Lesson 4.1.3: Solving Linear Equations (Days 69-71)

While eighth grade hasn't been quite as convoluted as seventh grade, this week I still must find a way to balance out this week's Benchmark Performance Task with the regular lesson. Just as with Math 7, I'm taking a 30-40-30 approach -- prepare for Benchmarks the first 30 minutes, take the Benchmarks the next 40, and give the regular lesson the last 30.

There is one question on the eighth grade Benchmarks that I definitely don't like. There is a graph that shows time in seconds on the x-axis and distance in yards on the y-axis, and the question asks to find someone's average speed -- in miles per hour. Even most math teachers probably don't know how many yards there are in a mile -- unlike 12 inches to the foot and three feet to the yard, the number of yards to the mile isn't regularly taught.

(Indeed, the only reason that I know the number of yards to the mile is that as a young student, my PE teacher -- yes, that PE teacher -- would have us run 440's, a lap around a quarter-mile track. There might also have been 880's, a half-mile run. Indeed, my performance in the 440's was the first hint that I was destined to become a Cross Country runner. Double the length of the 880's and we arrive at the length of a mile as 1760 yards -- but then again, we never said we ran "the 1760" -- what we ran was "the mile.")

As for the main lesson, our use of worksheets continues, as there are Kuta (or Kuta-like) worksheets for solving equations with variables on both sides, combining like terms, and distributing. I've decided that I'd much rather do example problems from the worksheets than rely on APEX. For one thing, some topics, such as combining like terms to solve equations, aren't covered well on APEX. So doing problems directly from the worksheet is helpful to them.

On the other hand, equations with no/infinitely many solutions are covered much better on APEX. There is a worksheet with variables on both sides, but the coefficients don't match. Thus the variables never drop out completely, and so each equation on that worksheet has a unique solution. I'll have to go back to more examples of this later on. Notice that neither seventh nor eighth grade has an APEX quiz today. The students work hard to get through their Performance Tasks, so let's not torture them with an APEX quiz on top of that.

This will be my last post for now with the "Eugenia Cheng" label, as I'm getting ready to turn the book back in to the library. I'm mentioning her book again now because today I meet with a parent whose seventh grade daughter is shy and has trouble speaking up in classes. (She's a special ed student, but of course, any further discussion there is inappropriate for blogging.) When I randomly choose her name, she usually does participate -- but I don't choose her name that often. Sometimes I fear that she's slipping through the cracks -- she might not understand the material, but I don't realize this until it's too late. This is what Cheng wants us to watch out for -- girls who struggle to speak up in class.

It's back to my usual blogging and tweeting schedule this week. So you can expect to see some tweets from me on Thursday and Friday.