2 comments on “How big is Mega Maid’s vacuum bag; “Spaceballs””

How big is Mega Maid’s vacuum bag; “Spaceballs”

Artifact

Scene from Mel Brooks’ classic, Spaceballs. Start off by simply showing it (or any combination of the split scenes) to your students (apologies if there are advertisements, you can skip them in like 5 seconds):

Now, I’m not sure if you’d want to show the entire scene in a classroom setting, both because it’s rather long and because there are some, *ahem* cruder moments (“sir, she’s gone from suck to blow“). Personally, I think starting off the first five minutes of class with the entire scene might engage the kids, make them laugh, wake up, etc. But then, I don’t have any administrators or parents to answer to at the moment. Regardless, I’ve broken up the scene into five pieces, which I share below.

Guiding Questions (GQs)

Personally, this scene brings up a ton of questions for myself. Hopefully after watching the scene there will be several GQs from your students. Here are the two primary GQs (a.k.a. “Need to Knows” for you PBL types) that will lead to the mathematics behind this scene that I have.

  • How much air is in Planet Druidia?
  • How big is Planet Druidia?
  • How far above the surface is the “air shield”?
  • How quickly can Mega Maid suck the air out of a planet?
  • Did Mega Maid blow out the air faster than she sucked it in?

Solutions to GQs

Here is Planet Druidia again.

The two questions we really can’t answer for certain are “how big is Druidia?” and “how far above the surface is the ‘air shield’?”. But, you know what? Planet Druidia looks a lot like Earth to me, so let’s run with that.

What we need to find for the volume of air is the volume of a spherical shell. Or, the volume of two concentric spheres of differing radii.

So for this particular problem, we have

or,

where R=radius of Druidia/Earth+altitude of air shield and r=radius of Druidia/Earth.

The radius of the earth is about 6300 km (or 4000 miles). But how far up is the shell ceiling? Or, where does space begin?

According to famed astro-physicist and Nova Science Now host Neil de Grasse Tyson,

So, that’s 100,000 additional meters, or 100 km. So now the volume equation is

Which comes out to a volume of 50671795107 cubic km of “air”, which is how big Mega Maid’s vacuum bag would have to be.

However, I did leave out one potentially crucial fact that would add a whole extra level which we’ll revisit in the future: air is less dense as you ascend in the Earth’s (and presumably, Druidia’s) atmosphere. So I gave the volume of “air” in quotation marks, but as any good Coloradoan knows, there’s a lot less air at higher altitudes. At this point it becomes a density problem involving integration of the shell. As I said, we’ll revisit this problem in the future, but for now, since we’re just starting out, let’s stick with the volume problem. We’d hate to make a critical math mistake already.

Also unanswered is the rate of sucking/blowing portion of the problem. A stopwatch and some division should do the trick. Although, once we tackle the calculus portion of the problem we could get a nice interesting plot of Air in Mega-Maid’s Vacuum Bag vs. Time.

0 comments on “Please, make yourself at home”

Please, make yourself at home

Welcome.

This is a blog dedicated to math instruction and curricula. You always hear “Math is Everywhere!” from Math teachers and wall posters that came with their new set of precious textbooks, but often it’s more difficult to than you’d hope. And it’s even more difficult to get students thinking about Math outside of the Math classroom. With any luck, we’ll hopefully be able to provide some inspiration for interesting math projects and problems found as we travel through life. Think of this blog as a Math brainstorming site. Ideas are just going to be thrown out there. A lot of them will be discardable, but hopefully a few of them will inspire teachers to more fully develop them and use them in their class.

Some ideas/posts will be more fleshed out than others. Some posts will just be links to or pictures of something we think might be Math relevant, but we’re not quite sure how. It’ll be up to you to fill in the blanks. Sometimes we’ll even provide solutions to problems.

Typically, we like to adhere to student-driven learning. That is, we like for students to come up with the relevant questions upon seeing an artifact. Often it will take a little teacher guidance, but when students come up with the questions, good things happen. Therefore, a typical Emergent Math post will look like this.

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[Artifact: i.e. a picture, a video, a fact, etc. Just basically anything that exists.]

(from Indexed)

[Guiding Questions (GQs): questions that your students have about the artifact, possibly some teacher questions sprinkled in.]

  • At what age does the kink in the graph occur?
  • Would the slope eventually decrease?
  • What are the units for “eyebrow density”?

[Suggested activities (optional): what will the students do once the GQs are made manifest?]

  • Discuss.
  • Estimate eyebrow density of people of various ages.
  • Take measurements?

[Solutions to GQs (optional)]

  • 47.
  • No.
  • Hairs / m²?

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Lastly, we’ll try to keep the commentary to a minimum. Let the administrators worry about that. We’ll also try to keep it PG or PG-13 at the most mature, but no promises there. After all, I used to be a teacher and now work with teachers.

Still in its infantile state, Emergent Math will certainly evolve as it gets older, we hope for the better. See more about the blog here and the author here.