Tag Archives: Functions

Day 47: In-N-Out Part II

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.

Day 46: In-N-Out

Today students started Day 1 of In-N-Out by Robert Kaplinsky.  My whole department does this activity to kick off functions in Algebra 1. I did this activity last year and have made a few modifications…

We started by talking about our favorite fast food places. Since Montana doesn’t have any In-N-Out it is nice for a student to mention the place so it doesn’t come across as forced. Last year we started with the 100 x 100 pictures. I mixed things up this year and showed students a video instead.

At this point we dive into 3-Act world.

Write down the first question that comes to your mind.


The +6 shows that 6 other students found that question interesting.

In this period the main question How much would a 100 x 100 cost? didn’t come up. That’s ok. I helped them along.


We took estimates. Sometimes I get crazy low estimates and that doesn’t bother me. However, this year I have been feeling that students are starting to take advantage of the amount of openness they have in math… So I took a page from Andrew’s comment here and asked students “Take a minute to look at the range of estimates we have, convince why any of them might not make sense” 

I didn’t just blow off the fact that Alex’s name was attached to one of the estimates, after someone called him out, I gave him a chance to respond.

After I showed students what a cheeseburger and double double look like.


And asked them what they noticed about each.

They came up with pretty much everything; same number of buns on each, same condiments, different number of patties and cheese.

Students created a wish list of information they wanted to answer the question:


I added a new piece here that I REALLY liked… by asking students: what would you do with this information?

I then gave them this picture and set them loose to answer the question.


About half the class was done in two minutes.

There were two main misconceptions I saw….



Instead of showing these pictures right off the bat I asked students “I am seeing a lot of different calculations. If we use a double double to find the price, shouldn’t it be the same as using a single cheese burger to find the price?”

They agreed. Then we worked through $2.65(100) and $1.75(100). They weren’t the same. We talked about what they were calculating.

******A big difference this year… This incorrect answer seemed to be discouraging. Students weren’t even sure if the 100 x 100 existed. So at this point in time I showed them the picture


I loved the reactions and students had a good idea of how they needed to calculate the price.

In some classes we reached final calculations and looked at the receipt. I am saving that for the continuation of this post… coming tomorrow!

Day 44: Functions

Today I gave my first work packet… ever.

I have mixed feelings on this and probably won’t do it again. It felt like there was a lot more groaning that usual (which isn’t always a bad thing). But it felt like I was almost punishing students with the amount of repetition that went on from page to page.

I like the packet; it transitions really smoothly into adding values to graphs. I just probably won’t give as much of it next year.I found it floating around the internet last year (I don’t remember the source!) Anways… I am feeling pretty burnt out. I just spent a whole lot of time creating this pumpkin (which was a lot of fun) for my Geometry to see and model off of tomorrow in Des-man.


Day 42: Graphing Stories

In Algebra we talked a bit about Water Line. Students concluded that when comparing water height vs. time a steep line indicated a fast fill rate and a more horizontal line indicated a slow fill rate. I was impressed with how well they could generalize.

We spent the rest of the period working on Graphing Stories. I had students describe the first few using only words then move into graphs. I also put up the page and had a random student pick whatever one they wanted to do.

Geometry wrapped up Hotel Snap. It was pretty chaotic and I struggled bringing everything together. The winning team had a score of $19,265 with the $1,000 bonus.

Here is their hotel


Day 41: Waterline + Hotel Snap

I have been wanting to try Water Line by Desmos for almost a year. Today was finally the day!

I wasn’t quite sure how much I should pre-load students on graphing functions when going into this… So I didn’t give them any.

We went into the computer lab, I gave them directions how to access the activity and they worked….

For the entire period.

I used by iPad to monitor and help a few struggling students along the way.


But, as the day progressed that happened less and less. I found that the students who were plotting points or had holes in the graph were self correcting. Once they were able to create their own vase and solve others, a majority of the misconceptions and struggles had been sorted out.

By the way… Desmos has an awesome dashboard when you can follow students through the learning process.


Today I was less helpful than most days, which was uncomfortable. There were a few students off task here and there but for the most part all students were engaged. In my opinion it is incredibly important to have days like this; where the teacher steps back and just lets things happen. I am by no means leaving students at this place and moving forward, but allowing students to begin the learning process and come up with their own questions without the direction of a teacher is awesome.

Tomorrow I am bringing up the cupboard for each class and we will discuss difficulties and answer questions, then move onto Dan’s Graphing Stories.

In Geometry students started Fawn’s Hotel Snap. I have no real reason for the timing of this activity (we are in the middle of parallel/perpendicular lines) but I wanted to try it!

I am really interested in how student’s hotels will pan out, every design is different.






The discussions among students were great and they seemed to all be happy with their final designs. More on this tomorrow!