Figuring out How to Present a Lesson

      I often know what topic I’m going to teach and have an idea of how to present it, then before class starts I’ll change my mind a couple of times about how I want to present it. For example, today I am teaching function operations with 7^th hour Algebra II. I made these function dice so we could have some fun while adding and subtracting functions. But today I’m feeling a little low on energy and don’t want to stand up in front of the class doing all the work at the board, so I thought I would get them to present. I’m sitting here thinking about it, and I’m not sure how I would get that to work. So then I thought I might split them up into four groups and have them each study an operation and present it to the class. But then we don’t get to use the function dice, and if they used them in their groups it wouldn’t be as exciting as the whole class using them together. Then I thought about Mr. Turner’s idea of showing them what happens to the combined function on a graphing calculator. How do I incorporate that? Now I’m thinking I’ll have students roll the dice to get the functions, have one student scribe or solve the combined function on the board, and then have them all enter the three functions into the calculators and talk about what is happening. I have to make sure I do some functions with different domains, though, so we can talk about how domains affect function operations. (The function dice are all quadratic or linear functions.) Then with dividing, we can really talk about how domain matters when you have a fraction, and especially when you cancel expression on the top and the bottom. I think this could work, but it’s a couple of elements going on at once, and I’m not sure if it will all come together or get confusing. I still have a hard time remembering what to do when and how to hold it all together. I think the function dice and the student writing the combined function on the board will be the minor parts, and us talking about what’s going on in the calculator will be the important part, especially in terms of domain. With all of this, I don’t do any of my original presentation, which was to show that if you solve each function for a number, say f(3) and g(3) and add these two together, you get the same thing as if you add the functions first and then solve for (f+g)(3). This is also interesting. I had a worksheet on it, but I don’t think it got across what I really wanted it to. It’s interesting that there are a couple of ways of presenting the topic, and I really don’t know which is best. It would be great to touch on all of them so students could see some connections, but there’s not time for that. And sometimes it gets confusing when you present multiple representations at once. (Although it is important to try to use different modes so that students have different access points to the lesson.) I am not planning on using the calculators with 4^th period. We will definitely do the function dice, and I might try to show them how plugging in a number works for both the two original functions and the combined one.

Update:
We did the lesson as planned, and it went pretty smoothly. The kids definitely liked throwing the dice. I figured they would roll them on their desk, but they're a little big for that, so they threw them at the board and let them bounce off. We went pretty quickly through how to add, subtract, multiply, and divide functions. I asked them if they felt comfortable with what we had done, and they said yes. I hope that they got it. I feel like they did, but I wonder how well it really sunk in and how much of it will stick. Once we finished the basic functions, we had more time, so I went ahead with the graphing calculators. Although we didn't go in depth with what was happening, I think it was good for them to see the two original functions and the composite function, whether it was added or subtracted. So overall, everything I had planned fit into the lesson, which was great! And we had fun with the dice, too.


On a side note, two of my kids were so excited to come to math club today that they skipped chess club! I am amazed that they are so excited by math, and I love blowing their minds with things they've never thought of before. The looks on their faces are priceless.