Negative Numbers

I see issues with negative numbers all the time, even from calculus students.
I think I can pinpoint three key things that really helped me understand negative numbers. Hopefully they will help you, too.

 

Here is a free online game to practice negative numbers:
http://www.mathsisfun.com/numbers/casey-runner.html

My First Video

This is a video that expands the lessons Factoring and FOIL. I work through an example, then check my work.

I would love some feedback. Is this a good way to teach lessons? Does it help you understand any better? Does it confuse you? Is it an awful video in general?

Factoring

Factoring is the exact opposite of FOIL-ing (see last post). Instead of multiplying out two binomials to create a trinomial, we will be breaking a trinomial into two binomials.

This is probably the most important skill you will learn in algebra (not counting all of the skills that are used for this one). So when your teacher says it's time to begin the chapter on factoring, sit up straight in your seat and pay attention.
While there are something like 8 different factoring methods, I am only going to present one. This is for a reason: this method works for every single factorable trinomial (yes, there are many methods that only work in specifc cases but I will not be showing those to you unless you ask nicely).

Here is another example, which introduces the case of a trinomial with negatives:

FOIL

This is an algebra lesson.

To multiply two binomials (polynomials with two terms), you must use a distribution method called FOIL, which stands for First Outer Inner Last. Multiply the two first terms, then add the product of the two outer terms, then add the product of the two inner terms, then add the product of the two last terms.

To give this a more visual approach, here is what it looks like using letters instead of numbers:

Memorization

This is a post based on a question.

I'm going to sixth grade and I still haven't memorized my multiplication tables. Help me?

This is more of a series of helpful hints than an actual lesson.
While the vast majority (and most exciting parts) of math involves critical thinking, problem solving, and multi-step processes, there are certain parts that just require some simple memorization. For example, once you have the concept of what multiplication actually is, it is immensely helpful (perhaps even necessary) to simply memorize multiplication tables for all combinations of numbers 0-12. Likewise, in Calculus it can greatly improve your test-taking speed by just memorizing certain basic derivatives and antiderivatives.

Before I go any further, I must make an extremely important point: the goal of memorization is not to substitute for understanding, but to increase mental speed. That is, you should know what I mean when I ask what 4x6 is, and not just know the answer. You must first deeply understand the concepts before memorizing the numbers.

I have a few tried-and-true methods for memorizing simple facts, such as times tables and derivatives. It is best to try all of them and see which works best for you. Everyone's mind works differently and there are numerous learning styles to take into account when selecting a method.

Please Respond to My Poll

I have added a poll to the sidebar; I am very interested in what my viewers think.

I am considering opening a YouTube account and making lessons as videos instead of typing them. It would be faster, and I have a nice new HD camera and some basic editing software to put together some nice videos. I would write on notebook paper or a whiteboard and narrate as I teach, similar to many of the math lessons already on YouTube (the difference is that I would be responding directly to YOUR questions).

If you are interested in seeing some of these videos, opposed to the idea, or even neutral, please let me know by responding to my poll. You may answer more extensively in the comments section below this post.

The Math Geek Is Back

I am back from vacation and ready for questions. So put me to work. What are you having trouble with?