Understanding Variables

Algebra/Standard

• GLE 0506.3.2 Develop and apply the concept of variable.

• √0506.3.1 Evaluate an expression by substituting non-negative rational number values for letter variables in the expression.

• √0506.3.2 Use variables appropriately to represent numbers whose values are not yet known.

Understanding Variables

What is so important about variables?

Understanding VariablesImagine having two cars that together cost $2.00

and a car and a dog that together cost $5.00.

What is the price for a car? What is the price for the dog? Explain how you found your answer.

$2

$5

VocabularyCar + Car = $2.00; Car + Dog = $5.00. Instead of using numbers, students can used representations to find out the value. Give a definition of a variable.

A variable is a letter or symbol that can stand for any number

Variable Machine• On the three-centimeter-wide strip of lined

notebook paper, write the letters of the alphabet in order down the left side of the paper. 

• Down the right side of the five-centimeter strip of notebook paper, write the numbers from 0 to 25. Then attach the ends of the number strip together with a piece of tape; wrap the letter strip around the number wheel, matching the letters to the corresponding numbers:

• A to 0; B to 1; C to 2 and so on.... and tape the ends of the letter strip together, as shown below:

ExploreHave the students find the value of their first names, using

their variable machines; for example, the value of Amy's name is 36: 

A = 0, M = 12, Y = 24 0 + 12 + 24 = 36

Have the students find the value of their last names, and ask the following questions:

Which name has the higher value - your first name or last name? 

What is the difference in the values of your first and last names?

 

Students should explore the values of various words. For example, ask students to find words:

whose values are equal to 25, 36, or 100.

Cracking the CodeUse your Variable Machine to answer the questions which

follow.

1. What is the value of your last name? _______ What is the value of your first name? _______What is the difference of these two values? ______

2. What is the value of each of these words?a. variable ______b. machine ______c. algebra ______d. mathematics ______

3. Find three different words whose values are each equal to 25. Record the words below.

ExtensionAssign the values on the Variable Machine as decimals:

A= 1‚; B=2‚; C=4‚If A = $.01 and Z = $. 26 what words will equal exactly $1.00?

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Understanding Variables

• Example 1:Dexter had three baseballs. After practice, he found several more baseballs. Write an expression using a variable.

• What the does the variable stands for?• The variable stands for the number of baseballs

Dexter found after practice. • Solution: 3 + B

Understanding Variables

• Example 2:  On her birthday, Kristin brought 30 cupcakes to school. She gave a cupcake to each student in her class.

• Write an expression using a variable. • What does the variable stands for?• Solution:  30- c

Understanding Variables

• Example 3: If p = 88, what is p – 30? Rewrite the expression substituting the value for the variable in the expression, then solve.

Understanding Variables

• Example 3:  Evaluate x ½ ½ using the order of operations.

x = 1/3• Step 1: 1/3 + ½ ½• ½ ½ = ¼ Multiplication• Step 2: 1/3 1/4 = 1/12 Addition

• Solution:   1/3 + ½ ½ = 1/12

1

Your Turn!!!

Let x = 12• 3x • x + 79 • 56 - x• x / 6

Check your Answers

• x = 36• x = 91 • x = 44• x = 2