Concepts Of Circles And Volume Of Spheres Through The ORBEEZ Lens

It’s nice when there is the coincidence of a Common Core Standard, and the perfect experiential activities for your grade level.  To explore concepts of circles and volume of spheres, (CCSS 8.G) I adapted Dan Meyer’s Orbeez lesson.

The Orbeez marketing materials are so wonderfully sickening.  I made my Orbeez Orbinizer to match the color scheme.  Many of my students do better with a set of boxes like these to give them some boundaries, and I create an extra version with lines inside the boxes for a few.  Some do all of their work on graph paper, and staple it to the organizer, and one or two turn in much of their work electronically.  Good thing I’m easy.

My kids love being skeptical almost more than they love being sarcastic, and when I suggested that the marketers of Orbeez might be having us on when they claim that “Orbeez grow to 100 times their original volume…” they got all riled up, totally outraged, and were off and running.

What I Did

• I asked them to work in pairs, played the Orbeez advertisement video, and put up the above image of the Orbeez materials (I blurred out the word “volume” and changed it to “size” so that kids would have to decide what the makers meant by “size.”  See below for the doctored image).  We brainstormed questions.  I fanned the flames of outrage, and then passed out the Orbinizer.  I ask kids to fill these out individually.  Even if they’re working in pairs, they each have to have individual writing as an artifact of what they’ve done.

• Once we decided on the things we would measure, kids needed to strategize about how to go about this.  They thought of some ingenious methods of measuring the tiny beads; my favorite was lining up 10 dark colored Orbeez on white tape, measuring with a ruler, and dividing by 10 to get an “average” Orbee (Can that really be the singular for Orbeez?) size.  At a certain point, they realized that they needed to be able to calculate volume of a sphere to find the truth.  “Hey Nat, how do you find the volume of a sphere?”  Gotcha! Join me at the whiteboard…
• Some direct instruction here.  There is interesting math in deriving the volume of a sphere, and if kids know the Pythagorean Theorem, they can wrap their heads around this – even if it did cause a little smoke to come out of their ears by the end.  I used THIS Archimedean logic as the basis for my discussion.  Even though my kids aren’t ready for calculus, they could understand conceptually what was going on here, and I think that it will help them to remember the ideas if not the formula.
• I gave them the sphere volume and surface area formulas, and let them go for it.  They measured diameter, converted their measurements, and came to individual volume averages.  We averaged the whole class’ data as well, and got the Orbeez soaking for the next day.

Next Day

• Kids got to class bursting to check on their Orbeez expansions.  Ensue fierce calculating.  Actually ensue “What was the formula again?” and, “Eww these things are GROSS.”  Then fierce calculating. Exclamations as they mostly confirmed the claims.  Some unexpected outrage that a few Orbeez actually grew BIGGER than they were supposed to.
• Brought the class back together, and showed them how the makers had come to their claim.  The discussion on Dan’s blog made for very authentic experience for them.  We averaged the class’ findings, and sure enough our results came to almost exactly 100 X the original volume.  Usually the world is a little grungier, but it worked for us this time.  I’ll take it.
• We settled down for some traditional work on a problem set about sphere volumes.  I suppose you have to at least expose the kids to what a textbook looks like.  :)

THE MATERIALS:

Orbeez Orbinizer

2 thoughts on “Concepts Of Circles And Volume Of Spheres Through The ORBEEZ Lens”

1. Genevieve Morris

What is the average volume for the orbeez before they grew? I’m doing a class science project on this concept, and I don’t have enough time to work out the math myself. Please answer back as soon as possible!

1. Nat Post author

Hmmm. This was a few years ago, and I’m living in Cyprus now, where I don’t have any Orbeez available, but they are pretty small. I would estimate that an un-expanded Orbee would have a radius of about 1 mm, so the volume would be 4/3 pi, or approx. 4.1888 cubic mm. Hope that this helps. Curious what you’re doing with them!