**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.*

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I really enjoyed reading through how you implemented this lesson. It certainly is challenging figuring out how to best walk the line of challenging them without giving them too much help. Certainly you are doing a great job and only getting better. I appreciate the amount of discourse opportunities you gave them and it was definitely clever how you handled the low guesses. Regarding letting them do their own graphs, consider letting one class be the guinea pigs and then using their work samples with future classes and ask them to discuss things they would change or keep.

Great job overall.

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Thank you for the encouragement. I really like the idea of looking at one classes work samples when setting up the graphs. Thanks for stopping by!

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