I am always amused when people become fascinated with simple demonstrations of the power of even basic mathematics. We have become mostly a jaded society depending on the technological progress of corporations to give us more and more electronic gadgetry and the like. We have forgotten how all this technological stuff originates: via the harnessing of the knowledge of mathematics and science and their applications in practical ways.
Thus as educator and mathematician, I always enjoy a big smile when I can demonstrate the practicality of knowing even rudimentary mathematics. A good and solid understanding of basic geometry, arithmetic, and algebra can go a long way toward understanding many fundamental laws of nature and even permitting a high degree of general problem solving abilities. People are always amazed when I explain to them how I can tell time at the beach using the sun, or use probability to make general predictions, or to do seemingly amazing human calculator multiplications in my head. Yet all these feats are quite achievable even for the ordinary person.
Having said this, I can move toward the interesting sounding title of this article and explain how basic mathematics can be used for even such an odd sounding thing as finding a parking spot in a busy mall. We all know how frustrating this can be particularly around the holiday shopping season. Now man is a clever animal and if you ask people their method many will quickly volunteer that they have a great system. These systems range from stalking people who leave the mall to circling like hungry sharks waiting to feed on the next open spot.
Personally, I had always had a problem with the methods mentioned above and for this reason, I suppose, one day I thought about the problem and asked myself whether mathematics could solve this problem–or at least come up with a more practical method. Being a mall rat largely because of my wife’s intense love of such locale, I had many opportunities to drop her off in front and then begin the process of “search and destroy,” or more simply put, to wait for parking spots. Being a fan of the two mathematical disciplines of probability and statistics, I decided to see whether using some basic facts within these two areas could help me solve the problem. Thus sitting by the mall waiting for an open spot (mind you the times we would go to the mall were usually on Saturdays when choice spots were rare, and I would always want to park in a particular area near Macy’s where spots were even more limited because of the smaller parking area), I began to make some basic assumptions and to cogitate deeply.
Almost as by happenstance, I pieced together a rudimentary method, did some quick calculations and tested the underlying hypotheses. I surveyed the fully occupied parking area, targeted my preferred area to park, and predicted that within an interval of no more than five minutes one of those preferred spots would become available. Lo and behold within five minutes, a spot opened up. I was amused. Over the next ten or fifteen visits to the mall I tried and tested this method. Success after success after success. I analyzed both the basic assumptions and mathematics used and tested again and again. Always worked. I even demonstrated the method with people in the car. The reaction was always one of amazement when I could tell them within how long a spot would open up. To them, this always seemed like magic; however, a little thoughtful contemplation joined to some basic mathematics was the glue holding the mix together.
In a follow-up article, I will reveal the method and the basic underlying assumptions, as well as the mathematical principles involved (for those who are squeamish about mathematics, fear not; for the explanations will not involve anything beyond the scope of layman mathematics, and my particular strength is the ability to boil down the esoteric and make it understandable). For those who have read this far, I think you realize the broader implications of this: if mathematics can help you find a parking spot in a busy mall, what else can it do? See you in Part II.
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By: Joe Pagano
Posts Tagged ‘Multiplications’
Finding a Mall Parking Spot Using Mathematics – Part I
April 26th, 2010Teaching Children Using Math Board Games
January 1st, 2010Board games can be used for a number of educational purposes, as they have proven to help stimulate the minds of children in a fun, informative way. Learning things like multiplication tables, long division, or even more basic tasks like simple addition and subtraction can be difficult for young children, usually depending on their age and the amount of attention they have received on the object. It has also been long proven that most children have a better time learning skills when they are presented in a fun, interactive format, giving educational math board games a great platform on which to make their stand.
Math Smart is one such board game which helps children to easily begin to master the skills of basic math. The game plays out across a table, much like dominoes. There are 100 durable cards in each set of the game, which come in editions for each basic math skill. Some set focus on addition, while others help players learn their subtraction, multiplication, and division skills. The easy format helps any player to adapt quickly to the game and with a fun, slightly competitive environment, the learning aspect of the game may even go entirely unnoticed!
