We used to teach the geometric proof for the distance formula. Why did we get rid of it?

[schanzer]

We had this lovely section in our pre-remix distance formula unit:

Is it worth bringing back to our distance formula lesson?

[flannery-denny]

@schanzer I was excited to take a look into the way back machine, but I'm not sure this snippet would add much. tova's video is part of the current lesson. open to talking further about tackling teaching the distance formula in a student discovery way rather than a lecture.

[schanzer]

@flannery-denny I think students would benefit from a kinesthetic activity where they assemble differently-shaped triangles and see this for themselves, rather than passively watch a video. Why did we get rid of that?

[flannery-denny]

@schanzer The wording from the old lesson plan you had linked to doesn't do it for me, but I see the value to the kinesthetic materials you are suggesting including.

I can't answer the question of where old materials went. As a teacher who'd been working with old materials (and didn't have any idea that the lesson plans I was working with were getting updated every year), I remember being appalled when I saw how much of the great stuff I was using with my students had gotten axed for the 2020 release. Those changes happened before my time. And I have built out a bunch of distance materials since coming on board, because I thought this section was extremely scant.

I used to teach a different geometric proof of the distance formula to my students... so a little part of me wonders why this is the (only?) one we want to focus on.

[flannery-denny]

@schanzer you mentioned a page that students could print and cut for this proof. Is that something I should make or something that already exists in the archives?

[schanzer]

@flannery-denny we have some old, hard-coded images here and here. I've seen some really similar - more awesome - Desmos activities that do the same thing as well. I bet @retabak has one or two in mind already that could be used in place of the paper manipulatives.

[flannery-denny]

@retabak do you already have Desmos activities in mind that teach pythag as es guesses or should I look for some?

[retabak]

@flannery-denny -

I poked around. Here are a few things I found. Suspecting these will be a source of inspiration (meaning we borrow pieces and adapt) rather than something we just grab and use. The only activity on the Pythagorean Theorem that is actually created by Desmos (e.g., more polished) is this one, but it's practice - not proving.

2.3.2 Proving the Pythagorean Theorem by Brenda Coughlin, adapted from CMP - slides 8 and 9 are nice

Pythagorean Theorem Proofs without Words by Steve Phelps - whoa, this is bananas!

Pythagorean Theorem Proofs by Sarah Blick Vandivort

U3L14: Proving the Pythagorean Theorem by Brett Egan, adapted from IM

LMK if you need help editing / adapting / combining pieces of any of these preexisting activities. The one by Steve Phelps seems the most promising, but it is of course interesting to see how IM and CMP approach this concept.

[schanzer]

@flannery-denny and @retabak I LOVE the bananas one. I'd be thrilled if we provided that, with some instruction for what we want kids to DO with it. (Suggestion: "choose one slide that appeals to you, and replicate the transformation by cutting pieces of construction paper and demonstrate the transformation in front of the class."

[retabak]

okay, as much as I am a desmos fangirl, I just followed Steve Phelp's link to the geogebra version of this desmos activity (also by Steve Phelps), and I actually think it looks cleaner - and would be more accessible for teachers who might be scared of desmos. Here it is: https://www.geogebra.org/m/jFFERBdd

[schanzer]

@retabak @flannery-denny ooooh, even better! Let's use this (with some instruction), and cross this one off the list!

[flannery-denny]

@schanzer While i'm cleaning up this lesson, is it ok to make this page required

[schanzer]

@flannery-denny totally

[schanzer]

@flannery-denny if this work now has a required workbook page, should the milestone be moved up to Jan 1?

[flannery-denny]

@schanzer the workbook page has already been added. we agreed that the pythagorean theorem stuff would happen on desmos

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@flannery-denny https://github.com/flannery-denny if this work now has a required workbook page, should the milestone be moved up to Jan 1?

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[flannery-denny]

@schanzer this is ready for feedback

[schanzer]

@flannery-denny I made some small formatting/typo fixes, but otherwise this looks pretty good.

The one problem keeping this from being finished is that you've moved the "Why line-length?" strategy box to the additional exercises section, and offered no explanation in the lesson itself for why line-length is being used. The lesson does a terrific job explaining why we use (x2-x1), and then tells kids "see how we do something different, and see if you can do it too for the second problem".

We need at least one child-facing sentence explaining how line-length is (x2-x1), and why we use it.

[flannery-denny]

@schanzer ready for feedback. Noting that we explicitly do not teach the distance formula to students anywhere in this lesson. We teach them how to use the pythagorean theorem to use horizontal and vertical distance to calculate diagonal distance, which will serve them well! Given that you've made a choice to code line-length into the game, I see zero reason to teach students an algorithm they do not need to know and will not use in the lesson. Therefore, I have chosen to leave that text for teachers only.

[flannery-denny]

@schanzer Close if you're satisfied!