Scenario:
I thought I was being clever with this hands-on investigation of the Intersecting Chord Theorem.

It was a fail. There wasn't enough curiousity, the measurements were so all over the place that no quantitative regularity could be found to make a conjecture.

I had the students but a giant X through the front and and turn the paper over.

I asked them to make a grid with six columns and 5 rows.

Then I turned on the projector and trotted over to Geogebra.


I asked the students to make a column for BF, FD, CF, FE. Ss "Ms. Z there are 6 columns." Me: "I know, try your best to ignore them for the moment."

Nothing much interesting happened until I used the arrow tool to pull one of the points around. The students liked that. So I pulled Pt. E a bit away from Pt. D and we again wrote down the values. We did it twice more. And then I gave the students the remaining 2 columns: BFxFD and CF x FE. I then asked the students to notice and wonder. Now cool stuff was happening. I asked the STUDENTS how we could summarize this cool property. What could we call everything to make the property clear.

AND here is the kicker! I was too tired to make up my own example so I opened the textbook (can you believe it, I haven't opened that thing for months!) and just at that moment, Kelly, one of my most enthusiastic Geometry students,  asked, "Really Ms. Z, I don't mean to be rude, but WHY are we learning this?" And there in front of my eyes the answer:


So I drew the shard, but before we got into the mathematics, we had such a fabulous conversation about the archaeology of the shard.

• Where was it found? 
• What else was it found with?
• Was it made of material from the area?
• Was it a gift?
• What kind of plate was it?
• Did it have any markings on it?

We had just learned the construction for finding the center of a circle too. So I had to ask was there another way...does it matter the size of the shard?

So back to the question, did I own too much of the technology? And of course next year, I will schedule the computer lab way in advanced!

Also, my imagination went on such overdrive with the shard, that I am going to incorporate archaeology into one of the circle projects the students get to choose. When I get those more together, I will post them. What are your favorite Circle Projects?