Saturday, March 12, 2011

Special Quadrilaterals

We finished studying special quadrilaterals a while ago, took a test, and now the kids are trickling in for their retests. Ew. Something didn't stick or even get through to some students, and I'm trying to process how to improve it for next year.

Here is how I taught it:
parallelograms: I had 4 already printed on a paper, and they were to use their rulers and protractors to measure various things to discover the facts about the angles and diagonals.

squares/rhombi/rectangles: I had them neatly draw one each in their grid notebooks (I gave the instructions on where to put the vertices). Then I had them again use their protractors and rulers to measure various things and fill out a chart as to which had which properties (diagonals congruent, diagonals perpendicular, diagonals bisecting opposite angles).

trapezoid/kite: I had a sheet with some drawn we worked through the logic of things to get to their properties.

All this went in their notes. They had review problems. At no time did I have them (and apparently they didn't think they needed to) gather all the information into one place (foldable? 1/2 page) to have a quick summary. (I will change this for next year).

Okay, then test time. The usual suspects did well, but too many kids had no idea about things they should have. For example, when a student was coming in for a retest, and I asked her about what a rhombus was, she was silent. Oy! Now I know this particular student coasts by and can look like she's playing school, but .... Regardless, I want them to learn despite themselves.

I think something happened at another tutoring session that will make me either add a day to my lessons, or replace the previous lessons with this. I'm leaning towards add to the lesson.

Another student was studying rhombuses, so that she could take the retest, and she still wasn't understanding or processing things she should know. She couldn't even draw a vaguely accurate rhombus. I took a piece of colored construction paper, and pretty quickly used a ruler to cut it into a rhombus (it turned out to be approximately 8.5" per side). I liked that it was big enough to see things on and to write on and play with. Then I had her folding it to make the diagonals. Then we stared at it. It was clear the diagonals were perpendicular. It was clear that they were bisected. It was clear which angles were congruent (you could match them up and check). It was clear that the diagonals bisected the angles (again you could fold and check).

Then as she was trying to redo a test problem, I had her write the given information on the rhombus, and then figure out the rest. ... I don't know if this will stick. I guess we'll see when she actually does a retest, but maybe the extra visual and tactile properties of the shape will be clearer in her mind.


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  2. (Sorry I didn't realize my husband was logged in and left that first comment from his profile.)

    Hi! I am a fellow math teacher and enjoy reading your blog. Too many familiar stories! Anyway, when we teach special quads at my school, we have them get in groups and come up with a rap/song/poem about an assigned quadrilateral. The lyrics must include all properties (so for example squares must include all properties of a rhombus, rectangle, and parallelogram). Here's an example of a couple of my students' project last school year...

    They don't HAVE to pre-record it. They are welcome to perform it in front of the class, as well. I have a rubric I use to grade, but it's on my school computer. I'd be happy to send it your way!

    Good luck!

    P.S. Aren't foldables great??

  3. I had a similar experience with some elementary ed pre-teachers last year. I like your big shape to fold idea--maybe I'll steal it for next year. This year I'm having them do a lot of the activities from the book "Shape Makers" by Michael Battista--it uses Geometers Sketchpad (which I have, but they don't, so I've made some applets that do pretty much the same thing:

    The book has a lot of good ideas for different ways to ask students about quadrilateral properties: I think you might like it.

  4. Oh, they are too funny. Looks like they had a blast doing that, and yes, I would love to see your rubric. I'm horrible at rubrics and it would be nice to get some ideas. ... and YES, I think it's almost time for another foldable.

  5. Lsquared ... those applets are awesome and easy to understand. Thank you. I'll send the e-mail link to my students if you don't mind.

  6. I was just talking to my daughter (a college student and problem-solver) about how poorly my students did on the Parallelogram unit exam, and how poorly they seem to do every year despite my introduction of different graphic organizers, target skill worksheets, etc. It took me a week to grade the exams this year because I was so depressed with my own performance as a teacher.

    In any case, on Monday, I am planning a tiered exam review/recap lesson, which will include a foldable for those students who can't seem to remember the properties of the different quads. Any other ideas are welcome (although the applets on the langfordmath page crashed Firefox).

  7. " I'll send the e-mail link to my students if you don't mind"
    Please do--I love it when my stuff is useful.
    Mermaid--I'm sorry to hear that the applet crashed for you
    (geogebra is large-ish when running from the web, and sometimes is takes a long time to load, and sometimes it crashes). If you run geogebra, you can get my basic file of quadrilateral makers here: