Once kids possess a strong foundation in basic math, you need to to introduce them to algebra. While algebraic concepts are taught as early as kindergarten, actual formulas and introductions to variables are often saved for grades 6-8. These concepts will follow students through twelfth grade, into college or university and finally in the workplace. Since many degrees require calculus, which requires a strong comprehension of algebra, this topic is one that students can't afford to bypass. For younger students, however, it can be confusing. Precisely why are letters used together with numbers? Exactly what is a variable? Here, I'll briefly go over what these principles mean and how they may be more readily understood and applied.
While arithmetic concentrates on basic operations using addition, subtraction, multiplication, and division, algebra introduces a couple of new ideas.
First, that we can introduce an unknown number, usually represented by "x," and still have a math problem that actually works. As an example, if I have 3 cars in a lot, and four in another, I realize that I have 7 cars all together. Nonetheless, let's say I'm told that I have 7 cars all in all, and 3 in one lot. How many are in the 2nd lot? This is an elementary algebraic formula:
Arithmetic: 3 (cars in lot 1) + 4 (cars in lot 2) = 7 (cars total)
Algebra: 3 (cars in lot 1) + x (cars in lot 2) = 7 (cars total)
So, I'd then have to determine what "x" represents. In this instance, it's four. We will determine this by affecting the formula equally on both sides. That is easier than it sounds. In our case, we have 3+x=7. Now, let's subtract (-) three from the left side of the equal sign, and the right side.
3+x=7
3-3+x=7-3
Simplify:
0+x=4
Since 0+x=x, our solution is
x=4
Now we understand that we could have determined the number of cars there are in lot two simply by knowing our total and how many were in lot 1. We could do this with multiplication and subtraction as well, in exactly the same way.
Note that once we start doing algebra, we very often make use of a star or a dot (*) rather than an x, since we sometimes use x as our unknown value. If we are just dealing with a number multiplied by an unknown value (like x) we just put the number alongside it (5x=10). We assume that whenever two numbers or values are right alongside each other they are multiplied together. For division we are able to make use of a "/" to represent one value being divided by another (10/2=5).
Assume we have twenty cars all together. We all know there are four lots, each with the exact same number of cars in them. Put simply, there are 4 times (multiplied) an unknown number of cars, with a result of twenty.
4 * x = 20
4x=20
Since we are multiplying here, the opposite will be to divide. Let's divide each side by 4 (keep in mind that dividing a number by itself equals 1) and find out what we get.
4x=20
4x/4 = 20/4
Simplify the left side:
4x/4 = 1x = x
Simplify the right side:
20/4 = 5
So our solution is:
x=5
Easy, right?
This is actually the basis for straightforward variable and algebraic equations. Check back for my next article on how to handle a problem in case you have more than one variable.
If you're a student or the parent of a student who is having difficulty in math, you should contemplate hiring a tutor. Math tutors are affordable, knowledgeable, and can produce measurable improvements in your students' grades. One on one hands on instruction can't be matched for effectiveness in learning.
If you are in the greater metro area and have a student who's struggling or can use just a little extra help, look into a nearby home tutor service. A math tutor will help your student excel in their classes and prepare them for high school and beyond.
