Giving Geometry Some Love: Definitions & Logic/Proofs

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It’s been about 3 years since I taught Geometry and there are people doing a lot more creative and deep-thinking stuff than myself  (see: Jim, Julie, Lisa, Mimi, Shireen, and many others), but ugh, having to draw a geometry diagram in Word?

(Hint: draw it in Geogebra, then use the snipping tool to grab it and insert, but even then it’s a pain).  So just to save you some time and hassle, I’ll also be trying to share my Geometry files this summer; stay tuned to this page!  Since it has been three years, much of it will be presented without comment. 🙂

Ah, the dreaded first chapter full of definitions. I guess I hated it so much I didn’t keep many files, but here’s what I do have:

Geometry Files from megcraig.orgFile here.

Geometry Files from megcraig.orgFile here.

Oh, here’s one thing I’ve done that’s pretty creative: I made my own Angle Awesomeness Rap  (I used to have a bit of a commute and planned it out on my drive one day).  It even has a snazzy powerpoint:

Geometry Files from megcraig.org(file here) And NoteTakerMaker:

Geometry Files from megcraig.orgFile here. Yeah, I know, I’m the next Beyonce.

Then I guess I did some sort of other work, and then a review

Geometry Files from megcraig.orgFile here.

Now for Chapter 2: Logic and Proofs.  First up, logic! With symbols! And lots of corgi references!

Geometry Files from megcraig.orgFile here.

Geometry Files from megcraig.orgFile here.

Geometry Files from megcraig.orgFile here.

Geometry Files from megcraig.orgFile here.

Geometry Files from megcraig.orgFile here.

Geometry Files from megcraig.orgFile here.

Geometry Files from megcraig.orgFile here.

Geometry Files from megcraig.orgFile here.

Geometry Files from megcraig.orgFile here.

Now…dun dun dunnnnnnn….. PROOFS!  First, some properties:

Geometry Files from megcraig.org

File here. And hey, let’s figure out what we know from givens:

Geometry Files from megcraig.orgFile here.

Geometry Files from megcraig.orgFile here.

And then remind ourselves that We Can Figure Things Out (without a formal proof yet):

Geometry Files from megcraig.orgFile here.

Then, we do the same problems with some proof handholding:

Geometry Files from megcraig.orgFile here (and yes, the file has proofs for all 5 problems).

Then finally (finally!) we can start on some real from-scratch proofs:

Geometry Files from megcraig.org

File here. Also, look below at me being clever with using “G.I.F.T.” for proofs!  And also Color With A Purpose.  I also tell them that you should use every line in a proof, which is what the arrows are for.  It seems to help if they’re stuck, “Well, is there anything you haven’t used yet?”

Geometry Files from megcraig.org

Geometry Files from megcraig.orgFile here.

And also step-by-step powerpoints for the study guide!

Geometry Files from megcraig.orgOdds file here. Evens file here.

But I’m guessing we didn’t do so well on the test, as there is a “repractice” worksheet

Geometry Files from megcraig.orgFile here.

And powerpoint:

Geometry Files from megcraig.orgFile here.

So maybe now instead of making that 417th drawing in word, you can copy and paste from these and then:

Right?

Category: Geometry | Tags: , , , ,

3 comments on “Giving Geometry Some Love: Definitions & Logic/Proofs

  1. I have been following your blog alot recently and have just spend time on your geometry info. We teach concepts in a very similar way. Your sheet on “developing definitions” you ask for non examples, I introduce the term counterexample there so that they start using it. Your method of teaching proofs is almost the same as mine. I just called it If, then, Reason instead of Given, implied, Why… I might change to yours because in class, I won’t let students answer a questions without telling me why. Thanks for all the wonderful ideas and things you share. After 10 years, I still feel like a new teacher and am always looking for more.

    • Thanks so much for the kind words, Mary! I too always feel like a new teacher every year. 🙂 I hope to get some more geometry stuff posted this summer (before it’s been so long that I’ve taught it that it really feels like I’m a new teacher!). I always like it when I see/hear someone teach something in the same way as I do–“whew, guess I didn’t mess up to badly with this lesson!” 😉

      I like the idea of getting them used to counterexamples early. I’m also thinking to smoosh our two ideas together into “if, then, why” If then makes more word sense then given, implied!

  2. […] inspirations for this unit came from a couple fantastic blogs. First, Mrs. E Teaches Math, and also Meg Craig! Thank you for sharing what you do with all of us! Many of the pictures you see here are because of […]

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