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Understanding Variables
• 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 Variables
Imagine 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.
Car + 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:
Have 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 Code
Use your Variable Machine to answer the questions which
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.
Assign the values on the
Variable Machine as
A= 1‚; B=2‚; C=4‚
If A = $.01 and Z = $. 26
what words will equal
exactly $1.00?
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
x = 1/3
• Step 1:
• Step 2:
1/3 + ½  ½
½ ½=¼
1/3  1/4 = 1/12
• Solution: 1/3 + ½  ½ = 1/12
Your Turn!!!
Let x = 12
• 3x
• x + 79
• 56 - x
• x/6
Check your Answers
• x = 36
• x = 91
• x = 44
• x=2