Exploring Direct Proportionality

In this activity we aim at experiencing a direct proportionality function with OZOBOT. This activity focuses on two main topics:

1. Calibration of a measuring instrument

2. Physical meaning of a mathematical function

Material:

OZOBOT

Graph paper

Black felt tip pen

Procedure:

STEP 1 – Building the function

In this step you’ll set OZOBOT in order to have a fixed relationship between a length and the time OZOBOT takes to complete it.

1. Write a code to program OZOBOT to follow line with constant speed. Transfer the code on OZOBOT.

2. Draw a straight line on graph paper.

3. Measure the distance covered by OZOBOT in various time periods, repeating the measurements various time for each period.

4. Plot the distance vs. time graph, calculate the actual OZOBOT’s speed and write the distance as function of the time.

STEP 2 – Verifying the function

In this step you’ll verify if the mathematical function you’ve found works and how much the calibration you have done is sound.

1. Decide a time duration, and predict (basing on the function you’ve found) the distance OZOBOT will cover during that time.

2. Run OZOBOT on the straight line and measure the distance it covers.

3. Repeat for various time durations. Make the experiment for durations inside and outside the range you’ve used in step 1: is the accuracy of your prediction constant?

Extensions

Set OZOBOT with a different speed. What happens to the accuracy of your predictions?