Warm-up

• Ask students if they have ever heard of step functions before.
• Ask them to describe what they know about step functions.
• Write their responses on the whiteboard.

Introduction

• Introduce the concept of step functions as functions that take on a value of zero for any argument that is less than or equal to a specified value, and a non-zero value for any argument that is greater than or equal to the specified value.
• Give an example of a step function, f(x) = {0, x < 5; 3, x > 5} and graph it on the whiteboard.
• Ask students to explain what they notice about the graph.

Direct Instruction

• Review the definition of a step function, and then introduce the concept of a vertical step function, which is a step function where the specified value is equal to zero.
• Give an example of a vertical step function, f(x) = {0, x < 0; 3, x = 0} and graph it on the whiteboard.
• Ask students to explain what they notice about the graph.
• Introduce the concept of a horizontal step function, which is a step function where the specified value is equal to a non-zero value.
• Give an example of a horizontal step function, f(x) = {1, x < 1; 3, x = 1} and graph it on the whiteboard.
• Ask students to explain what they notice about the graph.

Guided Practice

• Divide the class into small groups.
• Give each group a set of values for a parameter of the step function, and ask them to solve for the corresponding value of the function.
• Have each group present their solution to the class, and discuss as a class what they noticed about the graphs of their step functions.

Independent Practice

• Give each student a worksheet with a step function problem to solve.
• Ask them to solve the problem independently, and write the solution on the worksheet.
• Have them work on this activity for several minutes, then have them swap their worksheets with a partner and check each other's solutions.

Closure

• Review the concept of step functions and how to graph them.
• Ask students to give examples of step functions and explain how they work.
• Remind them that step functions can have either positive or negative values, depending on the input.

Assessment

• Collect and grade the projects for understanding of the concept.
• Use the class discussions and participation in the group work activity as a form of assessment.