This is always a big question when a student begins to take their
first algebra course. Algebra encompasses relationships, the use of
symbols, modeling, and the study of mathematical change. The first
formal algebra course that most students enroll is Algebra I. Usually
begins in the ninth grade, although several students are starting
to take it in the eighth grade.
Some students say that I can not do algebra because I do not understand
it. The problem with this statement is that you have been working
on algebra problems every since kindergarten. The word algebra is
not used, but the ideas are used. You have used elements of algebra
when solving problems and when you solve word problems.
Here is an example: in grades three through five you investigate
the properties of whole numbers. You learn to multiply 18 times 14
mentally. First you multiply 18 times 10 and then multiply 18 times
4, and then you add the two products. This is called the distributive
property of multiplication over addition. This is algebra and algebraic
Algebra is a major component of math that is used to unify mathematic
concepts. Algebra is built on experiences with numbers and operations,
along with geometry and data analysis. Some students think that algebra
is like learning another language. This is true to a small extent,
algebra is a simple language used to solve problems that can not be
solved by numbers alone. It models real-world situations by using
symbols, such as the letters x, y, and z to represent numbers.
The vocabulary of algebra is similar to basic arithmetic such as
adding, subtracting, multiplying, and dividing. PEMDAS is still used
to solve algebra problems, because order of operations is strictly
followed in algebra.
There are several terms that describe algebraic operations. These
- Algebraic Expressions: is more of a phrase. It uses variables,
constants, and operating symbols such as plus and multiplication.
Since it is only a phrase it does not have an equal sign. For example:
5x - 2y + 3yz + 10. The variables x, y, and z need to be defined
with numbers and then the expression can be solved.
- Variables: are letters that represent numbers that are sometimes
known and sometimes not. The letters called variables because they
can represent any number. The typical letters used are x, y, and
- Coefficients: are the number parts of a variable, for example:
5y where 5 is the coefficient. If there is only a letter, such as
"x" the coefficient is 1.
- Constants: these are the terms in the algebraic expression that
only contains numbers, for example: 5y + 4 where 4 is the constant
because it does change and 5y changes because of the variable "y."
- Real Numbers: are a set of real world numbers such as: amounts,
distances, age, time, temperature, etc. A real number can be a whole
number, fraction, or decimal. In addition these numbers can be rational
- Rational Numbers: rational comes from the word ratio and can always
be written as a ratio or quotient of two integers. For example:
1/2 is the ratio of 1 to 2.
- Irrational Numbers: can not be expressed as a quotient of two
integers. Pi is an example of an irrational number because the decimal
numbers are non-repeating and non-terminating.
We use algebra everyday of our lives. Examples of ways that we use
algebra are finding the distance, perimeter of an area, volume, determining
the cost of something, renting something, time relationships, pricing
options for something you want to buy, and more.