**This is a continuation of Day 46**

Today I started Algebra by asking students to create a rule to find the cost of an N x N burger. I saw quite a few students take .9(n) + 1.75 or .9(n) + 2.75

Misconceptions are so much easier to address when they are about cheeseburgers…

After a bit of questioning students realized they were double counting some burgers and modified the equations to .9(n-1) + 1.75 and .9(n-2) + 2.75.

I stopped after this point last year, but after looking at Robert’s post I had students model the 100 x 100 case using 4 different representations: **Numbers, Pictures, Symbols, and Words.**

I probably helped students a little more than I should have. I am still uncomfortable having them set up their own graphs… what if they put 100 values in their table?!?! I am still learning.

My district has some English Common Core Writing Protocols, so after this point students wrote a short paragraph describing their solutions using those.

We also had a great discussion on why the table represents a function:

*T: “Why does it make sense for the relationship we see in the table to be a function?”*

*S: …?*

*T: …. waiting….*

*S: Each number of patties is paired with a single cost?*

*T: Why does that make sense?*

*S: I don’t want to pay a different amount for a double double than someone else.*

*T: Yeah… that wouldn’t be fair.*

I am excited to try this activity again next year!

**My Reflections on this…**

**I liked using the video as Act 1 then revealing the 100 x 100 picture later in the lesson.****I used the modified receipt from Tim’s post in one class then decided to go back to the original (I got called out and it kind of halted the class).****I still helped students too much.****The four representations were a great way of bringing the activity full circle.**

*Here are a few other posts on this activity I came across.*