Variables and Expressions

Contributor: Marlene Vogel. Lesson ID: 10319

Does the thought of algebra put a sour expression on your face? In this lesson you will ease into using variables and expressions (and M&Ms!) to learn these important skills! "Hundredaire" included!


Expressions and Equations, Pre-Algebra

learning style
personality style
Beaver, Golden Retriever
Grade Level
Intermediate (3-5), Middle School (6-8)
Lesson Type
Quick Query

Lesson Plan - Get It!

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Here is an interesting puzzle.

  • Can you solve it?

You are saving for a skateboard that costs $125. Your aunt gives you $45 to start and you save $3 each week.

  • How much will you have after 4 weeks, 10 weeks, and 20 weeks?
  • When will you be able to afford the skateboard?
  • You really want to know, don't you?

Read on!

Welcome to the beginning of your journey into learning algebra!

Starting with this lesson, you will become familiar with the terms (vocabulary) used in algebra lessons and the skills and steps needed to solve algebraic problems.

Word problems, like the one at the beginning of this lesson, seem less difficult when you have all of this knowledge at your fingertips!

Whenever you are at the threshold of learning a new skill, the first step is to become familiar with the vocabulary used when discussing the skills.

Visit Algebra 1 Vocabulary List - Math Vocabulary to discover the definitions for the most common terms in algebra. However, for this lesson, you only need to understand the following terms:




Take a few moments to read through the pages of the website that defines those terms. You will complete an activity that will help you apply that information.

At the end of this lesson we will revisit the opening problem and solve it!

Let’s begin the activity!

Take a look at the following information:

The price of a visit to the dentist is calculated according to the formula 50 + 100n, where n is the number of cavities that the dentist finds. On your last visit to the dentist, 2 cavities were found.

  • What was the cost of your visit?

The n is the variable. The variable is always a letter. The variable is the unknown number for which we are looking.

The numbers 50 and 100 are the constants. The constants are always numbers. The constant is known.

The entire 50 + 100n is an expression.

The difference between an expression and an equation is that an equation has an equals sign (=) and an expression does not. As you can see, our problem does not have an equals sign, so it is an expression.

Here is some interesting and important information for you to know:

  1. Because variables are letters, we can no longer use an x to represent multiplication in an algebra problem Instead, we use a dot (4 • x), or we simply write the variable and the constant next to each other (4x).

Either way, it is telling you that you need to multiply 4 times x. That may seem confusing right at this moment, but it will become more clear as we move along.

For now, just remember that the letter "x" does not mean "to multiply."

  1. When you are told to evaluate an expression, you are being asked to find the answer.

  1. When working on an algebraic problem, neatness is extremely important! If you arrive at an incorrect answer, you want to be able to go back to the beginning of the problem and look at each step to see where you may have gone wrong.

If your work is not neat, you will not be able to do this successfully.

Let's evaluate the expression x + 5 where x is equal to 1, 2, and 3.

This means you are going to substitute the numbers 1, 2, and 3 for x in the expression. You are going to do the substituting one number at a time.

As stated in number 3, above, it is important to keep all of your work neat.

One thing that can help you during the evaluation stage is to develop a table. On a piece of paper, copy the following table:

Take a look at the table. In the top row you have x and x + 5. In the x column you have the numbers 1, 2, and 3.

Notice that the x + 5 column is blank. That is where you are going to put your answers.

This table will help you keep your information organized. Now you need to work on evaluating the expression.

  1. Step one is to always write the problem. x + 5

  1. Step two is to substitute one of the numbers for x. Start with the number 1. 1 + 5

  1. Step three is to perform the operation — in this case it is addition — and arrive at your answer. 6

  1. Step four is to write your solution in the table next to the number 1 but in the x + 5 column.

Try substituting the numbers 2 and 3 for x and write your answers in the table.

For more practice evaluating expressions, refer to the Evaluating Expressions worksheet located in the Downloadable Resources in the right-hand sidebar.

Take a look at the solutions for the expression x + 5:

  • Do you see a pattern in the solutions?

Take a look at your solutions from the Evaluating Expressions Answer Key (found in Downloadable Resources).

  • Are there any patterns in each of the problems?

Stop the lesson at this point and discuss with your teacher what the patterns are.

When you are ready, go on to the Got It! section to see if you got it and can get it with some fun practice!

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