Can you hop? Jumping up and down on just one leg isn’t easy. Even bunnies don’t “hop” for real: they really jump off both back feet. So hopping is the big challenge in the game hopscotch. More than 1,000 years ago, soldiers in the Roman army got exercise by hopping through numbered squares drawn on the ground. Little kids liked the game so much that they copied it. They drew their own smaller squares, and that’s where hopscotch came from! In hopscotch you can write whatever numbers you like, throw rocks to block squares, and make up your own rules. So you can invent your own new game every time.

*Wee ones:** *What shapes do you see on this hopscotch board?

*Little kids: *If you write the numbers 1 through 8 in order on your hopscotch board, what number do you write before the 6? *Bonus: *If your hopscotch board has spaces 1 through 10, how many hops do you do if you land only on the odd numbers once each?

*Big kids: *If 6 people and their 6 pet bunnies start hopping, how many feet are hopping all together?* (Remember: *bunnies hop on 2 feet, but we don’t!) *Bonus:* If you number 1 through 12, and skip all the multiples of 4 as well as the non-4-multiple square your rock landed on, how many hops do you do to hop to the end and back?

*The sky’s the limit:* If a bunch of people and bunnies play hopscotch, and there are 8 players in total but 1 more bunny foot than people feet hopping, how many bunnies are playing?

Answers:

*Wee ones:* Squares and rectangles (both are 4-sided shapes), and at the end, almost a half-circle.

*Little kids: *The 5. *Bonus: *5 hops: on the 1, 3, 5, 7, and 9.

*Big kids: *18 feet. *Bonus: *16 hops, since you do 8 in each direction. You skip 4 squares: the 4, 8, 12, and rock.

*The sky’s the limit:* 3 bunnies, who hop on 6 feet while the 5 people hop on 5. You can start with 8 people on 8 feet, and each time you swap in a bunny for a person, the bunny feet go up by 2 while the people feet go down by 1, so the gap grows by 3. The gap started at +8 for the people and you need a gap of -1, so you have to change the gap by 9. You’ll need 3 swaps to do that, so 3 bunnies.

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.