Limits review...he was actually on it! Material that I thought was going way over his head last week was processed and we had some really good conversations about different types of problems. Great questions were asked, showing that he's actually thinking about what he's doing and why, too. (There are, of course, still some trouble areas like knowing when to factor/rationalize and what numbers will "help" in the simplification process, but it's a process, right?).
Then, we did some free fall problems, applying limits and previewing derivatives. It was so great to actually apply what we've been talking about to a real situation and make it mean something. Here's the problem we spent time looking at, and some of the humor that came out of it...
A construction worker is working on a building that is 1000 feet tall. (side note, we took a tangent to see how many stories that would be, because 1000 ft is just an strange number to envision). Suppose the construction worker accidentally drops his wrench. If he immediately yells "Look out below!" (or something similar), how long will the person standing on the ground below him have to get out of the way before the wrench hits the ground? What will the speed of the wrench be at that time?
We took a tangent to talk about finding speed (using the limit definition of derivative, but he doesn't know that yet) at 5 seconds, and then at the time the wrench would hit the ground. We also had a good conversation about why the velocity is negative. When we found the velocity (-160ish ft/sec at 5 seconds, -252ish ft/sec at impact), we talked about how fast that really is, relating it to a football field. He couldn't believe the wrench could fall that fast.
When we had spent a lot of time talking about speed. He asked, "Wait, we didn't answer our question yet, can the person get out of the way in time?" *GRIN*
ASL is so visual with these kinds of problems...I love it.
Quick question: is your calc class only one person?
ReplyDeleteSam:
ReplyDeleteQuick answer: Yes. That's the class where I'm teaching Math Remediation (one student) at the same time.
Just outta curiosity, what makes ASL so visual w/ those problems?
ReplyDelete@ninJa
ReplyDeleteASL is visual, period, but with these problems when you're talking about an object falling, it's explained visually the same as negative values on the y-axis. It's easy for students to see that the slope is negative before tangent lines are even talked about.
Your thoughts?