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

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.

Fractions

In this lesson I will show you how to add, subtract, multiply, and divide fractions. Then I will show you how to simplify your answers.

Addition/Subtraction

These are done almost the same way. First, you find a common denominator (you need the same number on the bottom of both fractions). Then, you add or subtract across the top of the fractions and keep the bottom the same.

The hardest part of this is the common denominator. If you are good with numbers, you are trying to find the smallest number that both denominators can multiply to. If you are not good with numbers (don't know the times tables or need to use a calculator often), simply multiply the two bottom numbers. REMEMBER: whatever you do to the bottom you must also do to the top, and whatever you do to the top you must also do to the bottom.

I'll provide a few examples.