Geometry Right Triangles

Special Right Triangles

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Let’s take for granted that these students don’t have conceptual understanding of the Pythagorean Theorem, because if they did, then they wouldn’t make these mistakes. (I actually think that we need to be more careful with the ways that we toss around phrases like “conceptual understanding” but whatever.)

What do these mistakes reveal about how these kids think about right triangles and the Pythagorean Theorem in theĀ absence of conceptual understanding? Why does this ever make sense to the student?

Thanks to Michael Fenton for the submission!

Geometry Geometry Pythagorean Theorem Right Triangles

Sqrt(1) and Right Triangles


This mistake seems ripe for theorizing. Would a kid make this mistake if the hypotenuse was 4 instead of 10?

Distance Between Points Geometry Trigonometric Functions Trigonometry

Estimating cosine ( + Distance Bonus Mistake! )



What does this response reveal about this student’s understanding of the basic trig functions?

(Bonus! What’s up with that response for distance? Can you explain why that mistake is a tempting one to make?)