I’ve been reading books, articles and blogs. I go to training meetings and conferences and see presentations from experts with great ides. I am always inspired to try new things. So, I do. But, they don’t stick. Finally, I’ve found the right combo, the right approach, the right attitude.
I am exploding with ideas. But, I’ve finally found a formula – that I don’t intent to stick to all of the time, because that will cause problems too, in terms of engagement.
I am starting the day with an open question. To get kids to enter where they are. For example, yesterday’s question was “How many solutions are there to the equation x+1 = x^2-1 ?” They worked in pairs and also had to answer, “How do you know?”
These questions allowed for multiple entry points, and was an effective and engaging differentiation strategy. Some students used guess and check and found one or two solutions. Some students combined like terms across the equation and either factored or analyzed the discriminant, much to my delight. No one graphed. I knew what everyone had done because I had time to circulate, discuss methods and ask questions that moved kids into engaging more deeply with the problem.
For the students who analyzed the discriminant, I asked them if they could then find the solutions. This was puzzling for them at first. For those using guess and check, I asked, “how do you know when you have them all?” They went back to the drawing board and asked other students what they did. It was great to watch.
Using a “You, We, I” strategy, thanks to CMC-North conference and Steve Leinwald’s presentation, I then brought the class together and tell them I saw three great strategies used. We discussed the merits of each. Then decided which might be best for that particular problem. This was the ‘We’ part. We started with the ‘You’ part, where they generated their own ideas and tried to articulate their reasoning.
Then came the ‘I’ part. I asked them what they would do if the functions were higher degree. I asked them which of the strategies would still work. I also asked them what they would do if the expressions weren’t factorable. I asked them if they’d like to learn a method that would work every time, for any two expressions, from an isolated constant term to a higher degree polynomial or other more complicated function. Of course, they were hooked and interested.
Thank you, Desmos! I graphed and displayed the functions on the overhead. They could easily see the intersection of the linear expression, x+1, and the quadratic expression, x^2-1.
Here’s the handout to students, Desmos Intro and Parabolas.
From there we went into the lesson. More You, We, I. Then into a short homework assignment. This is the 2-4-2 idea (not perfectly executed by me) that I learned about from the same Steve Leinwald presentation. I also asked for feedback. Today, when the kids came in and had to turn in the sheet, one student let me know she really appreciated it. I can wait to read their feedback. I would have done it then and there, but, y’know, lots going on in a room of 28 Algebra 2 students.
The lesson itself was really a summary of the structure of both the standard and vertex forms of the equation of a parabola. It was meant to introduce them to Desmos and better demonstrated what a, b, c, h and k, do in the equations. I wish I had known about teacher.desmos.com and the calculator with so many pre-existing awesome tools. If you are not aware of Desmos and it’s many wonderful capabilities, you have got to yourself educated on Desmos. It’s easy to learn. The team there seems to be a great group of people, thinking up wonderful activities. Next week, the kids will use Marbleslides for rational functions to review graphs of rationals. I can’t wait.