Exploring Inverse Proportionality

In this activity we aim at experiencing an inverse 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 – Calibrating OZOBOT

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. Draw on graph paper calibrated segments of various lengths.

2. Write a code to program OZOBOT to follow line with constant speed (or use it without any code). Transfer the code on OZOBOT.

3. Measure time needed to complete the different segments, repeating the measurements various time for each length.

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

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. Draw on graph paper segments of various lengths, other than ones used in step 1.

2. Basing on the function you’ve found in step 1, predict the time OZOBOT takes to cover each segment.

3. Measure the time OZOBOT takes to complete each segment: which is the agreement with your predictions?

Extensions

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