Catapults and Algebra 2

In a previous post, I talked about how I used Sean Sweeney's catapult lesson in Calculus. I also used it in Algebra 2, as an enrichment project for two students while the rest of the class was gone for a sports event. I also talked here about how I introduced the project without actually being there.

Unfortunately, time for the actual project was cut short by an assembly that ran long. From what I could gather from sub notes and the notes that the students left, they enjoyed it. Unfortunately, with the short amount of time that Algebra 2 gets (and it keeps getting cut shorter when the kids leave early for sports games!!), they never finished it. It might be something I resurrect once the pressure of the SOL test is finished. There is just so much material to cover and I want to be able to take the time to actually *teach* the material instead of just showing it to them last minute.

Maybe it'll work better next year...?

p.s. this post was started on October 13th...it's now October 30th. Where does the time go?


On Catapults and Calculus

I stole Mr. Sweeney's catapult project and tweaked it (more like, added to it) for Calculus class.

It was fun! We not only calculated the equation of the parabolic motion of the projectile, but at the end we talked about how fast it was going using the limit definition of the derivative at different points during its flight. It was a really great discovery point of how the velocity is zero at the maximum height. We were also able to then talk about why that "makes sense".

The next goal was for my calculus student to help my Algebra 2 students with the project while I was at a conference...stay tuned to hear how that went!

(I started writing this post 1 1/2 weeks ago...and the other one has been started, too...just waiting for some TIME to finish up!)



Last week was a definite high. Things were going great! My observation went well, I was excited for the projects that I was leaving for while I was going to be out, and the substitute teacher that was scheduled to cover for me knew the language *and* the math! It was all looking good!

I arrived back at school to find my plans weren't completely followed. I know this is not unusual, but in preparing I thought I was ready for everything that could happen and that I had thought of everything...organized, etc. I guess not.

My Algebra 1 class that was solving 2-step equations like crazy on Wednesday bombed a quiz that they took on Friday (which they were supposed to take Thursday...but that's another story entirely). I felt like I needed to start from scratch again, and that everything from the week before was lost.

I had no Algebra 1 class today, so no chance to redeem. Tomorrow is a new day, though. We're going to correct the quizzes and then move on. We can't be solving 2-step equations forever, but we need it as a foundation!


Encouraged, Again

Last Monday I was feeling overwhelmed. I go through these phases when I plan ahead, get a few days worth of lessons/notes put together, and then I get through one day and realize I'm not really ready for the next day at all because things didn't go the way I planned. These phases often leave me frustrated and irritated that I spent time up front that seems to be wasted. In the long run the time spent is not wasted, but it's still frustrating to *think* you're ahead and then *realize* that you're just as far behind as you normally are, despite the extra time you put in.

Anyway, that's how I was feeling Monday. And Tuesday I was supposed to get observed for the first time this school year. "Great," I was thinking, "just great." I had a less-than-stellar lesson planned, introducing graphing one-variable inequalities and solving one-step inqualities. Not something normally covered in Alg1 (it's a middle school concept), but that's what my kids need. I sent my lesson overview to my principal the day Monday and continued brain-storming ideas on how to make it more interesting.

I arrived Tuesday morning, less frantic than Monday (did I metion that I slept through my alarm on Monday morning, too...talk about a rough start to the week), and prepared myself mentally for the lesson and observation. Class started and I knew it was going to be a good day. I picked my best class for this observation. To provide some sort of closure from the day before and transition to the new topic, I had 2 students present problems from earlier (one- and two-step equations).

I was blown away as they were presenting. Without my prompting, they were explaining why the balance method for solving equations worked.
ex. 4x-7=9. I first added 7 to both sides because it's the opposite of the negative 7 that you have right now. I can cancel out the -7 and +7 because they equal zero. Then 9+7 is 16. I pull down the 4x = 16. Next I need to divide because it's the opposite of the multiplication that's happening now. I end up with x = 4
This type of reasoning and explanation never happened voluntarily in my classes last year. It's something I really have been working on with the students by asking a lot of "Why?" and conceptual questions. While the student was presenting, I kept thinking, "He's answering every question that I would have asked him!"

Later in the class, I found a way to make a boring part interesting by having the kids move around a bit. They needed to decide whether or not to flip the inequality. If it needed to be flipped, they stood up. If it could stay, they stayed sitting. One student made a mistake and stood up when the rest were still sitting. He felt silly at first, but his neighbor looked at him and explained why it didn't need to be flipped. He even gave an example of a situation (using the same numbers) where it would need to be flipped.

