Category: High School: Number and Quantity

Complex Numbers The Complex Number System

Complex Division

Thanks to John Burk for the submission. He writes, “I know this student wouldn’t simplify (6+2x)/(3-x) this way.”

So: if the student wouldn’t simplify (6+2x)/(3-x) this way, then how did the student end up messing it up for (6+2i)/(3-i)?

Vector and Matrix Quantities Vectors and Matrices

Perpendicular(?) Vectors

What’s the mistake? Why did the student make this mistake, in particular?

Thanks again to the tweeting and blogging Kate Nowak for this submission.

Vector and Matrix Quantities Vectors and Matrices

Perpendicular Vectors

Assignment: reconstruct what was going through the student’s mind as she solved this problem and, apparently, answered the problem with confidence.

This mistake has been brought to you by Kate Nowak, who blogs and tweets and stuff.

Arithmetic Negative Numbers The Real Number System

Order of Operations, Negative Numbers

Post author By mpershan
Post date October 2, 2012
2 Comments on Order of Operations, Negative Numbers

Say something smart about this in the comments. When you’re done, go check out the blog from whence this mistake came.

Complex Numbers Quadratic Functions The Complex Number System

Complex Roots and Quadratics

Post author By mpershan
Post date October 1, 2012
1 Comment on Complex Roots and Quadratics

Here’s the work:

Can you make sense of it? What’s the cause of this mistake? How could you help?

Complex Numbers Quadratic Functions The Complex Number System Uncategorized

From complex roots to a quadratic equation

Post author By mpershan
Post date August 28, 2012
2 Comments on From complex roots to a quadratic equation

How did this student end up with the answer he did? What does it seem that he knows about complex numbers?

Complex Numbers N.CN.2

Adding Complex Numbers

What is it about complex numbers that this student finds confusing? Do you think he would make an identical mistake on $(12 + 3x) + (2 - 3i)$ ? Why or why not?

N-RN.2 Radicals

A classic: Subtracting radicals

Post author By mpershan
Post date August 15, 2012
3 Comments on A classic: Subtracting radicals

This mistake is a classic in my classroom. What does the student understand about combining like terms, but what is the conceptual model that makes this sort of mistake so enticing?

exponents N.RN.1

Classic: Zero exponents

What makes this idea so attractive to students? Why should it be true that $2^0=0$ ? How do you help them see the light?