Tuesday, July 5, 2011

Day 14

Today's opener reviews the distributive property and solving two-step equations.

Last year I just assumed that students were pretty good at two-step equations (they've had them before and they had the video for homework), but I think I need to spend another day to help solidify this. So we'll spend some time practicing with two-step equations and then extending our procedure to deal with equations with variables on both sides.

For homework they'll watch the Solving Equations with Variables on Both Sides video.

Sunday, July 3, 2011

Day 13

Today's opener reviews solving one-step equations, distributive property, and direct and inverse variation.

Today's lesson is an introduction to multi-step equations. We start by doing some magic:

We then reveal the secret behind the magic:

We then talk about working "backwards" and "undoing" the steps (doing the inverse operation/opposite).

Their homework for tonight is then to watch the Solving Two-Step Equations video.

Friday, July 1, 2011

Day 12

Sometime right around here I'll lose a class period to MAP Testing, so I'm just going to plug it into Day 12 as a placeholder for now (I won't know the exact date until a week or two before).

Day 11

Today is a PLC day, which means we start two hours late and classes are 40 minutes long (instead of 59). Today's opener reviews one-step equations and direct/inverse variations.

Partially due to the shortened classes, and partially due to it just being time to do some skill review, today is a "Carnegie Hall" day. ("How do you get to Carnegie Hall? Practice, practice, practice.") I'll provide the students with a worksheet and they'll work in groups to complete the problems. I haven't decided yet whether to break out the whiteboards for this or not, right now I'm thinking not. With about 10 minutes left in class we'll begin working through them on the smart board so that the "key" is posted to the blog and to try to clear up any remaining questions.

While I think it's fine just to have a "boring" practice day, I'm open to suggestions for how to spice it up a little. Just keep in mind that sometimes I think the students like just cranking away on problems like this, so I don't necessarily see a big problem with it (and they definitely need a little repetition/practice).

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.