Day 10

Today's opener reviews solving one-step equations, dimensional analysis, and direct/inverse variations.

Today's lesson is looking at bicycle gears as an application problem for direct and inverse variations. I bring in my bike and put it on a stand so that it's easy to rotate the pedals and have the wheels turn. I give them the following handout (because I learned last year that it takes some students a really long time to copy down a table and that wasn't the best use of their class time even though it was more friendly to our budget).

We then begin to work through how many times the rear wheel turns for one revolution of the pedals in different gears. We start by leaving the front sprocket alone and changing just the rear sprocket. I have three students come up: one to rotate the pedals, one to catch the wheel after one revolution (this takes some practice and multiple tries), and one to write the number of revolutions (estimated to the nearest tenth of a revolution) in the table on the smart board.

This turns out to be an inverse variation. We then leave the rear sprocket alone and change the front sprocket, and then do the same thing.

This turns out to be a direct variation.We then try to come up with a proportion relating front teeth, rear teeth, wheel revolutions and 1 pedal revolution, and then try to calculate how many times we have to pedal in different gears to travel 1 km.

If we have time then I give them a couple of dimensional analysis problems involving Lance Armstrong (or possibly give them as homework on the blog).

In 2005 Lance Armstrong won the Tour de France for a record seventh time. Over the course of the race, his mean (average) speed was 41.7 km/h.

a) Find his mean (average) speed in ft/sec.

b) It took him 86 hours, 15 minutes and 2 seconds to complete the Tour de France. How many feet did he go?

If you're interested in cycling, then you might be interested in these videos - The Science of Cycling (part 1, part 2, part 3).

I really like this activity, but last year I felt like the students didn't really "get" it completely. I've simplified a few things and provided them the table (which gives us some extra time), so I'm hoping that helps, but I'm open to any brilliant suggestions on how to make sure they understand it.

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 8

Today's opener reviews Order of Operations, integer operations, and Dimensional Analysis.

We then move into a lesson on Direct Variation, attempting to connect it to our work with rates and proportions (with a touch of measurement and dimensional analysis thrown in). First we do some converting between kilograms and pounds, write an equation for that relationship, and graph it.

Then we see if we can apply what we've learned to a unit rate (price) problem.

Their homework is then to watch the Solving One-Step Equations Video. This is something they theoretically already know how to do, so it should be a review for all of them.




I don't feel great about today's lesson. It's okay, but I feel like I have to lead them through so much that I'm not sure it's that helpful in terms of their learning process or the actual content, and perhaps just 40 minutes of skill practice might be more effective. What do you think, would it be better to can the semi-interesting problems and just practice a bunch of dimensional analysis and then direct and indirect variation problems?