Math Tricks that Hurt

Change Sides, Change Signs

The other day, I noticed that my students were struggling with rewriting an equation in Slope-Intercept Form (Solving for y).  So I created this desmos activity.  CLICK HERE.

One student in particular would always have his signs incorrect.  Like every single problem and every single term.  I investigated a little bit more and he was using "Change Sides, Change Signs".  This 'trick' implies that terms are moving and changing signs.  I can see how this might be the case with adding and subtracting terms, but with multiplying and dividing this 'rule' falls apart.  

Instead, let's teach our students that the sign isn't changing, the operation is.  Not only is it true, it works in every case and in much simpler than a catchy slogan.  

This isn't a negative 3 that will turn into a positive 3.  Rather, this is minus 3 and we want to do the inverse: add three. 

For this one, that student understood that he needed to divide by 2, but he had it stuck in his head that he needed to change the sign as well and divided by -2.  Let's go with inverse operations and divide by 2.  

FOIL

Next on my list is FOIL.  This is how I was taught to multiply binomials, and this is how I taught my students to multiply binomials, until recently.  For me FOIL is now in the category of 4-letter words.

Again, let's look for something true and simple.  When we teach our students to FOIL, we are limiting them.  This allows them to only multiply two binomials.  Instead, if we teach them that polynomial multiplying is just distributing, we open more doors for them.  Now, they can multiply binomials, monomials, trinomials, whatever-their-hearts-desire-omials.  

What are you least favorite math tricks?