[WCYDWT] Orbeez, Ctd.

Sharon Cohen, the brand manager at Orbeez, checks in on the last post:

The disparity (150/100) is based on the fact that growth depends on ionic content of the water–the purer the water the larger they grow. The very same Orbeez wll grow to a different size depending on the water purity. The number we chose ended up being a marketing decision (100 is a powerful figure) but we should have been consistent. It’s impossible to choose one accurate number.

BTW: Sharon Cohen sent along Orbeez’ internal measurements of expansion given different water sources.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. Smart Water 13mm; 13.45mm
    Dasani 13.62mm; 13.45mm
    Fiji 10.2mm; 11.85 mm
    Market Pantry 13.3mm; 14.3mm
    Arrowhead 9.4mm; 10.68mm
    Aquafina 13.4mm; 13.96

    Sharon: Are there repeated measurements with each kind of water? That (and the ensuing analysis) is what it would take to know that the numbers above aren’t noise…

  2. Thanks for sharing your data Sharon! It seems like there are two main variables that need to be considered when talking about Orbeez growth: water purity and time. But even when these are held constant, there is still a good deal of variation in growth from one Orbeez to another. (What causes that?)

    The starting diameter of Orbeez seems to be right about 2mm. Using that number and looking at the data you shared (mean diameter size after 4 hours of soaking) you get these results:

    Smart Water: 274.5 times original volume
    Dasani: 315.7 times larger
    Fiji: 132.6 times larger
    Market Pantry: 294 times larger
    Arrowhead: 103.8 times larger
    Aquafina: 300.7 times larger

    So, the average for four hours of soaking ends up being 236.9 times the original volume. It is important to ask how many Orbeez you used for your samples. The more Orbeez you tested, the more we can trust the averages.

    But, one question to pursue is how much difference soaking time makes. After 8 hours your data average increased to a growth of 278.95 times the original volume. Your manual says to soak for 2 to 3 hours, or longer. Looking at their growth rate, an interesting question is how much difference there is between the 2 , 3 , and 4 hour marks.

    It is interesting to think about your task, “how do I market them”? People may soak them for different time periods in different types of water… You mentioned that you chose 100 because it was a “powerful figure”… Can you fill as in on some of the discussion you and your coworkers had in these marketing decisions? Was it a quick decision? What figures were you debating?

    P.S. I talked to a friend of mine who teaches AP statistics, and later this year he is excited about having his students design some experiments to do some statistical analyses on your product ☺

    P.P.S. Its more descriptive to say “up to 100 times the volume” than “100 times its original size”…. The term size isn’t a specific mathematical term and could refer to radius, diameter, circumference, volume….

  3. The test was done once on each type of water. We grew about 100 of each, but measured just 18 of each using a caliper. You should also know that we did not measure the exact same Orbeez after 5 hours and after a day and a half–which accounts for the results for Dasani.

    Excuse the non-scientific nature of my conclusions–I have grown hundreds of thousands of these and can gauge size difference at a glance. The reason for this particular test was to detemine if we should be instructing customers to use bottled water over tap water in order to achieve better consistency in size. We know that not all tap water is equal. These results showed us that instructing the use of bottled water would not help create greater consistency.

    This might be interesting–and help you understand the difference in size between the Orbeez grown in the same suspensions. Orbeez start off as a liquid during manufacturing. The ingredients are mixed in a large vat and then strained through a large sieve. Droplets land in oil and harden as they cool and travel down a funnel. This accounts for the size differences and the fact that some have taills –like tadpoles.

    The marketing decision was not a long-drawn out process. It was also based on our reading about SAPs in general. The test results you are seeing now were conducted more recently and not for that purpose. It seems now that “up to 200 times the volume” would be more accurate?

    Would be happy to help out in any lesson planning or testing you or your colleagues are doing.

    Thanks for the interest. Happy to send the raw data if you send me an e-mail address.

  4. So you could have students use tap water, then tapwater with a tsp of salt. That would make an obvious difference… I like the idea of using stats on an entire class of data (+30 students) and then you can even study the null hypothesis – there is no difference in growth between the groups. True or false?

  5. @ Sharon

    I was thinking about your marketing decision, and realizing that many factors play a role. Mathematically, could you say that Orbeez can grow up to 300 times their original volume? Yes, you could. In fact I have had some that grew to over 500 times their original volume. But, intuitively, I think people’s notion of volume tends to be mathematically incorrect. If you show people an “unsoaked” Orbeez, and asked them how big it would be if it were to grow 300 times its volume, my guts says that they would way overestimate the new size. So sticking with “100 times the volume”, while it is a very conservative number, is still a “powerful figure” that people generally won’t feel like they are being misled. Maybe it’s all in the wording… one could say “”Depending on soaking time and water quality, Orbeez can grow from 100 to 500 times their original volume!” But I think that may lack that “marketing punch” you were looking for :)

  6. Adam–I agree–people will feel misled if we were to assert “300 times its volume”, and changing a marketing statment midcourse is also undesirable.

    Louise–adding salt is a good idea. It is also ineresting that if you grow Orbeez to full siize and then add salt, they will gradually shrink down to the same volume as if you had added salt at the outset. But not at the same pace as the growth–also worth measuring.

  7. I want to see a time series for the growth of Orbeez in one particular liquid. There’s probably ample room there to sneak in some pretty interesting calculus-related concepts.

  8. I stumbled upon this when trying to determine if my daughter putting some orbeez in her fish tank is the reason we now have dead fish. But now I have an experiment to use in my AP stats class for studying hypothesis testing.

    Always fun visiting this site. Thanks Dan.