Day 9

Today's opener reviews Order of Operations, solving a one-step equation involving multiplication, and a Dimensional Analysis problem. While they are working on the opener I'll be walking around checking to make sure they have at least the Self-Check problems from the video they were supposed to watch for homework.

Then today's lesson is to learn about Inverse Variations in the context of speed (d = rt). First, we take a look at this.

I solicit guesses but am not counting on them guessing - at least not until I pick up a tennis ball and start tossing it in the air and catching it. Then, perhaps. Then I'll show them this:

Again, they won't see this entire slide at once. I'll show them the top two images and ask them what question(s) we could ask. Hopefully they will come up with at least "how fast is it moving" and perhaps "how high was it dropped (thrown?) from. I'll then ask how do we figure out speed (based on last year, most students don't seem to really know this). I'll then display the equations and the additional pictures (and, with the picture of the meter stick, I'll open the original so we can zoom in on it to see the markings on the meter stick better).

After we figure out speed, then we'll work through these questions:

I'll then display these pictures for context and to see whether our answer seems reasonable.

Assuming that goes well (that may not be a good assumption, the students struggled with this last year), we'll move on to another rate problem. Using an excerpt I've edited from this video, we'll see if we can figure out Rich Eisen, Tim Tebow (bonus, since he's a Denver Bronco and a hot topic around here), and Jacoby Ford's (average) speed (again, borrowed from Dan Meyer). We'll then do a quick table of values and sketch the graph to (hopefully) notice this is not a straight line, and then define inverse variation.

If we have time, we'll then do a couple of skill practice problems (if not, we'll pick up with this tomorrow).

I'm not sure at this point whether I'll give them any homework or not, depends on how it's going. Most likely their homework will be to review their notes and determine what areas they are feeling comfortable with and what areas they need some extra help on.

Day 6

Today's opener reviews proportions and percents and integer operations, and also gives them a more open-ended estimation problem.

As they work on the opener I'll walk around and ask each group if they had any questions about how the online pre-assessment worked last night (and I'll also talk briefly about it after we finish the openers as a class).

Today's lesson is designed to solidify their understandings of ratios, proportions and percents. We'll start with a quick skill review, with students working in groups and then coming up and explaining their work at the board (or possibly on their group-sized whiteboards, I'm not sure which yet).

Then we'll look at an example with the chemical formula for TNT and one with the stock market. (Again, note that I'm displaying the entire slide for you, but I would use the window shade function to reveal only parts at a time.)

Then, thanks to Dan Meyer, we'll watch about a minute of The Bone Collector and then I'll turn them loose (with printouts of the footprint/dollar bill and rulers handy - bottom image is hidden until we discuss it).

Their homework will be to prepare for the Solving Proportions and Percents Assessment that they will take first thing tomorrow. They can do that however they'd like: review the video, review their notes, review everything that's been posted to the blog, review the online pre-assessment, do some practice problems online or from the textbook, work with a friend/parent/sibling, etc., as much or as little as they think they need.

Thoughts?

Day 5

Well, I did better on the timing today, but still not good enough. I had one extra example built-in that I had to skip, and I had wanted to give the students a few minutes to work on five quick review problems in class but we didn't get to those either. On the positive side, I think they were reasonably engaged in what we did do (although it's awfully hard to tell with teenagers in a first period Algebra class that starts at 7:21 am).

We started with an opener (pdf) like usual. I really liked the first problem and I shared my thinking with them when we went over it. I'm struggling a bit, though, with my expectations on the other ones. At this point my assumption is that they should be able to do the third and fourth one fairly quickly and easily, as we've spent several days on this. And some students are definitely there, but just not as many as I had hoped. That's at least partially because they are (so far) choosing not to do some of the things I've asked them to outside of class. We're still in the stage where I'm giving them some leeway to figure this all out, but pretty soon they are going to need to step up if they're going to be successful with the variable schedule that our high school runs. Is it unrealistic to expect high school Algebra students to do problems 3 and 4, with a calculator, fairly quickly after several days of practice?

We then went through several applications of proportion and percent (lesson, pdf). Borrowing from Dan Meyer (I'm going to be writing that a lot), I started with a clip from The Bone Collector. The character played by Angelina Jolie needs to take a picture of a footprint before it gets washed away by the rain, but places a dollar bill in the picture first. I showed the clip and asked, "Why did Angelina do that?" We then talked about needing a reference for scale and how to use proportions to figure out the length of the footprint (see the lesson for a still from the movie clip). Tip: It's always helpful to get a $20 bill out and put it on the document camera - gets their attention. We then figured out the length of the footprint, which I think is kind of cool. (Figuring out the length of a footprint created on a stage somewhere in California eleven years ago just from a still picture? Yeah, I think that's cool.)

We then looked at similar triangles and the fact that the lengths of corresponding sides are proportional (didn't derive that or anything, just asked what they noticed). We then used that to try to figure out the height of our gym from a picture I had taken a week ago. I think some of the students really got this, but some of them just thought it was more noise. Not sure what to do about that.

The third example was some basic sampling, following up on our capture-recapture work from Friday. We talked about whether our class was a good sample for the question (yes for lunch, no for driver's license), and then I actually went across the hall to Mr. Swomley's class to get the actual number for the dog question. (Aside: not sure if the student are appreciating my humor or quirkiness yet.)

Due to time, I skipped the fourth example about the chemical formula for TNT. I thought that was a nice, quick connection to Chemistry, but my inability to plan for time correctly is killing me.

We then finished with the stock market example. I really thought this was a good one when I was planning it, and I think it worked okay just in terms of practicing percents, but I think perhaps the stock market isn't quite something most of them relate to right now.

The last page of the lesson includes the problems I was hoping to get them started on, but instead suggested they work on as part of their review for the assessment on Wednesday. Visit the post on the class blog for the description I gave them of the day and their full homework (more on the upcoming Skype session in a future post).