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/
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’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:
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.