Category: Expressing Geometric Properties with Equations

Expressing Geometric Properties with Equations Midpoint

“Find the midpoint between (2,5) and (2,396)”

Post author By mpershan
Post date April 7, 2014

"Find the midpoint of the line segment connecting (2,5) and (2,396)," at the beginning of the unit. Can you predict the top three responses?

— Michael Pershan (@mpershan) April 7, 2014

What would you predict? Here are some twitter responses:

@mpershan Is (0,391) one of them? That seems like a way to get an answer from those two numbers.

— Evelyn Lamb (@evelynjlamb) April 7, 2014

@mpershan (3.5, 199) (2, 200.5) (2, 198)?

— David Wees (@davidwees) April 7, 2014

@mpershan (2,198) is probably one of them. Maybe(1,198). But I am otherwise stumped. Oh! (201.5) maybe?

— Christopher Danielson (@Trianglemancsd) April 7, 2014

@mpershan er…(2, 195.5) as a top answer.

— Christopher Danielson (@Trianglemancsd) April 7, 2014

@mpershan I’ll bet at least one of the top 3 responses includes *two* points.

— Chris Lusto (@Lustomatical) April 7, 2014

—

Here’s your answer key…

First Place:

Second Place:

Third Place

Pythagorean Theorem and Ladders

Post author By mpershan
Post date January 21, 2014
4 Comments on Pythagorean Theorem and Ladders

What is this student doing? Where is their misunderstanding? @mpershan #mathmustakes pic.twitter.com/7YQNGnopwi

— Lisa Bejarano (@lisabej_manitou) January 20, 2014

Let’s help Lisa out in the comments, mmk?

Algebra in Geometry Expressing Geometric Properties with Equations Vertical Angles

Verticle Angles

[Re: the title, I know I’m not the only one who has seen “vertical” misspelled in every possible way.]

It’s easy to say that this is sloppiness on the part of the student. And maybe it is. But it’s the sort of sloppy mistake that I would rarely make, and that beginners often make, which leads me to think that there’s something else going on here as well.

We’ve talked about reading on this site before, and it’s something that I don’t know a ton about. But it seems to me that part of “looking for and making use of structure” is something like what I’m trying to get at. If you’re really experienced at math, then you start seeing a problem like this as rigidly structured into two separate and equal expressions. I’d bet that for a student that doesn’t have a lot of experience with these sorts of problems that sort of structure is less apparent, and this sort of mistake is less apparent.

Did that make any sense?

[Thanks to Nora for the submission!]

Expressing Geometric Properties with Equations