Let’s talk about records today, not the auditory ones, but the records of extreme feats. We’re awed by these achievements because it demonstrates great perseverance, or often because it tickles our need for novelty.

Take a spin at a selection of this week’s problems culled from “*The Guinness World Records*”. That book is published annually listing world records of both human achievements and extremes found in nature. The book itself is a world record holder, being the best-selling copyrighted book of all time; thus proving that we’re just fascinated by extremes.

**Lower Elementary**: *Question*: The world record for the greatest number of hula hoops spun at the same time is held by Marawa Ibrahim from Australia. She can spin 200 hula hoops at once (on November 25, 2015). If Ruby can spin 150 hula hoops right now, how many more does she need to spin to break the world record?

**Upper Elementary**: *Question*: The record for the largest pizza was broken when a restaurant called NIPfood (in Rome, Italy on December 13, 2012) made a pizza that was 1,260 square meters in area. If that pizza were cut in half, then each piece were cut in half, then each piece were cut in half again, over and over, until the pieces had been halved 10 times, how many pieces would there be?

**Middle School**: *Question*: There are 2,700 residents of Casey, Illinois, home of the world’s largest mailbox. The mailbox is so big that a group of people can stand inside it. If there are 135 people standing inside the mailbox, what percentage of the population of Casey is in the mailbox?

**Algebra and Up**: *Question*: Sweet Pea the dog holds the world record for the fastest 100 meters walked with a can balanced on her head. (Seriously.) She traveled the 100 meters in 2 minutes and 55 seconds. What was Sweet Pea’s average speed measured in meters per second?

These records are easily understood statistics, usually a simple single comparable record number, e.g., how __fast__ Sweet Pea walked while balancing a can. That allows us to compare the speed of another dog to determine which is faster. However the conditions under which the records are achieved must be scrupulously defined. For example, Sweet Pea holds numerous records for performing exactly the same task of balancing a can, but under different conditions: walking forwards, walking backwards, and walking down stairs. No walking up stairs yet, but that’ll probably be added at the next *Guinness Book of Records* refresh! That rigor is necessary to define “sameness” of the record value. Sameness is something we intrinsically understand – just listen to a child crying “It’s not fair!”. At Mathnasium, we don’t assume that intrinsic understanding of “sameness”; instead we specifically teach “the law of sameness” to explain why certain numbers are the same so that comparisons (and operations) are fair. Therein lies the difficulty of understanding statistics!

Ignoring all that talk about statistics, let’s answer those questions by talking through them and seeing how the answers speak to us.

**Hula**: How many more hoops does Ruby need to break the world record? Ruby can spin 150 hoops. For Ruby to reach the world record, she needs 150 and (+) how many more to reach (=) 200. How many more is 50 to reach the record. To break the record, she’ll need 1 more, or 51 hula hoops.

**Pizza**: Each time we halve the pieces, we're doubling the number of pieces in total. So, after the pizza is cut in half once, there are 2 pieces, then 4, 8, 16, 32, 64, 128, 256, 512, and finally 1,024 pieces. We teach this doubling sequence repeatedly because it’s the foundation of binary numbers and demonstrates exponentiation. We just did 2^{10 }, or 2 to the power of 10. By the way, we can talk through the question of what 2^{0} means. Many students start at Mathnasium thinking it’s 0. Since the power means each step of the operation, 0 means the starting condition. At the start, we have 1 gigantic pizza. Hence 2^{0} = 1. The first split is 2^{1} = 2, the second split is 2^{2} = 4, and so on.

**Mailbox**: Let’s first answer what 135 people represents as a comparison to Casey’s population. That comparison is the fraction ^{135}/_{2700 }that simplifies to ^{1}/_{20}, which means that 1 person for each 20 people in Casey can fit in the mailbox! How do we express that as a percent? The word percent is a compound of “per” and “cent”, or “for each” “100”. That means we need to convert our comparison of “person for each 20 people” into “persons for each 100 people”. We do this simply by multiplying by 5 since there are 5 twenties in 100. That means, “1 for each 20” is the same as “5 for each 100”, or 5 percent, or 5%. Once we understand that concept, we can simply say that ^{135}/_{2700} = ^{1}/_{20 }= ^{5}/_{100} , and that last fraction says 5%.

**Sweet Pea**: First, we need to know how many seconds are in 2 minutes and 55 seconds. Two minutes is the same as 120 seconds, and 55 more makes 175 seconds in total. A hundred meters over 175 seconds is ^{100 meters}/_{175 seconds} = ^{4 meters}/_{7 second} = ^{4}/_{7} ^{meters}/_{second} = ^{4}/_{7 }meters-per-second. You can variously interpret this as:

- Sweet pea travels 4 meters every 7 second, or 4 meters per 7 seconds.
- Sweet pea travels
^{4}/_{7} meters per (1) second or 0.571428 meters per second.

And that’s what learning and teaching at Mathnasium is like. A lot of talking through problems to create the sentences that lead to answers that should speak meaningfully back to us!

__Contact____:__

Ruby Yao and Benedict Zoe, Mathnasium of Fort Lee

201-969-6284 (WOW-MATH), [email protected]

246 Main St. #A

Fort Lee, NJ 07024

Happily serving communities of Cliffside Park, Edgewater, Fort Lee, Leonia, Palisades Park, North Bergen, West New York, and Fairview.

Picture: //www.cbsnews.com/pictures/bonkers-new-guinness-world-records-2016-edition/12/ (credit *Guinness Word Records*)