# Exploring Rates of Change

This summer I rented a car whose dashboard gave information that I knew would work well for this class. A picture below will prompt your teacher brain as well I think.

I took six such photos during the course of my trip. Tomorrow, I intend to give each of my groups of students (I have them in groups of three) three of the pictures. I’ll scramble them up a bit so different groups should have different subsets of the data. I intend to ask them some pretty simple questions that should generate some good conversations. I want to ask them the following questions:

1. What was my average speed between any of the two pictures? (So each group should have three answers for this)
2. Can you determine my maximum velocity in that time interval?
3. I want to raise the average to 42 MPH. How far would I have to travel at 60 MPH for this to happen?

These are not terribly deep questions, but they feel rooted in an example of real world data (I was inspired by Denis Sheeran’s wonderful bookÂ Instant Relevance for this data driven experiment) I also think that this will continue to scratch at the itch that will make the breakthrough of being able to find the IROC feel more meaningful.

I have all the photos together in a WORD doc on my dropbox. You can find that file here. I would love to hear any clever ideas about how to play with these images/this data.

## 2 thoughts on “Exploring Rates of Change”

1. Seems like there is an opportunity to ask some informal mvt based questions here, and push at these ideas:
what can you deduce/not deduce from discrete data?
The idea that you iroc is continuous. (What situation could produce a non continuous roc? Maybe students could chew on that for a bit)
Even if you don’t go all those places this time, you should be able to return to this context to flesh out understanding throughout the year.

Nice start!

1. Leanne

Thanks for dropping by and sharing some ideas. We have not named MVT yet, but we have already touched upon it. Once I reassured the students that all pictures were taken while the car was at rest, they realized that I must have exceeded the intervals AROC at some instant. A follow up post will highlight some of the good questions that came up.