You probably don’t remember the day you learned to walk. But you can bet it was exciting to put one foot in front of the other and cross the room. Luckily, we have only 2 feet to move. What’s it like to have 4 legs like a horse, or 6 like an insect, or 8 like a crab? If we people number our feet 1 and 2, walking is just 1, 2, 1, 2. For a horse it’s trickier: with front left/right feet 1 and 2 and back left/right feet 3 and 4, a horse’s steps are 3, 1, 4, 2, then 3 again. An insect walk cycle mixes it up: the very back left and very front left step at the same time as the middle right leg. Then on the next step, the back right, front right, and middle left all step together. In what order does a crab or spider move its legs? Let’s find out how they keep from tripping over themselves.
Wee ones: Who has more legs, a horse with 4 or a ladybug with 6?
Little kids: If a horse’s steps are 3, 1, 4, 2, then 3 again to repeat, which foot takes the next step after that? See if you remember the pattern! Bonus: Which foot takes the 11th step?
Big kids: If a crab steps with all 8 legs before repeating the pattern, how many total steps has it taken when every leg has stepped twice? Bonus: In a video of a walking crab, the legs on the left side step in the order 1, 3, 2, 4. If the 4 right legs are numbered 5, 6, 7, 8 and follow the same order at the same time, which 2 legs together take the 30th step?
The sky’s the limit: If leg number 6 on the crab takes the 6th step, then the 14th step, then the 22nd, and so on, when will that 6th leg take a step again that ends in a 6? Which step will be the next one after that to end in a 6?
Answers:
Wee ones: The ladybug with 6 legs has more.
Little kids: Foot #1. Bonus: Foot #4.
Big kids: 16 steps. Bonus: Legs 3 and 7.
The sky’s the limit: The 46th step, then the 86th step. After the 6th step, we need to add a multiple of 8 that is also a multiple of 10, to keep a 6 in the final digit. 5 x 8 is the smallest multiple that works, adding 40 each time.
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.