Category: Algebra 1

Completing the Square

What do you notice in this student’s work?

Thanks to Matt Owen for the mistake.

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!

exponents The Number System

Why kids mess up exponents

Post author By mpershan
Post date April 9, 2013
2 Comments on Why kids mess up exponents

I’m trying very hard to get people as excited by exponent mistakes as I am. I just think that they’re really cool and interesting. I gave kids this survey today in class to 9th graders who have never seen negative or rational exponents before, just to see what they’d do.

The results did not disappoint. The mistakes they made will find their way to the site soon enough, but for now, drop by Rational Expressions and let me know what you think of the experiment and its results.

Here’s one result of the survey to whet your appetite:

If you decide to give your students the exponents survey, or make a survey of your own on exponents or any subject, I would sure love to see it. Send it my way, if you will.

Radicals The Real Number System

Over-rationalizing

What’s the fastest way that you could help this student?

Yo, thanks KFouss!

Distributive Property The Number System

What is the Distributive Property?

Post author By mpershan
Post date April 7, 2013
2 Comments on What is the Distributive Property?

Here are a bunch of responses to the same question:

If this is your class (and this is the Spring!) then how do you respond?

exponents Expressions and Equations

(-2)^5 + (2)^0 = 0

Open comment thread.

A tip of the hat to Gregory Taylor for the submission.

Distributive Property Expressions Standards for Mathematical Practice

“Prove the following conjecture: The sum of any 3 positive consecutive odd integers will be divisible by 3.”

Post author By mpershan
Post date March 31, 2013
1 Comment on “Prove the following conjecture: The sum of any 3 positive consecutive odd integers will be divisible by 3.”

First, I just love the question. Second: theorize! What happened to this student? What are some good signs in the student’s work?

Thanks to Bree for the submission.

Also: I categorized this under “Standards for Mathematical Practice.” Does anyone have another CCSS standard that fits this problem and work?

Exponents Expressions Expressions Expressions & Equations Feedback

PEMDAS and powers

Post author By mpershan
Post date March 24, 2013

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

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.

Arithmetic with Polynomials and Rational Expressions exponents Exponents