Category: Geometry

Estimating cosine ( + Distance Bonus Mistake! )

Post author By mpershan
Post date March 19, 2013
4 Comments on 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?)

Missing Side of Triangles

Here’s a mistake from a trig class. Would the question be easier in a Geometry class?

Here’s my theory: teachers underestimate how weak most of our students’ knowledge is, and how weakly in transfers. In particular, this problem became twice as difficult as soon as it was offered in the context of a trig class, without carefully writing the right angle in there with the lil’ square.

Am I right? Wrong?

Thanks to the Uncanny Tina Cardone for the submission.

Equations of Parallel and Perpendicular Lines Linear, Quadratic, and Exponential Models* slope

Holy cow, there’s a lot to dig into here. Read this post carefully.

Post author By mpershan
Post date February 21, 2013
6 Comments on Holy cow, there’s a lot to dig into here. Read this post carefully.

There’s a ton to comment on here. I doubt you’ll need much in the way of a prompt, but here goes: what mistakes are missing? You grade this test on Sunday; what does Monday’s class look like?

Thanks to Tina Cardone, who is not-so-slowly taking over this blog, for the submission.

Geometric Measurement and Dimension Pythagorean Theorem Right Triangles Similar Figures Similarity, Right Triangles and Trigonometry

A whole bunch of questions about right triangles

Post author By mpershan
Post date February 20, 2013
2 Comments on A whole bunch of questions about right triangles

What other mistakes would you expect to see from this problem? How do you teach so as to help students avoid these pitfalls?

Thanks to Tina Cardone for the submission.

Similar Figures

What’s the fastest way to help this student?

Thanks to Nico for the submission.

Circles Circles Feedback Pythagorean Theorem

Circumference and Right Triangles

Post author By mpershan
Post date December 19, 2012
4 Comments on Circumference and Right Triangles

Say something smart in the comments about why kids forget “little” things on problems. Or, alternatively, disagree with the premise of my first question. (How’s that for a lousy prompt?)

Thanks to Mark Kingsbury for the submission!

Tags Circles

Geometric Measurement and Dimension Geometry High School: Geometry Pythagorean Theorem Quadrilaterals Similarity, Right Triangles and Trigonometry

Baseball Fields and Geometry

Post author By mpershan
Post date November 7, 2012
1 Comment on Baseball Fields and Geometry

What made this question hard for the student? How come they got it wrong? Why did the student get it wrong in this particular way?

Today’s submission comes from Tina Cardone, who blogs at Drawing On Math.

Geometric Measurement and Dimension Geometry

Hexagons!

Define “Hexagon”:

What does this student know about hexagons? What does the student think he knows, but doesn’t? What does the mistake reveal about his thinking, and what would you do to help?

G.CO.10 Isosceles Triangles Proofs

Problems with Proofs

The proof above isn’t great. In the comments, take on any of the following questions (or any others):

Sometimes kids slap stuff together when they’re confused, and other times they’re substantively mistaken. Which is this, and what evidence supports your position?
How would you help this student recognize that the logic in his proof doesn’t flow?
What would your next steps be in working with this student? What sorts of problems would you ask him/her to solve?
From the picture above, what evidence of knowledge do we have?

Tags G-CO.10

Geometry Isosceles Triangles

ITT Support

This one is a little bit hard to read, so I’ve transcribed the student’s writing below the image.

What’s going on, and how could you help?