Review Quadratics lesson

[schanzer]

• [x] Make sure all pages that need to be in the workbook are
• [x] Audit section overviews
• [x] Make any small changes
• [x] Check with Flannery/Emmanuel if they're online and there's a big change, otherwise just go ahead and make it
• [x] Emmanuel adds annotated table showing growth
• [x] Flannery cuts "other forms" section, adds beta teaser

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[retabak]

first section:

• [x] In the starter file, we say that speed is "the speed at which the car was tested." We need to specify that it is miles per hour. (I'm assuming that's what it is?) @schanzer - can you update?
• [x] We need to launch the lesson with some general "hook" questions asking kids what they know about fuel efficiency, e.g. what do they think affects fuel efficiency? Do they know anyone with a fuel-efficient car? Is it possible to be a fuel-efficient driver?
• I was just wondering if the Fuel Efficiency dataset included hybrid vehicles, so checked the Read Me tab and learned that the dataset is fictional. Perhaps it's obvious (the models are just letters) but I think we need to disclose this in the lesson. I'm actually not sure how, though. I also do think that kids will want to know if the dataset includes fuel efficient cars. [added this to issue #1345]
• [x] The revised "Read Me" needs some love. It currently has text about Brown students and COVID data.

second section:

• [x] I really think "classifying plots" should just be deleted. I teach sixth grade and I think my kids would be offended at how easy it is. I really cannot imagine a high school teacher finding any use in this, especially if their kids have ANY familiarity with quadratics (which they ought to... right?). Deleting it... if someone feels strongly about it, defend it and put it back! It's also potentially confusing... what if we're just looking at a zoomed in (limited) view of some data? Then, couldn't any of these potentially be quadratic? (This sounds like an argument Shriram would make.... really, I'm mostly concerned that this is WAY too obvious.)
• [x] Changing the other optional worksheets so that they are @printable-exercise, which needs to be the case unless this whole section is optional.
• [x] The formatting on classifying-tables.adoc is very confusing. We definitely need all of the problems to look like 2, with the linear / quadratic / neither options immediately below the table. I also think it would be preferable to make this a 4-column table, with 2 super skinny columns to put just the problem number. I checked out the asciidoc and got confused / overwhelms (there are lots of comments and I didn't want to mess with it). I think this might be a job for @schanzer ?
• also on classifying-tables.adoc - I don't understand the hint in the directions. What's "the first and second difference"? We need to explain this or provide an example. I could image kids graphing these, or trying to find the equation in the space below. OOOOOOOH, nevermind. I read the definition of quadratic that we provide, then did some goolging, and I understand what you mean. We need to add some explicit instruction in the lesson on this whole "first and second difference" thing. We are making a major assumption that kids know what the heck that first/second difference means. I don't think I ever learned this way of doing things. I wish I could add that instruction, but I actually don't know if I like this way of approaching things? (see next bullet....) I'm changing the hint and opting NOT to add that instruction to the lesson. Added this to Alg 2 wishlist #1345
• [x] on that note, I really hate our defintion of a quadratic relationship. I promise you, I know what a quadratic is, and I had absolutely no idea what our definition was all about. I had to watch this video: https://www.youtube.com/watch?v=tBdA6ltSi1w .... do we want kids thinking about quadratics so rigidly / procedurally / algorithmically?
• adding to the wishlist #1345 that I think we can do better with parabolas.adoc. The graph at the bottom is huge; I suspect we could use this space better (e.g., include the graph, but also find other ways to get kids thinking about / practicing the terminology they've just learned). Okay, I think this would be easy. We should include prompts like: Draw a parabola with a y-intercept of 5; draw a parabola with a y-intercept that we can't see on the current display; with a minima at y=3; etc, etc. The big graph should just go.
• [x] I moved the "Interaction Effects" pedagogy box because it didn't make sense where it was (right by all of the parabola terminology), but I'm not sure if its new home is better?

third section:

• [x] moved the thing about a dip at 40mph to here, because it was previously in a section of the lesson that wasn't about the fuel efficiency data?

[retabak]

OK - my biggest changes involved adding a hook to section 1, moving chunks of text around (within and between sections), clearly flagging for teachers what's coming up next (we were jumping into and out of the dataset without any warning, which was gave me whiplash), changing the formatting of a table in the lesson that looked ugly and wasted white space.... and I think that's about it?

