Geogebra To The Rescue And Some Help From The Textbook

I worry about being in control of all the technology in my classroom. I worry about asking students to all take out a device, because there will be a few who don't have one or don't have data to jump online. So what do you do to preserve the teachable moment when you haven't booked the the Lab or Chromebooks weeks in advanced? I take control (unfortunately) of the technology. Am I not helping when I assume that at least I am capturing the moment? My husband just opined from the other room that if I use a formative assessment to measure if they have learned what I intended then it is not a problem.

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?
I went back to the question, what kind of plate was it? I asked if there was more than one kind of plate. This usually quiet male student pipes up, "we have salad plates." (That comment made me happy!) We talked about the significance of the size of the plate, was it a platter? An offering plate? 
About this point the students knew what I was on about and were begging me to draw in the chord. They had to fuss a little to remember that if the diameter it perpendicular to the chord, it bisects the chord. Was it possible to find the perpendicular bisector of the chord, sure! And every thing fit together nicely. Thanks Textbook. 

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?

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1 comment :

  1. Interesting! It isn't totally apparent to me what you'd do if every student had her own laptop or device. Can you elaborate?


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