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.

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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.

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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.

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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.

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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:

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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.

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About half the class was done in two minutes.

There were two main misconceptions I saw….

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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

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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.

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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

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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.

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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.

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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.

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