I also added several things to the wishlist issue.

Now, I am going to try to see if we can piece together a narrative in the last section ("other forms of quadratic models") using the worksheets that already exist.

[schanzer]

Overall I like the changes in section one. I simplified some of the wording in places (you are so clearly a grad student!), and adjusted some of the voice to be consistent with our other lessons. Overall no major changes on my part. A few questions:

• At one point you ask "What would a table of a perfect quadratic relationship would look like?". Do you expect students to know this already? Even after a fair amount of googling, I'm not even clear on what it means, myself RT: Agreed, this wording is dumb and confusing. Sorry. I just mean a good 'ol parabola. That said, this question was asked hypothetically in a previous iteration, and I wasn't sure if it was actually supposed to be discussed. And... I have no clue what students will know or not know about parabolas. What is our assumption around student knowledge when they are using our materials? If I were a teacher, I think I would use our stuff to supplement my normal algebra 2 instruction. Anyhow, I'll nix that question.
• I can't help but feel like we're tripping over ourselves to not teach about first and second difference. Consider this text, which is already in the lesson: RT: I added this text because I felt that the text about "increasing by fixed amounts" was unclear otherwise. I think we could add this first/second stuff in later, but there's is so much going on in this lesson already. I also think we need to get clear on what we think students know and do not know. I also think if I were a kid doing this worksheet, I would just label the distance between each pair of y-values and then make my decision? isn't that simpler?
• I absolutely love the parabolas worksheet! Awesome job, @flannery-denny
• The modeling section still has some vestigial text from when it came after teaching other forms. Now that it comes first, we don't need to name the form or tell kids why it's a good place to start. I cleaned up this text as well. RT: Sounds good.
• @retabak I notice that you do a lot of telling kids what's coming up. In one of the lesson instructions, for example, you format it as if these are separate instructions. But actually it's just four things kids will do in that one workbook page. We don't really do this elsewhere, do we? It feels jarring to me, and in a classroom setting this is a lot of words that will be lost unless you intended to have them work through it in separate pieces. Is that the intent? RT: I believe strongly in telling TEACHERS about what's coming up. In that one instance, I opted to tell kids, because I felt like, as a student, I would wonder why I was suddenly be learning about num-sqr. Overall, when the lesson text causes you to believe that you're about to do one thing.... but then we direct you do something else -- that is a problem! It's annoying to need to figure out on your own why you're being instructed to do something seemingly disconnected. I can change that information to be @teacher, though.
• I'm really not ok cutting graphing-models.adoc from this lesson -- teachers overwhelmingly thought it was one of our strongest pages in PD, because it really set them up with intuition for fitting their model later. I've brought it back and changed the framing slightly. This also obviates the need for a "translating quadratics" section entirely. RT: Like this worksheet a lot. I moved it to a different section of the lesson where it much more logically fits.

[retabak]

Just pushed a commit to respond to your comments, @schanzer. Also typed in some replies above.

[schanzer]

I'm happy with all your changes. Replies to your replies below:

• I don't think we should assume kids know what a parabola is before this lesson. But yeah, that doesn't impact the edits in this review specifically.
• I think your new wording for 1st difference is way simpler. Love it! But what I'm getting at is that you're essentially already teaching 1st difference. You're just not calling it that. That's why I feel like this lesson is itching for it. And it's not enough to just compute 1st difference and say "welp, it's not constant so it must be quadratic!" That's simply not true -- and telling part of the truth is worse than saying nothing. If we're going to talk about 1st distance, we need to talk about 2nd distance.
• I agree that we want teachers and students to see the big picture, but I don't think you're accomplishing that by telling them how all of the little pictures fit together ("we'll do this, then this, then this...). I think we just need a broader summary that gives them an overall sense for what needs to happen. I'd love to work on that, but I'm too fried right now for wordsmithing. If you want to leave this as a TODO for me tomorrow, that's fine.

[flannery-denny]

I've pushed some changes to:

• make sure that lesson dialog does not give away things we're then asking students to think about on workbook pages
• make a note about the fact that the patterns we see in tables of functions will not appear in tables of real world data sets, which don't perfectly fit the model

[flannery-denny]

fyi - I decided that since there are optional workbook pages for other forms provided in the Additional resources section and they have the forms described at the top, I wouldn't add the table back into the lesson plan