Category: Arithmetic with Polynomials and Rational Expressions

Constructing Trinomials – Where to go Next?

Post author By Bryan Penfound
Post date November 1, 2016
8 Comments on Constructing Trinomials – Where to go Next?

Hi everyone,

My name is Bryan Penfound. Awhile back I was asked if I would be interested in helping out at MathMistakes and I said yes not knowing how challenging this term would be for me. Now that I have settled in a little bit, I thought I was a bit overdue for a post, so here goes!

Recently while volunteering at a local high school in a grade 9 classroom, I had to opportunity to observe students’ answers to the following question: “Create a trinomial in the variable t that has degree 3 and a constant term of -4.”

Here are five of my favourite responses:

I would love to get some discussion going. Choose one of the polynomials above and try to deconstruct what the student knows and what the student still has misconceptions about. What follow-up questions might you ask to learn more information about how the student is thinking? What follow-up questions might you ask to help with any current misconceptions?

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!

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.

Arithmetic with Polynomials and Rational Expressions exponents

Simplifying exponents

How would you help this kid out?

Thanks to Chris Shore for the submission!

Arithmetic with Polynomials and Rational Expressions exponents Expressions Seeing Structure in Expressions Simplifying expressions

Combining Like Terms + Exponents

Post author By mpershan
Post date January 20, 2013

Here are 7 mistakes. There represent all of the variety of mistakes from a selection of 36 students. The first two mistakes were repeated by several students, but the last 5 were unique in the sample.

Which of these mistakes would you predict? Which ones surprise you? Can you make sense of them all?

Arithmetic with Polynomials and Rational Expressions exponents Rational Expressions Seeing Structure in Expressions

Cross-Multiplying

What’s the mistake? Diagnose the disease, and find the cure in the comments.

Thanks to Anna Blintsein for the submissions. Go follow her on twitter!

Arithmetic with Polynomials and Rational Expressions Distributive Property exponents

Classic Mistakes with Exponents

Post author By mpershan
Post date September 28, 2012
6 Comments on Classic Mistakes with Exponents

Here are two classic mistakes:

Whenever I see a mistake that recurs at all different levels, and with all different students, I wonder: what makes this mistake so attractive? What’s the misconception? And what can we do about it?

Say something smart in the comments, and then go check out this post from Fawn Nguyen.