Congruence Check-In

IMG_4434After the investigation I discussed in my last post, we spent the rest of this week learning about triangle congruence in my 3 geometry classes.   The students took notes, identified congruent parts, wrote congruence statements, and made flashcards.  [All files linked below.] An assignment in which they had to identify the appropriate shortcut from a marked-up sketch was fairly successful.  On Thursday, I introduced the idea of drawing secondary conclusions from given information, and actually writing down those conclusions and why they were justified (a.k.a. proof) using this great exercise from the Oswego City School District Regents Exam Prep Center:   IMG_4435

IMG_4437And then we began to talk about proving triangles congruent.  Many of these students have already taken (and failed) a term of geometry, and if they haven’t, they have heard from friends the perceived horrors of two-column proof.  I have thus deliberately avoided introducing that type of rigid structure, and I believe that it has kept many of the students who might have checked out in despair in the geometry game, willing to go further with this new subject.  But I could see from the one exercise we did that making this leap is a huge stretch for so many of them, and I am wondering this evening how to proceed.  Do I ‘super-structure’ it – create fill-in-the-blanks examples?  Do I switch to a more accessible activity?  Can I handle differentiating this topic?  The students are at such mixed levels to begin with, and with the added disparities in their Van Hiele levels of geometric reasoning, I am not sure how to create a meaningful activity which will bring them a little closer to understanding the nature of proof.  My dining room table is currently piled with the resources I have culled in my hours of researching.  The ideas are buzzing around my head  – both outside and in – and with 2 days to go before the holiday break, and less than three weeks when we return on January 5, I want to get the biggest bang for my lessons possible.

Too-Many-IDeasI’d love to do the MARS Analyzing Triangle Proofs formative assessment lesson, but I’m afraid I really, really don’t have time if I am going to cover the content that I need to by January 26 (and for those of you who say better to cover this topic in depth and leave out another topic, well, the Geometry Regents waits for no teacher, so to speak, and I need to hedge my bets).   But I’m also laughing at myself, because I am spending a weekend evening wringing my hands over Monday’s lesson, which will be taking place on December 22.

IMG_4437Writing this post has helped me realize one great thing – that my students, who do not generally like or succeed in math, don’t dislike geometry, don’t think it’s some Rosetta Stone of which only their math teacher can make sense.  They are willing to try the work presented to them every day, and believe they can learn it.  And that’s not nothing, believe me.

On an unrelated, but critically important topic, I want to share images of 2 quilts which the president of my quilting guild, Sylvia Hernandez made in response to recent events.  She is an inspiring woman, and her quilts about the deaths of Trayvon Martin, Michael Brown and Eric Garner and the disappearance of students in Mexico moved a room of 150 quilters to tears.  I envy her ability to put her feelings into fabric art so eloquently and efficiently.


Quilt by Sylvia Hernandez

Quilt by Sylvia Hernandez


  1. mrdardy

    I have a real bias against the two-column proof but I am noticing that some of my students crave it. It’s been interesting to see them inch toward a comfort level with proof. I am even noticing that some of them are getting flexible in recognizing that some proofs feel more comfortable to them in the two-column format. At times in front of class I have presented two versions of a proof to try and make the connection between a more narrative format and the rigidity (but comfort level) of the two-column format.
    Thanks for sharing your scribd docs as well!

    • Wendy Menard

      I agree about students needing the structure when starting out; many of them otherwise have no clue how to begin. I created this worksheet to help guide them, but for many of my students it was still a struggle. Thanks for stopping by!

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