I was astounded. I love my job because I get to see things like that happen. I get to see kids grow and learn and teach each other. And I get to sit back and just watch sometimes! LOVE it. *smile*


Really excited for this week!

I'm getting really excited for this week. Plans include catapults with Calculus and Algebra 2, complete with video instructions (really hoping that technology is my friend this week) and peer mentoring.

The goal for catapults is to work through the project in Calculus on Monday and Tuesday. We'll be taking it a bit more in depth than Mr. Sweeney's Algebra 2 project, talking about velocity and position relating to the initial discussions of derivatives. Then, on Thursday, Algebra 2 student will make a catapult from my model, and begin his investigation. Friday, Calculus student will join Algebra 2 student to help with the "math" of the project. All this will happen without me being there, which is why we need video directions!

I'm really excited for this, and the excitement easily turns into anxiety and thinking of all the ways it could completely bomb and blow up in my face when I return. But, it's worth a shot, right? Two-thirds of my Alg2 class is going to be gone Thursday and Friday anyway at a volleyball tournament, so here's my time to throw in a project for one of the more advanced students in my class.

Any words of wisdom?


GSP meets Algebra 1

I was pleasantly surprised when my ITRT (read: tech person) at school emailed and said she found out we had a lab license for Geometer's Sketchpad (GSP). Last summer I took an online course from KeyPress to learn how to use GSP and more specifically, how it can be used in Algebra classes. I was very excited to learn more about this software and to be given examples of how it can apply to the concepts we teach in Algebra classes.

Earlier in the year, I used GSP to demonstrate adding and subtracting integers. I was using it as a demonstration tool at first, projected on my SMARTBoard. One problem I found using it that way, was that the sketch itself was too small for the students to see, and I ended up having one student sit at my computer and do the manipulating. I tried to make it work, and to let students take turns doing the manipulating, but it just didn't work the way I wanted it to. It was good, however, introducing the basic concept of what I was trying to develop: adding and subtracting integers on the number line. We then took that concept/idea and went back to paper and pencil methods.

This time, I took the students to the lab. We are solving equations, starting with the basics and moving forward to multi-step. I started the unit asking them to find the missing number in some simple equations, to see what methods they intuitively used. Next, we talked about working backwards, doing the opposite of what is currently being done to the variable, in order to get the variable alone. Finally, I wanted them to be able to explore the balance method of solving equations. I found a sketch with a balance, using positive and negatives. Gave the students a guided worksheet to explore what happens when you do different things to the balance. Was looking for the students to discover some properties about balancing equations (i.e. adding/subtracting the same number from both sides keeps the equation balanced, a positive and negative "cancel" each other, whatever you do to one side you must do to the other).

The students (as could be expected) struggled with the software. It was the first time they used it and the sketch had too many other things they could explore. They were curious and excited to play with it. I was able to ask some higher level questions, and the students responded well because they could support their ideas with the sketch. Their reading level caused them to struggle, even with the simple worksheet I created. I spent a lot of time going from student to student explaining what to do next.

Hopefully I'll be able to use this program again with this class, because I think they will be more comfortable with it and it'll probably be more successful the more they use it. Just thought I'd share my experience. Any suggestions are welcome.

**Note: I can't figure out how to upload the GSP files, so if you want a copy, leave a comment or email me**

Becoming more Human

Wednesday I gave a test in Calculus. It was covering limits at a point, at infinity, one-sided limits, continuity, etc., even some free fall questions leading into our next unit on differentiation. The day before the test, I was nervous that the test was not going to go well. Review, things that should have been easy, was like pulling teeth. I was starting to doubt myself and my teaching.

During the test, I was looking through some stuff in my classroom and I happened upon my limits test from when I was in high school. I got a B+, and there was a calculator and no-calculator portion. I instantly thought, "Arg! I should've made a no-calculator portion!" Instead of dwelling on that, though, I just looked it over and found my mistakes...very interesting ones. Since the class finished the test with time to spare, I decided to show my test, and look at my mistakes. Looking at the problems I answered incorrectly, I asked the student to decide where I went wrong and what the answer should be.  We went through the whole test like this, and even on some of the questions I answered correctly, I asked why that is the right answer.

This little exercise was a time-filler, yes. I think it made my student view me as a co-learner and as someone who has gone through what he is going through. I'm not just a teacher, I'm a student and learner too. I make mistakes in the classroom all the time, so it's not that my students view me as perfect and error free, but I think showing my old test and what was expected made a stronger bond between us. While I don't have all of my tests from calc, so I won't be able to do this frequently, I do plan to share from my experiences in calc during high school, and I hope to bring in some of the activities that we used (and some others!)