I love that I am a HS teacher teaching 6th and 7th grade. I am their first stop in Algebra. And, I know what they really need to remember. However, I am afraid that I may forget what they mess up on a regular basis! Some things are obvious – like canceling out individual terms in expressions. But, some are more forgettable.
Tonight on Twitter, druinok posted
how to fix kids from doing 3|x+4| = 3x+12??
Ok, totally forgot about that one!
Yes, I did teach them the distributive property last week using, “THE CLAW!!!” and then two days later taught them absolute value and told them that they could not distribute into the | |. Give it one day, take it from them the next. The question is, are they EVER going to remember that random bit of miscellany until they do it for a few years? Doubtful. So, what do we do as teachers? Make it memorable! How am I going to do that? Well, since we aren’t graphing yet I can’t make them believe that. However, I can tell them that the BARS keep out the CLAW. I am going to tell them this ALOT and we are going to do ALOT of problems. Hopefully it will stick!
So, all of you Algebra teachers out there, if you want to comment to me what drives you CRAZY as you come to it so I won’t forget, I would really appreciate it! Hopefully, I can find a way to permanently imprint the correct way into their heads! : )
When solving equations, you have to add or subtract before you can divide. My kids are divide happy!
And when the variable is on both sides, get variables on one side and constants on the other!
In ordered pairs, every pair has an (x, y) and the x always comes first. I explain them as a couple, x and y, and ladies first! Or they are in alphabetical order.
Oh! I love the ladies first! I have never heard of that one!
But how many middle schoolers have had (or can remember) enough biology to get X and Y chromosomes right? Better stick to alphabetical order—there’s at least a 40% chance of them remembering the alphabet song (though it will take them 10-15 seconds to sing through the song before they remember that x is before y).
But you can distribute into an absolute value. 3|x+4| = |3x+12|, just as 3(x+4) = (3x+12). The difference between the cases is that the parentheses around (3x+12) are superfluous, but the absolute value bars around |3x+12| are not.
Dave – Yes, you can, but that is only because the 3 is a positive number.
and, you preserved your | | signs. When most students distribute into | |, they are used to “getting rid of” the parenthesis, so away go the bars!
In lieu of creating several rule exceptions and corresponding acronyms, might I ask: why do they need to distribute the three at all? What is wrong with 3|x+4|?
I couldn’t agree more with everything that you said in your comment. They DON’T need to at all. I don’t make a rule exception. I tell them to not distribute numbers into the absolute value bars. Period. But for some reason, some of them just can’t help it. I think they forget what the absolute value bars mean when solving an equation and just distribute through them.
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