Building Functions Negative Numbers Sequences and Series Series The Real Number System

Arithmetic Series and Subtracting Signed Numbers


What feedback would you write on this kid’s paper? Why?

(Thanks, KN!)

Building Functions Rational Functions

“y=x/(x+1) has got to be a line.”

We’ve been studying graphs of rational functions in Precalculus.

Me: “Take 1 minute with your group: what will the graph of y = x/(x+1) look like?”

One group, during discussion, asserted that it had to be a line, using a sort of process of elimination: it’s not a parabola, it’s not cubic, it’s not a hyperbola.

Interesting, right? Why does this seem like a linear equation? I guess that it sort of looks like one…

Building Functions Feedback Functions Inverses

Finding Inverse Functions





What can we say that this student does or does not understand about inverse functions?

Building Functions Inverses

One inverse functions problem, many mistakes

precalc 23

precalc 23 2precalc 23 3 precalc 23 4 precalc 23 5

You grade these tests on Sunday, and you see these kids on Monday. What does the lesson plan look like?

For more context and analysis, go check out the blog from whence these came.

Building Functions Linear, Quadratic, and Exponential Models* Solving for a Variable

Equations with multiple variables and constants


Are these two mistakes related? What’s the fastest way to help this student?


Building Functions Functions

Composition of Functions

In the comments, say something. If you’re looking for a prompt, how about “Give a theory as to why this kid made the mistake that he did.”

Building Functions logarithms

Solving logarithmic equations

Selected by: Christopher Danielson

Question: What’s up with this? Why does this piece of student work matter? Does it?

Building Functions Functions High School: Functions

Inverse Functions

What does the student know, and what does he misunderstand? How would you help?

Today’s submission comes via Christopher Danielson, who blogs at Overthinking my teaching.

Building Functions High School: Functions

Following a recursively defined rule

What does the student understand about recursive functions? What’s she confused by? How would you help?

Building Functions exponents High School: Functions

Matching a recursive function to a table

What does the student know? What’s the mistake? How would you help?