Race Against the Waves

Race Against the Waves

January 8, 2020

Have you ever watched ocean waves wash up on a beach? When the water runs back down the sand, it wipes out any sandcastles you built and holes you dug. So our friend Elena S. asked, how many footprints can a person make before they’re washed away? Well, the oldest sand footprints ever are about 1,500,000 years old — a million and a half years. The water couldn’t reach them, so they were saved and turned to stone, or “fossilized.” But how many could you make quickly between waves? If you’re tiptoeing near the edge of the water, you probably have only a few seconds between waves before the water smears your designs. But higher up on the beach, they’ll wash away only at “high tide.” Our moon pulls the oceans higher and lower twice a day, so every 12 hours the water comes very far up the beach. So let’s figure out how many steps you can stomp in 12 hours!

Wee ones: Fill a sink with some water. Splash the water gently 5 times to make waves!

Little kids: If before the next wave you hop on your left foot, then right, then right again, then the left foot to start over, which foot makes the 6th footprint?  Bonus: If you do 3 full left-right-right sets, how many more right footprints than left footprints do you make?

Big kids: If you can stomp 5 times per second and the waves come 7 seconds apart, can you make 30 footprints before they’re washed away?  Bonus: If you make just 1 step per second high on the beach, how many steps can you make in 1 hour — and for a megabonus, how many in the 12 hours between tides?




Wee ones: Count as you splash: 1, 2, 3, 4, 5.

Little kids: Your right foot.  Bonus: 3 more, since you make 6 rights and 3 lefts.

Big kids: Yes! You can make up to 35 prints.  Bonus: 3,600 per hour, which comes to 43,200 in 12 hours.

And thank you Elena for the great math question and lovely picture!

Print Friendly, PDF & Email

About the Author

Laura Overdeck

Laura Overdeck

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.

More posts from this author