Okay, first of all I can take no credit for this idea. I found this lesson at: http://mrpiccmath.weebly.com. The Link to his 3-act lesson, including video and sequel ideas is here: http://mrpiccmath.weebly.com/1/post/2012/07/3-acts-broken-calculator.html?
Here's how I implemented the ideas:
First, I didn't like the idea of using the video he included because I was sure my students would either think the video was fake, or disconnect with it themselves. So I went about finding the calculator he used. The Sharp EL - 531 X I found at Target for 9.88. Putting the calculator into pentadecimal notation was easy enough (second - equals).
I used a similar amount of patter, I talked about the virtues of using a calculator, that they can do such complex computations as 1 + 1, 2 + 2, and 4 + 4. At this point every student stopped with a bit of a dumbstruck look on their face. I knew I had them.
I then pasted the photos that Timon included in his post onto a little packet and had the students break into groups, each group had a packet and I told them to focus on making a rule that would work for each set of photos.
https://docs.google.com/a/roundup.k12.mt.us/document/d/1curjxT5Iy7Y-7-SP3BVPOSwWXLYIjaXOjllUHcF0a90/edit?usp=sharing
With my students I needed to stress not to shout out their answers, but to raise their hand and I'd put them on the right path with only questions. "Okay, so why are these correct, but these add 5? What's different?"
The set up for this inquiry was only about ten minutes of my time, and the students spent on average thirty minutes debating why one rule worked and another didn't. I even heard some students talk about different bases, and some pointed out that multiple of fives were involved somehow. Of course I heard some theories I would never have thought of before. One student was convinced the relationship was n squared - 15, and another swore it had something to do with adding multiples of 4.
As a sequel I immediately went to time, and asked them if it's 9:40 right now, what time will it be in 30 minutes. When they answered i pressed why. Here's the kicker. I put up on the board two equations:
940 + 30 = 1010 and 4 + 4 = 13. The light bulb moment was almost audible.
I followed up with some notes on modular arithmetic and an short worksheet using these ideas in a practical sense. I've included the worksheet.
https://docs.google.com/a/roundup.k12.mt.us/document/d/1LBkBxI-YbQ6v35EB6Xran_w7QKOsBlbCZQdeKTSGFhs/edit?usp=sharing
Here's how I implemented the ideas:
First, I didn't like the idea of using the video he included because I was sure my students would either think the video was fake, or disconnect with it themselves. So I went about finding the calculator he used. The Sharp EL - 531 X I found at Target for 9.88. Putting the calculator into pentadecimal notation was easy enough (second - equals).
I used a similar amount of patter, I talked about the virtues of using a calculator, that they can do such complex computations as 1 + 1, 2 + 2, and 4 + 4. At this point every student stopped with a bit of a dumbstruck look on their face. I knew I had them.
I then pasted the photos that Timon included in his post onto a little packet and had the students break into groups, each group had a packet and I told them to focus on making a rule that would work for each set of photos.
https://docs.google.com/a/roundup.k12.mt.us/document/d/1curjxT5Iy7Y-7-SP3BVPOSwWXLYIjaXOjllUHcF0a90/edit?usp=sharing
With my students I needed to stress not to shout out their answers, but to raise their hand and I'd put them on the right path with only questions. "Okay, so why are these correct, but these add 5? What's different?"
The set up for this inquiry was only about ten minutes of my time, and the students spent on average thirty minutes debating why one rule worked and another didn't. I even heard some students talk about different bases, and some pointed out that multiple of fives were involved somehow. Of course I heard some theories I would never have thought of before. One student was convinced the relationship was n squared - 15, and another swore it had something to do with adding multiples of 4.
As a sequel I immediately went to time, and asked them if it's 9:40 right now, what time will it be in 30 minutes. When they answered i pressed why. Here's the kicker. I put up on the board two equations:
940 + 30 = 1010 and 4 + 4 = 13. The light bulb moment was almost audible.
I followed up with some notes on modular arithmetic and an short worksheet using these ideas in a practical sense. I've included the worksheet.
https://docs.google.com/a/roundup.k12.mt.us/document/d/1LBkBxI-YbQ6v35EB6Xran_w7QKOsBlbCZQdeKTSGFhs/edit?usp=sharing