Category: High School: Algebra

Absolute Value Seeing Structure in Expressions

Value of Absolute Value

Kids just can’t seem to figure out absolute value. Pat writes,

“I’ve posted a mistake I see ALL THE TIME from my students when working on Absolute Value Equations. Looking for any advice on how other teachers are handling this issue. Thanks!”

Incidentally, I think that there’s a very good argument for this sort of thing being struck from the curriculum in its entirety. It’s entirely isolated in the curriculum, unconnected to anything else.

Thanks to Pat John for the submission!

Exponents Seeing Structure in Expressions

-3X as 3 Negative X’s

Check out this kid’s explanation for why you end up with “+3x” from “-(-3x)”:

“You have -3x, so that’s three negatives, and then you have this other negative and that makes four…”

You can find this explanation at around 3:33 in the video below:

Exponents strike again!

(Or, maybe I misunderstood the kid’s explanation in the video? Lemme know if I did, please!)

Thanks to Jonathan for the submission.

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!

Arithmetic with Polynomials and Rational Expressions Feedback Rational Expressions Rational Expressions

Factoring + Rational Expressions

Post author By mpershan
Post date April 24, 2013
2 Comments on Factoring + Rational Expressions

What’s the fastest way of helping these students?

Thanks to Anna for the submissions.

Arithmetic with Polynomials and Rational Expressions Multiplying Polynomials

Multiplying monomials and binomials

Post author By mpershan
Post date April 15, 2013
2 Comments on Multiplying monomials and binomials

$Math Mistakes - Heather$

There’s a lot going on here. What about this work do you find the most interesting? How would you help this student?

Thanks to Heather for the submission!

factoring Quadratics Reasoning with Equations and Inequalities

0 = -2

Post author By mpershan
Post date April 10, 2013
3 Comments on 0 = -2

How worried are you about this mistake?

Thanks again to Tina! Go Tina!

Arithmetic with Polynomials and Rational Expressions Exponents exponents

Negative Exponents with Tons of Variables

Post author By mpershan
Post date March 21, 2013
3 Comments on Negative Exponents with Tons of Variables

I think the temptation I have is to call this a “careless” mistake and urge more practice. Let’s probe deeper.

1. What does this kid know and understand about exponents?

2. What’s the fastest way to help?

3. What makes this mistake so tempting?

Thanks to Sadie Estrella for the awesome addition to our ever-mounting pile of exponents mistakes.

Arithmetic with Polynomials and Rational Expressions factoring Feedback

Factoring and Canceling

Kelli Prine submits the above, and asks “This student keeps factoring the terms and canceling. What can I do to clarify the process?”

I expect some excellent comments on this one. Don’t disappoint.

factoring Seeing Structure in Expressions

Factoring

You grade this on Sunday. What do you do on Monday? Go over the procedure that this student almost flawlessly executed? Again? What do you emphasize? Checking your answer?

Thanks to John Weisenfeld for the submission.