Expressing Geometric Properties with Equations Midpoint

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

What would you predict? Here are some twitter responses:

Here’s your answer key…

First Place:



Second Place:



Third Place


Expressing Geometric Properties with Equations Feedback Pythagorean Theorem

Pythagorean Theorem and Ladders

lisa b pythag ladder

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

Conics and their Equations

2013-05-26 16.13.24-1


Where does the 1/2 come from? Why did that seem especially tempting? What else is up here? What sort of help does this student need?

Thanks to Tina for the submission!

G-GPE.2 Quadratic Functions Quadratic Functions

Equation of Parabola

From the student’s work, what can we infer that the student knows?  What is the student thinking? How would you help?