Examining Structure in Special Quadratics with Google Drawing

I have taught “difference of squares” and “perfect squares” for over ten years using various traditional instructional techniques including “compare and contrast;” but this year I tapped into Google Drawing to increase the intensity of student engagement.  I copied and pasted a group of expressions from the exploration in our CPM textbook so when my student teams opened the drawing in their classroom stream, it looked like this:8.1.5

Each team chose a color selected an expression and put a matching border on it.  Then they dragged it away where there was room to factor it.  From my desk top, I called attention to cases that needed a second look so the teams could discuss and revise their work. Then that team could select another until all expresses were factored.  Without even peeking at their learning logs each class produced something that looked like this:


Up to this point, student teams made very few errors, but then I asked them to make two columns:  Difference of Squares and Perfect Squares to sort the expressions.  Many teams wanted to put x^2 – 19x + 25 in the difference of squares column because of the subtractions sign, and soon we had to stop to review what was written in the learning logs.  As I walked around the room, I could see some students had written good definitions, but showed no examples.  Others had examples but no explanations.  I had a major “duhhh” moment with respect to teaching inquiry learning that day.  Students not only need to be able to use good math vocabulary when they discuss concepts in the classroom, they must also write precisely so that they can recall nuances and details weeks later.

The final Google drawings looked something like this:

draw2But a few teams couldn’t leave well enough alone (really didn’t want to leave at all) so theirs ended up like this:

draw3But the real take-away was the importance of documenting their understanding precisely like this:



There are many viable STEM careers that require such precise descriptions, including technical writers, documentation specialists, QA test script writers, to name a few.  The skills related to teaching an learning with inquiry are new for all of us, and we just keep getting better and better together.






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