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?


Feedback The Number System

Converting decimals to fractions

andy zsiga2  andy zsiga3andy

What do you see as the issue here?

(Thanks Andy for sending these in!)

Exponents Feedback Linear, Quadratic, and Exponential Models* logarithms

Constants and Exponents

pam patterson 3


Open thread. Go wild!

(Thanks to Pam for the submission.)

Expressions and Equations Feedback Ratios and Proportions Uncategorized

Cross addition isn’t a thing

stadel proportion


Presented without comment, and with thanks to Andrew.

Arithmetic with Polynomials and Rational Expressions Feedback Rational Expressions

Rational Expressions



How would you help this student?

Another thought: would this student have made this mistake at the beginning of the problem? In other words, is this mistake more likely to happen as the problem goes on than at the beginning? If so, then what does that say about problem-solving?

Thanks to Anna for the submission!

Feedback Geometry Quadrilaterals

A Parallelogram is a Rhombus

ASN 6 2 ASN 6

These are some “Always, Sometimes, Never” questions. Like, “Is it always, sometimes or never true that a rhombus is a parallelogram.”

What’s the fastest way to help these students?

(Thanks for the submission, Tina C!)

Arithmetic with Polynomials and Rational Expressions Feedback Rational Expressions Rational Expressions

Factoring + Rational Expressions

IMG_20130331_171842 IMG_20130331_172201

What’s the fastest way of helping these students?

Thanks to Anna for the submissions.


Expressions & Equations Feedback Middle School

Multiplication and Exponents

pic5 pic8


Dip into the archive and check out our other exponent mistakes. What do you notice?

Thanks to Julie for the submission!

Exponents Expressions Expressions Expressions & Equations Feedback

PEMDAS and powers

Question: Evaluate the expression -z^{2} + x(3-y)^2  when x = 10,   $latex y = -2$, and  $latex z = -2$.

pic2 pic3 pic4 pic6 pic7


These submissions come from Julie, who posted about this stuff on her blog:

What happened?  First, I HATE PEMDAS AND ANYONE WHO USES IT.  This starts early, and students are already brainwashed by 6th grade when I get them.  All of the GEMS in the world can’t seem to fix this.  I hate PEMDAS because students see parenthesis and go into “I must do that first” mode, even when there is only ONE number inside the parenthesis.  Just because it is in parenthesis, one number, for example (2), does NOT a group make.

Discuss her evaluation of the problem, and her next steps, either in the comments or at her place.

Feedback Trig Identities Trigonometric Functions

Trig Identities are just really hard to prove

photo (5)


What’s going on here? Tell a story of how this kid wrote this stuff?

Thanks to Jonathan Newman for the submission!