Why does it take so long to get a Slurpee?

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I announced two nights ago that 7-Eleven was having a special for today and tomorrow: fill any container you bring to the store with a Slurpee for $1.50. (There’s some fine print, of course.)

So Biggie wanted to start his project time yesterday with getting a Slurpee.

“Hold on, now,” I said. “You have to pay for it yourself.”

“No problem,” said Biggie. We went to the spreadsheet of the Bank of Dad and made updates to his financial status. He had plenty of money, but we talked about what he wanted to save up for in the future (a Nintendo 2 DS), and whether he wanted extra cash on hand for our visit to the Gem & Mineral Show tomorrow.

“Now you need to pick which container to bring it in.”

We started emptying the cupboard of candidates.

“Which,” I asked, “could hold the most liquid? How could we find that out?”

Biggie first tried to measure half the circumference of each bottle.

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That seemed a little inaccurate. Biggie then noticed some of the bottles had markings along their side, which helped measure the ounces of milliliters of liquid inside.

Not all of the containers had markings, so Biggie used the existing markings as a reference to roughly extrapolate how much liquid might be in the other bottles, based on their heights.

“Let me ask you this: How do these bottles differ from each other?”

After some coaxing, Biggie noticed that they had different tops, different sealants, and different colors.

“Do the tops/sealants/colors matter as to how much liquid they hold?”

“No.”

“So how do they differ in ways that matter to how much liquid they hold?”

Again more coaxing. Height and circumference/diameter. The taller the container, the more it holds. The wider the container, the more it holds.

So I had him sort the containers from shortest to tallest:

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Then I had him sort them from skinniest to fattest. This was more difficult because he at first failed to see how the Starbucks thermos, for instance, had a thick insulating wall.

I intervened and traced the mouths of the containers on a piece of paper, to make it easier to compare the circumferences:

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Biggie could readily see, however, that even this comparison was problematic because none of the containers seemed to be perfect cylinders. He could see, though, that when you roughly sorted the bottles by circumference, the order was not the same as by height:

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Biggie seemed to want to calculate the volumes of each container, but I knew this was going to take more time and explanation than he probably would have patience for.

“So what do we do now? Can we think of some way, some test maybe, that will help us figure out which container holds more liquid?”

“We can pour liquid into each and then pour it out into a bigger container… and we could do that for each,” Biggie said. I wanted to hug him.

“Let’s do that.”

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In the end, we decided to bring the clear smoothie containers and a red water bottle to 7-Eleven.

When we got back, Biggie asked, “So how much time do I have left?”

“Oh, we pretty much used up all the time.”

“What?!”

He was indignant that all the hoo-ha about choosing the container ate into his project time but calmed down when I told him he could continue to do other things he liked; I just wouldn’t be able to give him my full attention.

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