How did it go? Great!
Here's how it all went down - outline here and observations after, of course colour-coded. I do that.
- I had them open this geogebra while I screen-shared to the whole class, and we went through the questions/instructions (the ones embedded in the ggb file) together:
- Once they were done with gasmin, then on their own, they did the same with: tosna, phyxyx, and drin, all the names of which came from this hilarious article. By now, they knew what each of those words really meant - addition, subtraction, multiplication, and division.
- Now it was time to play - they changed the blue and green function rules to see what function they ended up with.
- Once they made a really cool-looking one, they uploaded it to this padlet wall:
- First question was answered very quickly, and unamimously: How is the red dot obtained from the blue and green dots? (Adding the blue y to the green y, keep x's the same.)
- Next question was almost unanimous: What type of curve is the red dot forming? (linear)
- Now I had hoped for a bit of discussion: Why is it linear? (constant slope did come up, maybe next time I'll ask, will a linear plus a linear always be a linear? What kind of functions would you have to add to get a quadratic?)
- Using words like drin instead of the real ones was fun, but one student observed that at first those words intimidated her, so I'll have to make sure next time that it's clear at the outset they are nonsensical.
- This was definitely fun. I could tell because I only asked them to upload one, and many did more than that. I had trouble getting them to stop. Problems you want.
- Once someone figured out that the trig functions made waves, everybody jumped onto the band wagon. I'm not sure how or when, but I think they got the idea that the goal was to cover as much of the graph as possible. If it were possible to break geogebra, these functions would have done it.
- It just so happens that this week I am also having them start to learn how to use geogebra on their own, and during the course of doing this, I had lots of opportunities to reinforce some of the main ideas. It was a real hand-in-glove happening.
- OMG I love padlet! No sign-in, just double-click and upload whatever you want. So easy. I think I only had to explain that to one person, it's just so intuitive.
- And look at it! I of course had to pick a background from my garden.
Now for the algebra segue:
With 5 minutes left, I wrote this on the board and asked what is the y coordinate for the red point? No problem, all knew to find the blue y and the green y and then add them. One student said something about 11x - 6. Where'd you get that from, I asked? And lo and behold it was perfectly explained that one could add the polynomials together, then use that to find the red y.
Tonight they're watching the greatly reduced voicethread, and tomorrow we'll do the application problem. Last year, I remember having to work out the entire thing for them, so this year could not possibly be any worse. I'm pretty sure it'll be better!