A warning to anyone who is having some trouble with the math section of the SAT or ACT (or with high school math in general): Chances are your difficulties started far earlier than Algebra II or Geometry.

In my experience with tutoring math students, students often had trouble with these advanced subjects when they were also having difficulties doing the basic operations of math like multiplication or division.

At the high school level, these problems get covered up by calculators and whatnot.  But the fact of the matter remains that you aren't going to be able to solve all the problems on the ACT or SAT, and you're certainly not going to be able to tackle complicated geometry or algebra problems, unless you've got your basics down cold first.

The Basics

The basics of math are addition, subtraction, multiplication and division.  Everything builds on these four tricks.  

There is a trend in modern educaiton to not make kids memorize things.  Some textbooks and teachers emphasize that you shouldn't learn things "rotely," that you need to actually UNDERSTAND what you're studying in math and why it works.  They say it's more important to be able to figure things out instead of just remembering formulas.  As a matter of fact, this trend is probably behind the fact that you get access to a list of formulas on your standardized tests.  They don't expect you to memorize these things.

That being said, there are at least a few things that you have to memorize, or you just won't be able to keep things simple in your head sufficiently to solve a complicated math problem.  But I think this gets glossed over because of this trend.

Among the things you have to have completely, totally, amazingly memorized, to the point where they are hardwired into your brain and you can practically do them in your sleep with half your brain tied behind your back: addition, subtraction, multiplication and division.  When you're solving a problem you can't have to wait and think about these things.  You just have to know them.

How Well Do I Have To Know My Fifth Grade Math?

Let's just say that you should be able to answer the question, "What's 11 times 12?" as quickly as you could answer the question, "What's your name?"

Furthermore, you should be able to churn through more complicated arithmetic problems (like multiple digit addition, subtraction, multiplication and division) with a great deal of speed and certainty and no mistakes.

There's no point in learning how to putt in golf unless you know how to get the ball from the fairway to the green.  Likewise, not having your basics down to a point of excellence in math will keep you from realizing improvement on the SAT and ACT.

Tips For Improving Basic Math Skills

One great trick for improving multiplication is to build out times tables.  At first just pick a box and look at the head of the column and row for that box, multiply them together, and put your answer in this box.  This is a very easy way to quiz yourself on over 100 multiplication problems all at once.  

Then randomly fill in the top row and first column with numbers, instead of neatly numbering them 1 through 12.  Solve them all again.  Keep at this until you can do it extremely quickly.  Long after you can do it well, you can keep doing this exercise and improving.

Develop the ability to give yourself math problems.  I know this might sound crazy, but you have a real advantage if you can make up your own math problems.  This can be as simple as creating random numbers to add or divide on the page, or as complicated as making a similar word problem to what's in your textbook.

When I'm tutoring someone, and they have trouble with a word problem, I work them through it, then try to get them to answer many more problems that are similar until they've got it down cold.  It's easier to study if you're able to test yourself like this.

Repetition is a key to memorizing something like this.  It's not the only key, but it's a significant one.

Have any other techniques that worked for you on improving your math skills?