Want to take a swing, kick, or bat at a problem? This Word Problem Wednesday is for all you sports fans! And it’s all about games originating from very merry old England.
Check waaay down below for answers.
Soccer is an ancient game with games involving kicking a ball recorded as far back as 2500BC. However, soccer as we know evolved in Europe from the 9th century. In England, entire towns would kick a pig’s bladder from one landmark to another, even from one town gate to another! The playing fields and teams for modern soccer are considerably smaller. Each soccer team has the following players: 1 goalie, 4 defenders, 4 midfielders, and 2 forwards. How many players are on 5 soccer teams?
Golf is another ancient game originating in England – Scotland to be more exact – around the late 14th century. Players would hit a pebble around tracks using a bent stick. Some sports just stick around (get it?). Players were so obsessed that it was banned in the mid 15th century because it interfered with archery practice necessary for national defense! Today, players are just as obsessed. Jayce and Arianna are practicing their golf swings. They bring 32 golf balls to the course. Jayce hits all 32 first, then retrieves all but one. Then it’s Arianna’s turn to hit all the remaining golf balls and retrieve them, but she also loses one. If this pattern continues, who will take the 12th turn, and how many golf balls will he or she hit? Find a way to solve the problem without counting each turn.
The English have two games involving throwing and batting a ball: cricket and rounders. America’s baseball -- with references dating back to the 18th century -- likely originated from both games. What I find impressive about baseball is the amount of statistics thrown and batted about! Chad and Michael play on the same baseball team. Last year, they both had a batting average of .240. Michael’s batting average increased by the same amount that Chad’s batting average decreased. If Michael has a batting average of .270 this season, then what fractional part of Michael’s new batting average is Chad’s new batting average?
A final question, and it’s about football. American football, originated from another English sport called rugby. The first game of American football was played on November 6, 1869 between the college teams of Rutgers and Princeton in our beautiful state of New Jersey. Football is a misnomer because the ball is mostly carried, and the ball is technically a prolate spheroid – how cool is that! Magenta and Tavia are both running to intercept a prolate spheroid. Magenta is 28 yards away and Tavia is 33 yards away. If Magenta can run 2.5 yards per second and Tavia can run 2.75 yards per second, then how much sooner does the player who reaches the prolate spheroid first get there?
Ask John Urschel to define himself, and this is the sort of answer you’ll get: “John Urschel, pro football player, mathematician, professional mathlete.”
To put it mildly, Urschel is a rare commodity. He’s 6 feet 3 inches tall, a 308-pound offensive guard for the Baltimore Ravens and a man who once stated matter-of-factly that he loves "hitting people.” But he’s also a 24-year-old with ambitions of obtaining a Ph.D. in mathematics after his football career ends.
Urschel understands that he’s a bit of a statistical oddity, but he doesn’t think that his two passions stand in contradiction with one another. "There’s no contradiction when it comes to [my love of] football and math,” he told The Huffington Post. “I think they’re complimentary in a sense," he said. "Football really speaks to this competitive side of me, this aggressive side, whereas mathematics speaks to this side of me where I’m really curious and want to know why."
But Urschel knows not everyone shares his passion for math, and he believes he knows why, too: We’re not properly explaining to young children where a love of math can take them." (This is where Mathnasium excels and why John Urschel endorses us!) "One thing that really limits the amount of people that major in math is that growing up, kids don’t know what math majors do,” he said. “They think about a major in mathematics and they imagine just doing calculus for four years. Or just more factorization. And this isn’t what it is at all."
"What I see in math and what I wish a lot of young people would see is how it’s rooted in reality," said Urschel. "Mathematics is underlying so many things in our everyday life, and mathematicians are in such great need. The way that our world is moving, the way it’s becoming data-driven, the way that it’s becoming more and more modernized -- mathematicians are going to be central to this,” he said. "We’re in a world where we have so much data. It’s abundant, and it’s too abundant. We have all these resources and we don’t know what to do with them.”
That's why, in Urschel's view, "the 21st century is really going to be the century of the mathematician.” But Urschel says math shouldn't only be thought of as a means to a solid job and comfortable life. Fully utilized, knowledge of the subject becomes a way of solving problems both math-related and not. "You need to take the tools you have and the things you know and your experiences from facing other problems to find the best way to solve this problem and to think through this problem," he added. "And mathematics, all the way from when you’re a little child, all the way through college, is an exercise in training you for this."
Now for the answers…
Instead of adding each position individually, we can find the number of players on each team first. There are 1 + 4 + 4 + 2 = 11 players on each soccer team. So, on 5 teams, there are 11 × 5 = 55 players! When we instruct young learners, we use problems like this as opportunities to teach simple multiplications (10s and 11s) to build their confidence.
Did you get that by the 12th turn, Arianna hits 21 golf balls? Jayce has the odd numbered turns and Arianna has the even numbered turns. Since 12 is an even number, Arianna must have the 12th turn. By the 12th turn, only 11 (not 12) golf balls have gotten lost because the balls get lost at the end of the turn. So, Arianna hits 32 – 11 = 21 golf balls. If that’s too difficult to follow, we will ask the student to lay out the first few numbers in the sequence: 32, 31, 30 … from which we can reason that the 2nd number is 32 – 2nd + 1, the 3rd is 32 – 3rd + 1, the 12th must be 32 – 12th + 1 = 21.
Since Michael’s average goes up by .030, Chad’s must go down by .030 to .210. Next, we can find out what fractional part Chad’s batting average is of Michael’s by dividing .210 by .270. First, we multiply both numbers by 100 to get 21/27, then we can reduce the fraction to 7/9.
Magenta reaches the prolate spheroid 0.8 seconds before Tavia. If Magenta runs 2.5 yards per second, then it takes her 28 yards ÷ 2.5 yards/second = 11.2 seconds to reach the ball. Tavia reaches the ball in 33 ÷ 2.75 = 12 seconds. This means that Magenta arrived 12 – 11.2 = 0.8 seconds before Tavia.
By the way, an American football is a prolate spheroid because that’s the natural shape of a pig’s bladder that was originally used as a soccer and rugby ball!
John Urschel is an impressive renaissance man. Mathnasium was honored to have him as keynote speaker during our 2015 Mathnasium convention. Many of our students are heavily involved in sports and we hope that they can be inspired by John and devote as much love and time to math as they do to their sports.
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.
Article: //www.huffingtonpost.com/2015/06/29/john-urschel-math-problem_n_7687732.html
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