# Stepping to the Greatest Integer: The Greatest Integer Function

Recommended for High School.

## Introduction

Not all mathematical functions have smooth, continuous graphs. In fact, some of the most interesting functions contain jumps and gaps. One such function is called the *greatest integer function*, written as *y * = int *x*. It is defined as the greatest integer of* x *equals the greatest integer less than or equal to *x*. For example, int 4.2 = 4 and int 4 = 4, while int 3.99999 = 3.

In this activity, you will create a function similar to the greatest integer function graph by having a group of students stand in a line in front of a Motion Detector and then step aside one by one. The equation for this graph, in the general form, is

You can find appropriate values for the parameters *A*, *B*, and *C* so that the model fits the data.

## Objectives

- Use a Motion Detector to collect position data showing evenly-spaced jumps in value.
- Model the position data using the greatest integer function.

## Sensors and Equipment

This activity features the following Vernier sensors and equipment.

### Option 1

### Option 2

### Additional Requirements

You may also need an interface and software for data collection. What do I need for data collection?

## Standards Correlations

See all standards correlations for *Real-World Math with Vernier* »