Pythagorean Exploration

I don’t love this textbook task.

Too many substeps before students return to the question: what’s the relationship between the length of the sides of a right triangle?

“For each right triangle, write an addition statement…”? C’mon!

But I’m hesitant to join the down with textbooks revolution; I don’t want to associate myself with the back to basics movement. So in conversations where the suggested alternative is more worked examples, I soften my criticism.

Besides, it gives me something to modify. Instead of completing the table, I could challenge students to find right triangles and ask “What do you notice?”

One problem: this requires “attend to precision” to do some heavy lifting.

4-7-8

The 4-7-8 Right Triangle

This leads to some truly awkward feedback: “Are you sure it’s a right triangle? You might want to measure again.”

GeoGebra may provide a solution.

4-7-8 GGB
Click to view on GeoGebraTube
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One thought on “Pythagorean Exploration

  1. I remember in the 1980’s watching my geometry teacher drawing geometric shapes with infinite precision on the blackboard and then I tried to duplicate the drawing on my page with a straight edge and it ended up looking like abstract art. The great thing about Geometer’s Sketchpad and Geogebra is that you could say “Now try that with a=3, b=4, and c=5,” or some other combination, and your students can quickly create the figures. Much more opportunities for modeling and exploration, and your students don’t end up with abstract art.

    Glenn Laniewski
    Blog:
    autismplusmath
    Latest post:
    Math teachers, start baking your Pi Day pies early
    http://autismplusmath.blogspot.com/2014/02/math-teachers-start-baking-your-pi-day.html

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