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.


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

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
    Latest post:
    Math teachers, start baking your Pi Day pies early

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