Algebraic Expressions

Contributor: Danielle Childers. Lesson ID: 10775

Smile! Frown! Grimace! Faces express our feelings. Algebraic expressions show the value of numbers and symbols. Learn to translate word problems into algebraic expressions with video and online games!


Expressions and Equations, Pre-Algebra

learning style
personality style
Grade Level
Middle School (6-8)
Lesson Type
Skill Sharpener

Lesson Plan - Get It!


When someone asks you to give them a happy expression, what does your face look like? What if they asked for a surprised expression? What if someone asked you to give them an algebraic expression — what would you do?

Just like your face can show an expression of how you are feeling, a math expression shows the value of the numbers and symbols given.

In this lesson, you will review how to build, read, then solve an algebraic expression.

For a quick reminder and some hints on reading and building algebraic expressions, look at the notes below. Following these simple steps will help you when you are writing equations:

  1. You want to identify the unknown, which is the variable.
    Example: a number increased by 3 is 8
    You are trying to find out what number is increased by 3.
  2. Let "X" stand for the unknown number. Rewrite the sentence (You can use any letter to stand for the variable, but "X" is the most common).
    X increased by 3 is 8.
  3. Now, look for key words that help you finish writing the number sentence (equation).
    X increased by 3 is 8.
    Increased by tells us that it is an addition problem.
    By tells us to use the equal sign.
  4. Fully write out the equation:
    X + 3 = 8

The following KEY WORDS will help you write expressions:



  • more than
  • increased by
  • combined
  • plus
  • added to
  • together
  • total
  • the sum of



  • less than
  • decreased by
  • minus
  • fewer than
  • difference between/of
  • subtracted from
  • gave away
  • sold
  • used
  • lost



  • of
  • multiplied by
  • product of
  • times



  • out of
  • divided by
  • quotient of
  • per
  • a



  • is
  • are
  • was
  • were
  • will be
  • gives
  • sold for


Listen to Julie Harland, Your Math Gal, in Translating words into algebraic expressions (below), explain in more detail how to translate words into algebraic expressions. Be sure to try to solve them on your own before she solves the problems for you! You can reference the KEY WORD chart for help:


Here is another great video from LearnZillion, called Read and write an algebraic expression containing a variable. The video is free, but you may have to create an account (with your parent or teacher) to view this video.

Read and write an algebraic expression containing a variable | LearnZillion

When you are finished, continue on to the Got It? section to play some learning games!

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