When cavemen invented the wheel thousands of years ago, it was probably wood or rock. It probably wasn’t a rubber tire full of air, and they probably didn’t use it to go sledding. That’s called inner tubing: you sit or lie down on a giant donut-shaped balloon, someone gives you a push, and you slide down the snowy, slippery hill. It’s called an “inner” tube because it’s from inside an even bigger circle: a truck tire. Humans first started snow tubing in 1820 in Switzerland, a long time after the cavemen – but a long time before cars and trucks, so where did they get their tubes? More importantly, what happens when you spin as you slide? Lots of math, as you’ll see here!

*Wee ones: *If your inner tube spins once to the left, then once to the right, then once to the left, then once to the right…which way do you spin next?

*Little kids:* If you, 3 friends, and 2 snow-loving dogs all pile onto an inner tube, how many riders are there? *Bonus:* You can also ride tubes on waterslides. If you go 10 miles an hour on snow but twice as fast in water, how fast do you tube on the water?

*Big kids:* If you start sliding facing downhill, with the hill’s right side on your right, and as you slide you spin 1/2 turn to your left, then 1/4 of a turn to your right, then 3/4 turn to the left, which way are you facing now? *Bonus:* If 1/2 the tubes are double tubes (seating 2 people) and the other 1/2 are single tubes, how many tubes are there if they hold 18 people total?

*The sky’s the limit:* If your tube spins once around every 2 seconds, your friend spins once every 3 seconds, another friend spins once every 4 seconds, and the last friend spins once every 5 seconds, what’s the soonest you’ll all face forward at the same time if you all started facing forward?

Answers:

*Wee ones:* To the left.

*Little kids:* 6 riders. *Bonus:* 20 miles an hour.

*Big kids:* Downhill! The 1/2 turn faced you backwards, the 1/4 turn left you facing left, then the 3/4 turn spun you around to the front. *Bonus: *12 tubes in total: 6 singles, and 6 doubles which will seat 12 more people. If 1/2 are single and 1/2 are double, then each double and single forms a pair, and each pair holds 3 people. Then just divide that into the total of 18.

*The sky’s the limit:* In 60 seconds, the smallest multiple of 2, 3, 4 and 5. You don’t need to multiply 2 x 3 x 4 x 5 to get the smallest number, because if it’s divisible by 4, it’s already divisible by 2.

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.