Another popular game, Goose Egg, can help children learn how to complete their math skills more quickly. Coming with three 10-sided dice, answer boards, a timer, and chips, players will need to roll the dice, figure out the multiplications between the numbers, and quickly cover up the correct answer on their answer sheets, all within a 30 second time frame! This teaches children to think quickly, trying to encourage them to learn how to complete the skills within a short time frame. However, players must be careful about the dice they roll, for if they end up with 3 zeros in any turn, they have received a goose egg and may be out of the game. This game is incredibly popular, as it encourages quick thinking in an easy to learn, fun environment, and many children have greatly benefited from playing with it.
Totally Tut is a great example of a game that gives children the chance to learn a number of basic math skills and the order of operations potentially without them even realizing it. Racing across a board made of different pyramids, the players try to correctly solve math puzzles that have been presented to them. When the problem is correctly solved, that player gains a piece which will help them to build their own pyramid. However, the game is not as simple as just building pyramids by solving problems, for other players have the chance to either steal or swap pyramid tiles, helping to complete their own and ruin another!
This game raises the level of competition, making the game a high-paced, harrowing experience for any players participating. With such an exciting environment provided by the game, it is no wonder that all of these educational board games help players to learn their techniques so quickly. Teaching math to young children has never been easier or more fun!
By: Victor Epand
Times Tables – the Worst Way to Teach Multiplication
November 22nd, 2009Learning the “multiplication tables” is one of the first traumas that children usually face when learning arithmetic.
Ask ten elementary-school kids to tell you what, say, eight times seven is. Watch as they look up and to their left (or right) and go into, “let’s-see” mode. Often you’ll hear them say, “Um, ah…” before give you the answer. Generally, there’s a lot of hesitation. Only then, do they actually give you the answer. Sometimes it’s even correct.
I know, I was one of them. Maybe you were, too. Most children are victimized by the thoughtless, authoritarian, wrong way to teach the “multiplication facts” (what a stupid term!)
Why are “the tables” the wrong way to learn? Maybe I can illustrate it best by analogy. Imagine that you wanted your children to learn the names of all their cousins, aunts and uncles. But you never actually let them meet or play with them. You just showed them pictures of them, and told them to memorize their names.
Each day you’d have them recite the names, over and over again. You’d say, “OK, this is a picture of your great-aunt Beatrice. Her husband was your great-uncle Earnie. They had three children, your uncles Harpo, Zeppo, and Gummo. Harpo married your aunt Leonie…yadda, yadda, yadda.
Boring!
But what if you had them all over for the weekend, and you found out Earnie did magic tricks, Beatrice had been a rodeo queen, Zeppo always wore mismatching socks, Harpo played the, well, you know, Gummo picked his nose and wiped it on his tie, and Leonie could sing like an angel?
Well, then you’d have some relationship with them, wouldn’t you? The next time you saw Earnie, you’d ask him to show you a trick. You’d ask his daughter Leonie if she could teach you to sing, and you’d stay away from Gummo’s tie.
It turns out that you can build relationships with multiplications, as well. And they have relationships with each other. You already know some of them. Like the relationship of nine to ten. Nine is one less than ten, so when you multiply something by nine, just stick a zero at the end of it, and subtract the original number.
Take the example 8*9. Just stick a zero behind the 8 to get 80. Next, subtract 8 from 80, and you’ve got 72, which is the correct answer to 8 multiplied by 9.
That is the intuitive way for many people to multiply by 9. So why do they make you stare at the nine-times-table in school? It’s boring and fosters no sense of the relationship of nine to the other numbers. It turns multiplication into isolated “multiplication facts” (there’s that stupid term again).
If you had children multiply by nine with the subtraction method often enough, they’d know the answers in their bones after awhile. It would take less time than it would to memorize the nine-times-tables by rote, and it would have them actively involved with using the numbers. Imagine that!
This may be hard to digest at first, because learning the “multiplication facts” by rote has been ingrained into the school system for decades. Maybe that is why our children are getting worse and worse at this easy, important skill.
If you’re a teacher, you’re probably fed up with the bad mojo from the policy-makers. You need to get your own mojo working. Find out how to get started at http://learn2multiply.com
By: Brian Foley
