Exponential Functions Interpreting Functions Linear, Quadratic, and Exponential Models* Rational Expressions

Seeing Exponentials Where They Aint

Photo (4)


Did this kid just get excited by a coincidence? Or is there something deeper going on here?

(Thanks Tina!)

Functions High School: Functions Interpreting Functions Uncategorized


tina infinity


The question asked for the range of the function SQRT(x).  What are your thoughts about the way the student answered the question. What does it show about what this particular student knows.*

In the past, I’ve publicly kvetched about how the only questions that we grapple with on this blog are about the particularities, rather than the generalities, of student work. This is a time when I think that the most interesting questions are accessed through thinking about what this particular kid was thinking. I’d also be interested in hearing how you think this represents a trend in students’ thinking, in general.

Thanks to Tina for the submission!

Functions Graphing Interpreting Functions Uncategorized

A Contest!


Marshall Thompson is offering a substantial bounty for the correct explanation for this mistake. (He knows the truth from talking to the student.)

Who’s got it?

Functions Interpreting Functions

Range of a Function


Bob Lochel writes:

“I used this question as part of a benchmark assessment given to over 1,100 students at our high school, as preparation for the state test.  Only 14% of students gave the correct answer B, while 66% of students chose A as their response.  I’m not surprised that students would perform weakly on a domain/range question, but I am surprised that so many chose A.  I featured this problem as a set-up for a domain and range activity on my blog:, but feel free to share it with the mathmistakes crowd.”

So, what do we think about choosing A? Any theories?

Graphing Interpreting Functions

Graphing Stories



What does this question reveal about the student’s understanding?

(Also: do you agree with the mark given by the teacher?)

Interpreting Functions linear functions Linear, Quadratic, and Exponential Models* Solving Linear Equations

Solving for a variable


Why do kids make this mistake?

Graphing Interpreting Functions

Impossible Graphs

IMG_2584 IMG_2586

How would you mark these problems? What do the kids understand? What don’t they?

Functions Interpreting Functions

Function Notation

How do you teach function notation? How would you help your students avoid this sort of mistake?

F-IF.7 Graphing

“Can’t graph it. Too big a line.”

“The line’s too big.” So what? Why does this matter to the student, and what does this reveal about his understanding of graphing?