# Slip Sliding Away

A look at the slip slide method of factoring polynomials

Facilitator(s): Cynthia
Date of Meeting: January 8, 2016
Problem: pdf · docx

Cynthia started by showing us Kahoot, a free and easy way to run a quiz game in class with students buzzing in through cell phones. Kahoot allows you to create surveys and surveys. Students load Kahoot.it through their cell phone and are asked for a PIN. Once a student enters a PIN, they join the game.

 screen on computer or projector screen on cell phone (or tablet, computer, etc.)

We competed on a short math quiz Cynthia wrote. The final question was something like, “Which of the following is not way to factor polynomials?” The choices were “factoring out a monomial,” “the slip-slide method,” and “completing the square.” Most of us chose the slip-slide method, thinking that it was just something Cynthia made up. We were wrong. It turns out that the slip-slide method is a way to factor a polynomial…

Cynthia learned about this method from Jeffrey Steckroth’s article “A Transformational Approach to Slip-Slide Factoring” (Mathematics Journal, vol. 109, no. 3). In the article, Steckroth explains how he first learned the method from a student and then struggled to understand why it works. Cynthia started the discussion by writing out the steps on the board, but she didn’t explain what to do. She wanted to give us the opportunity to deduce that for ourselves based on the steps she wrote down.

Here’s the polynomial we’re trying to factor:

$6x^2+5x-4$

Here is the slip-slide method for factoring this polynomial:

Step One: $x^2+5x-24$

Step Two: $(x+8)(x-3)$

Step Three: $(x+\frac{8}{6})(x-\frac{3}{6})$

Step Four: $(x+\frac{4}{3})(x-\frac{1}{2})$

Step Five: $(3x+4)(2x-1)$

Cynthia showing us the slip-slide method

We then worked individually to follow the steps of this method and then try it out on other polynomials to see if we could make it work. After we all had a handle on how it worked, Cynthia asked us to come up with some questions we had about the method so that we could explore them together.  Some questions we generated were:

• Is there a different way to write this method so that there is continuity of equivalency?
• At what step does the process become equivalent to the original trinomial?
• Why are we allowed to scale up the leading coefficient and the constant term but not the middle term?
• If a trinomial isn’t actually factorable, at what point does this become evident when using the slip-slide method?
• What happens if the fractions produced during step 3 can’t be simplified?

At this point, the discussion really got going and everyone took turns going up to the board. Leo and Todd had some great ideas about why the slip-slide method worked, and they explained their thinking to the group. Then Todd and Maggie noticed some important connections between the slip-slide method and their preferred strategy, the A-C method.

Maggie takes us through the A-C method

Even though the meeting was scheduled to end at 5:00, no one was ready to leave! We still had lots of questions and wanted to keep exploring them. In the end, the board looked like this:

Down the rabbit hole we go…

We were never quite able to articulate why the slip-slide method works, even though we all left with a good understanding of how to use it. We also agreed that it would be great to tackle this topic again at a follow-up meeting, and I really hope we get the chance to do it.

Try the method and see what you can explain about why it works.

Here are some polynomials we factored in order to test the slip-slide method:

$6x^2+11x-10$

$6x^2+x-2$

$3x^2-8n+4$

Here is the article (Steckroth – Transformation Approach to Slip-Slide Factoring) that Cynthia shared with us. She only gave us the first couple pages so as not to spoil the question of why. You might want to try this out for a while before reading the article since it definitely seeks to explain why it works.

In attendance: Cynthia, Eric, Esther, Leo, Maggie, Solange, Todd, Tyler

Programs represented: CUNY PD Team, York College, BMCC, The Fifth Avenue Committee, The Literacy Assistance Center, DOE, Turning Point

Location: The Fifth Avenue Committee, 294 Smith St., Brooklyn, NY

Respectfully submitted by Tyler & Eric