Vernier Software and Technology
Vernier Software & Technology

Stepping to the Greatest Integer: The Greatest Integer Function

Figure from experiment 31 from Real-World Math with Vernier

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

{\text{y  =  A int (Bx)  +  C}}

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 »

Real-World Math with Vernier

See other experiments from the lab book.

1Walk the Line - Straight Line Distance Graphs
2Making Cents of Math: Linear Relationship between Weight and Quantity
3Pool Plunge - Linear Relationship between Water Depth and Pressure
4Funnel Volumes - Volume and Weight
5Keep It Bottled Up - Rates of Pressure Increase
6Mix It Up - Mixing Liquids of Different Temperatures
7Spring Thing - Newton's Second Law
8Stretch It to the Limit - The Linear Force Relation for a Rubber Band
9What Goes Up - Position and Time for a Cart on a Ramp
10That's the Way the Ball Bounces - Height and Time for a Bouncing Ball
11Walk This Way - Definition of Rate
12Velocity Test - Interpreting Graphs
13From Here to There - Applications of the Distance Formula
14Under Pressure - The Inverse Relationship between Pressure and Volume
15Light at A Distance - Distance and Intensity
16Chill Out: How Hot Objects Cool
17Charging Up, Charging Down - Charging a Capacitor
18Bounce Back - The Pattern of Rebound Heights
19Sour Chemistry - The Exponential pH Change
20Swinging Ellipses - Plotting an Ellipse
21Lights Out! - Periodic Phenomena
22Tic, Toc: Pendulum Motion
23Stay Tuned: Sound Waveform Models
24Up And Down: Damped Harmonic Motion
25How Tall? Describing Data with Statistical Plots
26And Now, the Weather - Describing Data with Statistics
27Meet You at the Intersection: Solving a System of Linear Equations
28Titration Curves: An Application of the Logistic Function
29Clock Design: Period and Length of a Simple Pendulum
30Graph It in Pieces: Piecewise Defined Functions
31Stepping to the Greatest Integer: The Greatest Integer Function
32Crawling Around: Parametric Plots

Activity 31 from Real-World Math with Vernier Lab Book

<i>Real-World Math with Vernier</i> book cover

Included in the Lab Book

Vernier lab books include word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.

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