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 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?

Day 7

Today is our first assessment over new material (the initial skills' assessment was theoretically over knowledge they already had). On assessment days last year when students entered the room they would see something like the following instead of an opener:

My thinking was to have them to begin to focus on the assessment as soon as they walked into class, giving them some scaffolding in terms of what I think they should be thinking about as they prepare. Then once the bell rings and everyone is settled, they begin the assessment (more on the assessment in a minute). The time it takes them to do the assessment, and for us to then go over it on the board, should be roughly equivalent to the time it takes to do a normal opener. This way we still have a "full" day of instruction even on assessment days.

While I like this plan, one thing I discovered last year was that some (many?) students really didn't prepare for the assessments. I've thought of switching to giving a short opener on assessment days, knowing they would do much better on the assessment, but I'm not sure that contributes much to their long-term understanding (and it would also reduce instruction time for the day). So I think I'm going to stick with just giving them the assessment without the opener, but I'm open to hearing your thoughts.

A very brief aside to describe my assessments just to give you an idea. My assessments are an imperfect implementation of standards-based grading. Instead of giving them a test over "chapter 3" or whatever, each assessment is over a specific skill(s). This allows both me and the student to get a better handle on what the student actually knows how to do (not "I got a 73 on Chapter 3"), and what they need more work on. It also keeps the assessments very short (usually only 2 or 3 questions) and very focused, which has the added benefit of making re-assessments take less time. (I've previously written about assessment here and here, so I won't repeat all of that.)

After the students take the assessment, I (or sometimes students) work through the actual problems on the assessment on the smart board, which then gets posted to the class blog (so students have the exact assessment, including worked out solutions, to look back at if they need to review and re-assess). To give you an idea, here's last year's (pdf).

Then we begin today's lesson with a measurement activity that will lead us into dimensional analysis.

Then I get a little more explicit about the vocabulary (rate, unit rate, dimensional analysis), and we do some unit conversions that are hopefully somewhat relevant to the students. The "Vehicle Stopping Distance" at the bottom is a link to a website that talks about average stopping distance to give a little more perspective.

We then do a couple more conversations based on track records at my school, then watch a two-minute video from Discovery Education about dimensional analysis using the cost of gasoline in Australia. I'll then have the students figure out today's cost of gasoline in Australia (in U.S. dollars per gallon). I provide them with links to the current exchange rate and average prices per liter in Australia.

While I anticipate we'll be out of time, I have one more slide where we figure out how much Steven Spielberg made per second he was awake in 2009 that we'll go to if we do have extra time.

Their homework tonight is to check their grade on the assessment on our online portal and, if necessary, make an appointment to come in and re-assess (or get help first, then re-assess) if they did not do well. Tonight is also our Back To School Night, so I'll ask them to remind their parents to come tonight.

Thoughts on today's plan?