Kiss those Math Headaches GOODBYE!

Archive for the ‘“Scaffolding” in Math’ Category

How to Remove Math Terms from Parentheses


How do you get math terms out of parentheses? And what happens to those terms when you remove the parentheses?

It seems like the process should be simple. But this issue often plagues students; they keep getting points off on tests, quizzes, homework assignments.  What’s the deal?

The deal is that there’s a specific process you need to follow when taking terms out of parentheses, and what you do hinges on whether there’s a positive sign (+) or a negative sign (–) in front of the parentheses.

But not to worry. This video on this page settles the question once and for all. Not only that, but the video provides a story-based approach that you can teach (if you’re an instructor) or learn (if you’re a student) and remember (no matter who you are). Why? Because stories are FUN and MEMORABLE.

So kick back and relax (yes, it’s math, but you have a right to relax) and let the video show you how this process is done.

And in customary style, I present practice problems (along with the answers, too) at the end of the video so you can be sure you understand what you believe you understand.

 

 

 

 

 

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Algebra Mistake #2: How to Understand the Difference between A x A and 2 x A without Confusion


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 …

 

How to Grasp the Distributive Property w/ Fun, Visual Symbols


Progress …

I made some progress yesterday helping a boy understand the distributive property, and it was mostly due to the use of visual symbols.

I’d like to share the process of my tutoring, for it shows how important it is to break an algebraic procedure into its constituent “baby” steps. I’d also like to share the process because I used a fairly unusual technique — using visual, non-algebraic symbols to take the place of algebraic symbols. As you’ll see, this technique has some interesting advantages.

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How to Decrease Algebraic Mistakes – Part 5


This is the fifth in a series of posts on how to help students make fewer mistakes in algebra.

No Mistakes

Let's Reduce Mistakes in Algebra!

So far I have introduced a form of notation I have developed, the double-slash, which looks like this:

//

and I have described some of the ways that students can use it.

I’ll continue the conversation by showing how this notation can help students combine like terms with greater care.

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How to Decrease Mistakes in Algebra – Part 3


When we left off, we were talking about the double-slash, a form of notation I’ve developed that helps students attain greater focus when simplifying algebraic expressions.

With greater focus, students make fewer mistakes. With the double-slash at their disposal, students avoid the mistake of combining terms that should not be combined. In the following example, students use the double-slash twice to simplify an algebraic expression:

     + 8 – 2(3x – 7)

=            + 8   //  – 2(3x – 7)

=            + 8  //  – 6x + 14

=            – 6x  //  + 8 + 14

=            – 6x  + 22

No Mistakes

Let's Reduce Mistakes in Algebra!

By cordoning off the section with the distributive property:  – 2(3x – 7), the double-slash allows students to see it distraction-free. With this heightened level of focus, students are more likely to work out the distributive property correctly, then continue on, simplifying the whole expression with no mistakes.

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How to Decrease Algebraic Mistakes – Part 1


Anyone who has worked with students learning algebra knows the truth to the maxim:  MISTAKES HAPPEN.

This is the first in a series of posts offering PRACTICAL SUGGESTIONS for decreasing the number of algebraic mistakes students make.

No Mistakes

Let's Reduce Mistakes in Algebra!

First, it’s useful to recognize a key fact:  we can’t help students with mistakes if we don’t know what causes those mistakes.

Years of tutoring have taught me a lot about why students make mistakes. And one major cause of mistakes in algebra is that students combine terms that should not be combined. Not all their fault, though. Students are often confused about what they may and may not combine. And it is tricky!

Take a problem like this:  8 – 2(3x – 7)

Certainly some kids can simplify this expression with no trouble. But in my experience, many struggle with a problem like this (when first learning it), and quite a few stay befuddled for quite some time.

The biggest mistake is that students think they can and should combine the 8 and the 2 through subtraction, proceeding like this:

8 –  2(3x – 7)

=            6(3x – 7)

=            18x – 42

Q:  How can we help students avoid this mistake?

A:  Use a mark that show students what gets combined and what stays separate.

I will start to elaborate on how I do this in tomorrow’s post.

Extra, extra!   I thought it would be interesting for you readers to send in comments on the kinds of algebraic mistakes that “drive you up the wall” the most. When I get a number of comments in, I will conduct a poll to see which mistakes people find most vexing. Should be “fun.”

“Math Cafe” Gives Students Options for Math Success


Sometimes when I tutor I tell students that they are “hanging the in Math Cafe.”

I explain that when I tutor, I like to offer students a “menu of math options.”

Math Cafe

Math Cafe, Open 24/7 = 3.42857 ...

Instead of showing students just one way to work a math problem, I try to present a “menu” of approaches, and I tell students that they need to listen so they can decide which approach works best for them.

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