So, you’d think that combining a positive number and a negative number would be a fairly straightforward thing, huh?
Well, unfortunately, a lot of students think it’s easy. They think it’s too easy. They think there’s one simple rule that guides them to the very same kind of answer every time. And that’s exactly where they get into trouble.
The truth is that combining a positive and a negative number is a fairly complicated operation, and the sign of the answer is dependent on a nmber of factors.
This video reveals a common mistake students make when tackling these problems. it also shows the correct way to approach these problems, using the analogy of having money and owing money to make everything make sense.
So take a look and see if this explanation doesn’t end the confusion once and for all.
And don’t forget: there are practice problems at the end of the video. Do those to make sure you’ve grasped the concept.
Ever thought this after you got back a math test … ?
“Why did I do that? I used a rule where it doesn’t apply!”
Yep, that’s exactly what we’re looking at in Algebra Mistake #3, a case of “overgeneralizing.”
The situation we’re dealing with involves over-generalizing everyone’s “favorite” property, the distributive property!
How’s that? Well, you’re supposed to use the distributive property when a number multiplies terms inside parentheses.
But sometimes students get a little bit — shall we say — “carried away” — and use the distributive property principle in other situations, too. The results are a tad bit comic, if you’re the teacher, but not so funny if you’re the student and you’ve made the mistake 19 times on a test with 20 problems.
Anyhow, after you watch the following video you shouldn’t have to worry about this again because we’ll get the two wires in your mind untangled so you never make this mistake again. So just relax, watch and learn.
And oh yes, don’t forget that we’ve provided some practice problems at the end of the video to help you make sure you’ve got the concept nailed down.
Now that you’ve gotten a taste for the benefits of analyzing algebraic mistakes, it’s time to explore a second common mistake. This one is so common that nearly every student commits it at least once on the road to algebra success.
As you watch the video, notice how by thinking hard about two expressions, we can think this mistake through to its very root, thus discovering the core difference between two similar-looking algebraic expressions.
And along the road, we’ll learn a general strategy for decoding the meaning of algebraic expressions. What I like about this strategy is that you can use it to understand the meaning of pretty much any algebraic expression, and you’ll see that it’s not a hard thing to do. In fact, it just involves using numbers in a nifty way.
Best of all, students usually find this approach interesting, convincing and even a bit fun. So here goes, Common Algebra Mistake #2 …