Basic Algebra Instructions for Teaching Kids
Algebra often gets a bad rap. It's said that it is hard, that it makes no sense, that it ___ (you fill in the blank). Actually, algebra is very logical, and it is not hard if you know how to add, subtract, multiply and divide. Here is an easy to follow, logical presentation of the basics of algebra.
Teaching Kids Basic Algebra
Basic Definitions
Before students begin solving equations, they first have to know the correct terms. Imagine how hard it would be solve for a variable if you don't know what a variable is! There are several very basic terms in algebra:
 Equation
 Two numbers or groups of numbers that are equal to each other.
 Constant
 A number that does not change. For example, five always equals five, 1/2 is always half of something and pi is always 3.14159+.
 Variable
 A number whose value is not known. It's often a value that will be found by working through an equation. In algebra these numbers are represented as letters, such as x, y, a, etc.
 Coefficient
 A constant that's placed in front of and multiplied by a variable. So 5 • y is written as 5y, and 5 is the coefficient.
Logic of Algebra
It can be helpful if you begin your instruction by walking students through the logic behind algebraic equations. Use the following steps below before beginning direct instruction.
1. Begin with an equation. The simplest kind of equation is:
 10 = 10
2. Change one side of the equation to an equivalent representation, such as 4 + 6.
 4 + 6 = 10
3. Now, write another equation, but this time, change the other side of the equation to an equivalent representation, such as 2 • 5.
 10 = 2 • 5
4. Explain your thinking aloud to the students:
 If 4 + 6 = 10,
and 10 = 2 • 5,
then 4 + 6 = 2 • 5
This explanation can help students understand the concept behind equations. As a result, when they see an equation like 4 + x = 10, they will have a better understanding of how to solve it.
5. Pretend you don't know one of the numbers (constants) in that equation:
 4 + ? = 2 • 5
Replace the ? with the letter x (a variable) and you have 4 + x = 2 • 5, a perfect example of a simple algebraic equation.
Basic Rule
One of the most basic rules of algebra is: what you do to one side of the equation, you must do to the other side. Before tackling an actual problem, make sure your students understand this rule.
For example, if you subtract 3 from the left side of the = sign (in our example: 4 + x  3), you must also subtract 3 from the right side of the = sign (in our example: 2 • 5  3). The equation now reads:
4 + x  3 = 2 • 5  3
Steps for Solving Equations
Now your students are ready to solve some equations. Solving an equation means you find what constant the variable stands for; in other words, what number does 'x' represent in this equation? Provide general steps to solving an equation so that students can apply these same steps for any equations that they solve in the future.
1. Combine like terms. Using the same equation, 4 + x = 2 • 5, begin by multiplying 2 • 5. As a result, the equation should now look like this:
4 + x = 10.
2. Isolate the variable. Get the variable, x, on one side of the equation by itself by subtracting four from both sides. Make sure students understand and follow the basic rule (what you do to one side of the equation, you must do to the other). You have now solved for x. The equation should look like this:
x = 10  4 = 6.
3. Check your answer. Remember to always plug the variable back into the equation to check your answer. For instance, you can be sure that the answer (x = 6) is correct because 4 + 6 = 10.
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