So my students have been a bit slammed with tests the last few weeks. Last week, my students asked me if we could just watch Spongebob instead of having math class one day. I asked the natural follow-up — “What mathematical questions can we ask about Spongebob?”

They had a bunch of absurd ideas, but after a bit of research I settled on one — how many Krabby Patties does Mr. Krabs sell over the course of the show?

**Side note:** I’ve been working hard to find ways for students to authentically practice explaining their reasoning and critiquing the reasoning of others. I’ve found that an important way to make this accessible for all students is to find problems where the mathematical skills are a step down from our content (Algebra I), but the reasoning still provides significant challenges.

I found a fun episode to show about 4 minutes of — it was Season 2, Episode 16, free on Amazon Prime, about opening the Krusty Krab 24 hours a day. That was a pretty good hook, and they bought into figuring out how many Krabby Patties were sold. I then gave them this information:

(the last one is fake because I didn’t feel like watching all the episodes, but there were a ton of Krabby Patties sold in the first episode (the attack of the anchovies, until Spongebob saves the day with his hydrodynamic spatula) and none of the kids batted an eye — I think these numbers are pretty reasonable)

Anyway, this is some really interesting information to put in front of kids. Lots of opportunities to attend to precision with the number of episodes — first, you better notice that seasons 6-8 are longer, that season 9 is ongoing, and that there is the implication of a tenth season. Then, the Krabby Patty data provokes some great questions. Is that first episode an outlier, to be ignored? (My students seemed to agree that it was not — there are plenty of episodes where an outlandish number of Krabby Patties are sold.) Are those five episodes representative of the whole series? (Mixed opinions here.) On top of that there’s sampling, and proportional reasoning, as well as the numerical literacy to know what this all means.

Anyway, I let kids go for a bit. Some dove in, others spun their wheels a bit. I pulled the whole class back to let them ask questions — either clarifying questions or more information they wanted. Each class went a different direction here, and it leads to a lot of authentic conversation about what these numbers mean. Then I released them to work through it on their own, and explain their reasoning so someone else could understand it. This time, almost everyone was engaged and producing some quality thinking.

**Getting meta:** This approach helps to solve some things I hate about my instruction of a few months ago. I tried to teach explanation by having kids write sentences to justify answers to word problems, mostly randomly based on when I thought it was necessary — more or less learning justification via obedience. Maybe not terrible, but I think there’s lots of room to grow here.

I love this problem because it seems to naturally beg for explanation. What did you use for your number of episodes? Did you give an exact number? Did you round? Did you give a range? What did you do with that 10,000? Why? These are *natural* questions that come up in this problem, and the explanation is so much more authentic than the standard quadratic word problem about a garden and a walkway. I also think it’s critical that, for this problem, what I’m really teaching is justification — the mathematics is more accessible because that’s not the point, the point is that they can justify the decisions they made.

**Giving feedback: **I’ve been trying to develop a rubric for problems like these, and I mostly hate every version I’ve used. In the current iteration, there are four parts, each graded on a 0-2 scale:

- Did you understand the problem, and persevere if you got stuck?
- Did you show your work so that someone else could understand it?
- Does your answer make sense?
- Did you provide a logical justification for how you found your answer?

I have students grade each others’ work based on this rubric, without an answer key — it’s their job to say if the work is legible and logical to them, and to evaluate that person’s approach, even if it’s different than their own. This feedback isn’t perfect, but it promotes deeper thinking during grading, and makes the feedback on neatness and logic much more authentic.

The piece I’ve been trying to emphasize is the difference between showing your work and explaining your work. They’re two different parts of the problem solving process — the *how* you came to your answer, and the *why* you chose that approach, and you know it makes sense. This problem requires both calculation (the how), and significant decision making on what calculations to use (the why). I hope my students are taking from my classes new ideas on the significance of these skills, and how they might look in practice.

Oh, and somehow none of the classes complained about turning Spongebob off in the middle of the episode. I think that was the most amazing part of this lesson.