When it rains, don’t you just want to run outside, open your mouth wide and drink right from the sky? Only if it’s warm out, of course — especially since it will take you a long time to get one full gulp. As Bedtime Math fan Jay A. asked us, how many raindrops does it take to fill a glass of water? Is it hundreds, thousands, or millions? There isn’t one exact size of raindrop, but we found a good guess: if a raindrop is a tiny ball 4 millimeters across (less than 1/4 inch), that ball holds 33 little millimeter-sized cubes of water, which comes to just 33 thousandths of a milliliter. You’d need 30 of those to fill one milliliter, and then about 240 of those to fill an 8-ounce glass. So that glass can hold thousands of raindrops. How long would it take to fill it? If you set a glass with straight-up-and-down sides outside in the rain, you’ll find that even a pounding rain will fill only about 1/3 inch per hour. But if you aren’t too thirsty and are willing to wait, it’s one way to get a drink.
Wee ones: If you fill your 1st glass with tap water (from the sink), then the 2nd with rainwater, then the 3rd with tap water, then the 4th with rainwater…what’s your next number glass, and what kind of water does it get?
Little kids: If you make 8 ounces of lemonade by mixing 1 ounce of lemon juice with water for the rest, how many ounces of rain does your glass need to catch? Bonus: If you start catching rain at 2 in the afternoon and catch 1 ounce every hour, when do you finally get to drink that lemonade?
Big kids: In the New York area it rains about 3 1/2 inches per month. How much does it rain in a year? (Hints if needed: A year has 12 months – and you can break the 3 1/2 apart by figuring it out for 3 inches, then 1/2 inch, then adding them together.) Bonus: If giant raindrops can fit just 20 per milliliter, and a glass holds 240 ml, how many raindrops will fill that glass?
Wee ones: The 5th glass, and it gets tap water.
Little kids: 7 ounces. Bonus: At 9 pm that night.
Big kids: 42 inches. Bonus: 4,800 raindrops!
And thank you Jay for the wet and wild math!
Laura Bilodeau Overdeck is founder and president of Bedtime Math Foundation. Her goal is to make math as playful for kids as it was for her when she was a child. Her mom had Laura baking before she could walk, and her dad had her using power tools at a very unsafe age, measuring lengths, widths and angles in the process. Armed with this early love of numbers, Laura went on to get a BA in astrophysics from Princeton University, and an MBA from the Wharton School of Business; she continues to star-gaze today. Laura’s other interests include her three lively children, chocolate, extreme vehicles, and Lego Mindstorms.