We all need snacks on a road trip, but some snacks (like apples) are easier to drag along than others (like piping hot soup). But what about a hot Runza? What is a Runza, anyway? It’s a tasty sandwich that Nebraska has been keeping secret from the rest of us. The bun is a doughy “bread pocket,” like a pita or calzone. The filling of beef, onions and cabbage (and whatever else you want to add) is held neatly inside. That means you can bring your Runza on the world’s wildest car ride without making a mess! You can also eat it while swinging – like on the world’s largest covered porch swing in Hebron, Nebraska. It’s 32 feet long, so you’ll want to bring some friends to help you get it moving.
Wee ones: Could you lie down on the world’s largest swing? Stretch out and measure your length, then compare it to the 32-foot long swing!
Little kids: If there are 5 of you in your car for your road trip, and everyone else has 1 Runza but you snuck in 2, how many Runzas are in the car? Bonus: If the largest porch swing can hold 24 kids or 18 adults, how many more kids than grown-ups can fit on it?
Big kids: If a Runza can hold 3 ingredients – beef, onions and cabbage – how many different ways can you layer them in the pocket? Bonus: What if you also throw in a slice of tomato? Now how many orders are there – and can you see a pattern for guessing at 5 ingredients without writing them all out?
The sky’s the limit: If the largest swing can hold 18 adults or 24 kids, and there are 15 adults on the swing, how many kids can you add?
Wee ones: There’s definitely enough room on that swing to stretch out!
Little kids: 6 Runzas. Bonus: 6 more kids than grown-ups.
Big kids: 6 ways. There are 3 choices for your 1st layer: B, O or C. For each of those, there are 2 choices for the next layer, so you multiply by 2 to get 6…and then there’s only 1 thing left in each case, so you still have 6. Bonus: 24 ways for 4 ingredients. There are now 4 choices for your 1st layer – B, O, C or T – and each of those has 3 choices after it, giving you 4 x 3 = 2 possible pairs. For each of THOSE you have 2 choices, giving you 4 x 3 x 2…and then that sets the order since only 1 choice is left for the final slot. So we have 4 x 3 x 2 x 1 = 24. That means 5 ingredients would have 5 x 4 x 3 x 2 x 1 = 120 ways to stack them!
The sky’s the limit: 4 more kids. The 15 adults on the swing mean that it is 15/18 full. 15/18 can be simplified to 5/6. So 1/6 of the swing is still empty, so it can hold 1/6 of the 24 possible total kids, which is 4 kids. Another way to figure it out: 3/4 as many adults as kids can fit on the swing, so if there’s room for 3 more adults, there must be room for 4 more kids!
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.