Three Geometry Lessons

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I love this assignment (from NCTM, I think). The kids shall too. So this front page of congruent_halves is for their final recording. In addition to the extra copy for them to mess around with, you can also give them dot paper to copy the shapes and investigate further. No cheating, see if you can figure out the solution before looking at the key — right, the attached key only gives answers to 3 of the 10 polygons. If you can’t figure out the rest, no worries, the students will never know because it’s THEIR job to come up with the answers. Just look cool and act cool. (Line I stole from Eddie Izzard.)

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This second lesson, classifying_polygons_using_venn_diagrams, is an 11-page document — pages 1-7 are student handouts, 8-11 are solutions. I love this assignment too. If you do give this to your kids, emphasize how much work you’d put into it, allow them a moment of silence to appreciate your awesomeness.

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I tried something new just this morning with my geometry kids. It totally worked!! I was about to do a guided instruction — aka lecture — on the congruent postulates of triangles. Instead, I asked, “How do we know that two triangles are congruent?” They replied with what I’d expected, “All sides and all angles are equal.” So I said, “But that’s kind of a DUH answer, right? I mean, it’s like saying that 2 things are equal because everything about them is equal. No shit.” (Like some letters in French, the last two words are pronounced silently.)

I said, “I’m going to randomly put you in groups of three. In your group, I want you to give me just enough — the minimal — facts about the two triangles that would lead to the conclusion that the two triangles are congruent… For example, do I need to give you all three angles of a triangle or can I just give you two?… Listen for your group names… Go!”

After a full period of fantastic conversations, conjectures, and arguments, I asked the groups to bring their boards up to the front. Then I picked up one board at a time and asked that group to share just ONE postulate (if they had more than one) with the class. They found the three that I’d hoped they would: SSS, SAS, and ASA. One group shared AS (if the angle opposite the congruent side is also congruent, then the two triangles are congruent), the class submitted increasingly convincing sketches as counterexamples of this — my heart was singing. They came up with the postulates all by themselves!!!!!

Their initial conjectures were uncertain, non-specific, rough — but it was really beautiful to see them polish and formalize their own wordings. (Those are strips of paper and BBQ skewers.)

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It’s 1:00 AM?

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One Comment

  1. Maureen Sikora
    Posted June 5, 2017 at 10:41 am | Permalink

    Was this your introduction to triangle congruence? Did they already have some knowledge of it?

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