When you walk down a hill, you have to work hard to keep from sliding straight down. If it’s really steep, you might have to zigzag back and forth sideways, so you go down the hill just a little bit at a time. That’s what we see in this photo of the “switchbacks” on the side of Beacon Rock in Washington state. The 848-foot-tall, blob-shaped rock might be the second biggest rock in the world, after the Rock of Gibraltar. In 1915 a guy named Henry Biddle bought the whole rock for just $1, and built trails so people could climb the rock and look out at the beautiful river next to it. These switchbacks let people walk from 248 feet above the river all the way to the top, and back down again. There are about 50 of these switchback pieces, so if you’re going to start the walk, make sure you’ll have enough energy to come back down when you’re done!
Wee ones: If you’ve walked up 5 of the switchbacks, what number comes next?
Little kids: Who’s climbed higher, someone who has walked up 9 switchbacks, or someone who has walked up 14? Bonus: If you could buy that whole rock for $1 yourself and you have a $20 bill, how much change do you get back?
Big kids: If each switchback takes you 6 feet higher up the mountain and you want to be at least 40 feet higher from where you are, will climbing 7 of them be enough? Bonus: If each switchback is 100 feet long and you walk all 50 of them, how many feet have you walked?
Wee ones: The 6th.
Little kids: The one who walked 14. Bonus: $19.
Big kids: Yes, since they’ll raise you 42 feet. Bonus: 5,000 feet — almost a mile!
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.