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## Tuesday, August 23, 2011

### Linear Equations Review Lesson for Algebra 2

So, I just spent two days making one lesson for one class! Yeah, this does not bode well for this year. This pays serious homage to the PCMI problem sets by Bowen Kerins and Darryl Yong, who I already know are way funnier than I will ever be.

The goals for the lesson are the students remembering and being able to... (NB, they should already "know" all this from their previous Algebra 1 and Geometry courses)
• Explain the meaning of all the terms in slope-intercept form
• Write equations of horizontal and vertical lines and know how their slopes work
• Sketch the graph of a line given various kinds of information about the line
• Interpret point-slope form
• Write the equation of a line in point-slope form given its slope and a point on it
• Find the slope of a line given two points on the line, or its graph, or its equation in either form
• Know how slopes of parallel and perpendicular lines work
Open questions
• Is this too ambitious and going to scare the bejeezus out of the poor summer-addled adolescent brains?
• How am I going to assess who knows what as the students are working?
• What's the best way to organize the kidlets so that they might benefit from some cooperation? I'm thinking groups of three or four with minimal guidance about how they "should" work together.
• Aside from the lame jokes in the marginal notes, how can I bring more joy into this exercise?
• Are there better ways to ask any of these questions that make them more tangible?

As always, I welcome your thoughts.

1. Hey, thanks for making my worksheet for next Monday! :) This looks perfect! (side note: do you have unlimited paper/copier resources?)

2. Yeah, pretty much.

3. It's hard to evaluate this properly without knowing how the instruction around it will look, but I'll give some suggestions.

I think the "Quick!" might be intimidating for some students, if they can't do that quickly.

What about the students creating their own sequence of terms, and following through on some of the same steps?

4. I had the same thoughts about "Quick!" but want to send the message that they should employ the new-to-them point-slope form to quickly/easily deal with the givens, instead of falling back on the familiar but cumbersome slope-intercept. Do you have any ideas about a better way to get that across?

Creating their own sequence like on the first page? Interesting idea. Hadn't occurred to me.

5. I like the worksheet as a good recap although I bet my students would have some trouble remembering all that from the previous year! I like all the notes and I feel like what you typed out is how I would talk. Haha! Maybe you can figure out the pattern as a class (so they have at least a starting point) and then make up a pattern as a group for another group to work out?

6. I'm afraid that if we figure things out "as a class", it's really just me "figuring things out" and the 5-10% of students who both pay careful attention and volunteer to speak during those interactions.

I like the "make up their own sequences" ideas, but if I stop there, I only meet a couple out of the many goals for the lesson.

7. I'd say groups of 3 should be good. A good chance that someone knows what they're talking about, but hard to be a freeloader.
The jokes aren't lame for math jokes, in fact math jokes are supposed to be lame, so well done.

If I were in your class, I'd skip the first challenge question to get to the second. Maybe it's just me, but it's a juicier problem.

Nice warmup for the kids. First day?

8. I love this new worksheet approach! I also love how you've incorporated the BK/PCMI-style of humorous but prodding "reminder commentary." I am definitely going to have to figure out how to steal that idea. It must be helpful to have worked through some of those great sequences.

I'm excited to see how you integrate more of this as you go along!

9. To my eyes the first page looks a lot different than the next four. What if you only gave the first page and then see (or plan out) where the discussion leads? There are a bunch of important things going on there, as well as different ways to explain the equation and interpret the representations. Also, consider taking out the PCMI-esque sidebar comments. They're fun and all, but they are distracting. Instead, these could be things you say as you work the roam (label those axes, kid in the red shirt!)

From problem 8 and on, they might need more or less help (maybe direct instruction or some examples). Obviously you be the judge. My only final advice is that after my PCMI experience last year, I started putting "tough stuff" in my "problem sets." But no one did the tough stuff!

10. Page 1 gave me the idea of integrating the linear equation review with the start of a topic on sequences and series. I would follow it, like David says, with student made (linear) sequences. I can see how you need the questions on the other pages to make sure you encompass perpendicularity etc, but they seem a bit disconnected from each other and there are so many of them! I'm wondering whether it wouldn't be possible to have two larger problems, perhaps more open ended, that encompass everything you require. I'll see what I come up with.

On a side note, I LOVE the "whoa!" part of some questions. It's so open ended and fun, lets the students giggle and figure out what's going on by themselves.

11. right off the bat:
surely case 0 oughta be
**
**
**
(i.e. on my model,
my case "n+1" [shift
the vertical axis by
one unit; one might
[[though not with this
class!]] go so far as to
say (x,y)|---> (x-1, y);
i posted a bunch of stuff
on transformations in S'09]).

but this is a quibble.
very nice work here