Discovering a Variable

I wanted to see if I could get students to "create" or "discover" the idea of a variable.  To try this, I completed the following in my ESL (English as a Second Language) math class.


We first started with a discussion around language, and how math is the "Universal Language".  Next, we talked about "What is the best way to learn a language?"  The students agreed that we should learn how to translate from our language into math would be a great start.  I then told them how I once ordered 2 pepperoni pizzas and 3 Hawaiian pizzas and it cost $70.00, and I asked the class if there is a way we could translate this into math?  One student came up and wrote,

2 Pepperoni + 3 Hawaiian = $70.00 

We then had a discussion how, currently, we would not be able to deduce how much each pizza cost, however this would count as a translation.  I then asked how would you translate "4 Pineapple Pizzas, 3 bottles of Coca-Cola, and 1 Meat lovers, costing $92.00"? Another student came to the board and wrote

4 Pineapple + 3 Coca Cola + 1 Meat Lovers = 92

The class again agreed this was sufficient.  At this time, a student in the back was getting irritated at how easy and time consuming this one.  I asked him to go to the front and in front of everyone translate "3 super size fries, 2 Extra large Coca-cola, and 1 double, extra bacon, cheeseburger costs $21".  He let out a big "UGH!", and asked me to repeat.  As I repeated he wrote...

3 F + 2 C + 1 CB = 21

He looked at me with a smile, and some of his classmates started to laugh.  I then told him "I said supersize fries, not Fs", which he responded with "Yeah this F is supersize fries".  We then had a dialogue around what CB could mean.  After some time, a student asked "Could that be Cheese times burgers?",  and almost immediately a student yelled "but C is coca-cola, so coca-cola times burger?". The student, at the board then changed his answer to   

3 F + 2 C + 1 B = 21

I then wrote on the board

3D +2C = 13

and asked "What does that mean?".  The answers ranged from "3 Dogs and 2 cats cost 13" to "3 bags of dill pickles and 2 bags of cheetos is $13".  We then decided, as a class, that it is important to create a legend at the top.  Therefore we went back and wrote legends such as "F is Super size fries, C is extra large Coca-Cola..."

This was my attempt at students creating their own knowledge of variables.