Mathematics, Algebra and Function

Grade 5- 8

### Objective

Students learn about the basics of algebraic expressions.

### Directions

Introduce to students the following information about algebraic expressions.

Facts to Know

Algebra is a branch of mathematics that uses numbers and letters that stand for numbers to solve problems. In algebra, if a number is unknown, any letter of the alphabet can be used to stand for that number. Letters are called variables because the values of the letters vary from one problem to another. In one problem, x may stand for -2. In another problem, it may stand for 43.

Writing Algebraic Expressions

An algebraic expression is a statement made up of numbers, variables, and signs of operation

(+, -, รท, x). The phrase "a number" indicates the use of the variable.

Combining Like Terms

Sometimes algebraic expressions can be shortened by combining like terms making them simpler to understand. An expression is made up of smaller parts called terms. A term can be made up of numbers, variables, or numbers and variables. In an expression, terms are separated by only plus and minus signs.

Examples: 15, x, xy, 5xy, 4x/y

A numerical coefficient is any number in front of a variable in a term. If there is no number in front of a varible, the numerical coefficient is understood to be 1.

An exponent tells how many times a number has been multiplied by itself. Examples: 4

^{2}, 8w

^{3}, 10n

^{3}
Terms that have all of the same variables (xy, 3xy, 5xy, etc.) or variables with the same exponents (4a

^{2} + a

^{2}), are called like or similar terms. Like terms can be combined by combining the numerical coefficients.

But an algebraic expression like 9y

^{2} + 2y cannot be combined because y

^{2} and 2y are not like terms. One has an exponent of 2 and the other has a coefficient of 2.

Evaluating Algebraic Expressions

Remember that in algebra a variable can stand for any number. However, sometimes in an algebraic expression, you are given the value of the letter. Then you must replace the variables with the numbers they represent to solve for the value of the whole expression.

Distribute the activity sheets and have students complete the activity.

### Resources

- Working with Algebraic Expressions activity sheets
- pencils