Summer Lesson Building (Geometry: Surface Area and Volume Ratios)

I’ve been looking for a way to bring up surface area and volume ratios that isn’t a forced “here’s some non-contextual geometric solids to calculate arbitrary values for linear, area and volume measurements.” After looking through some resources and reading some blogs, I found an idea for introducing them: Orbeez!

If you don’t know what Orbeez are, go here: http://www.orbeezone.com/

I’m going to have my students explore their claim…or rather figure out what their claim is:
Orbeez Surface Area to Volume Ratios_1

They’ll have to figure out what’s blacked out. They’ll ask for some measurements, so I had the chance to buy some Orbeez and play with them!

Orbeez Surface Area to Volume Ratios_2

Orbeez Surface Area to Volume Ratios_3

Orbeez Surface Area to Volume Ratios_4

Orbeez’s claim is about how much the volume grows. I wanted to leave that little tidbit of information missing. My hope is that the students start with the diameter grows approximately 4.8 times larger. Next, I hope they go to where the surface area grows approximately 23 times larger. Finally, I hope they figure out that the volume grows by a factor of around 109. We’ll come to some conclusion of a class as to which one is the best to help sell the product and they’ll see:

Orbeez Surface Area to Volume Ratios_5

This isn’t meant to be stand alone as a surface area and volume ratio lesson. It’s going to give us a starting point to look at the relationship between the values (the 4.8, 23 and 109). Hopefully they’ll infer what the relationship is and we’ll finish the lesson.

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