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By The Count, on September 16th, 2009
A lot of math is broken down into processes. Start with a problem, do this, do that and, voila, you have the answer. Most people in America learn the same processes for doing most basic arithmetic, and it’s easy to forget there might be other ways to solve these problems. The positional decimal system developed by the Indians (of India) is the standard taught in every school I’ve ever been in, but it’s not the only way to multiply two numbers1. The following is a description of another method I like for its enforced structure and visual guides.
Continue reading Alternative Math Methods
By The Count, on August 14th, 2009
Shortcuts are a great way to do a lot of math in your head. You know the guy in the office that always responds when you ask “What’s 25 times 56?” He’s using shortcuts, and so can you. The best thing about these so-called tricks? They always have a real math basis, or they wouldn’t work! Here are a few multiplication shortcuts. Learn them, and you’ll see how often the situations for which they are useful show up.
What’s the square of [some number > 20]? Does this come up for you very often? Well, maybe not, but from the square you can get great estimates on other products, and you’ll be surprised how often you come across the problems when you can easily solve them. Now, no one really expects you to memorize all the squares to 100 but, with a few shortcuts, you can compute most of them fairly easily.
Continue reading The shortest path
By The Count, on August 1st, 2009
You may have noticed that I like math. This is not a new thing for me. Math has been a part of my life for as long as I can remember, and not in the organic sense of counting blocks or birthdays. My parents, both with degrees in mathematics, spent a good amount of time making sure I had no troubles in school in any field, but especially math. Now that I have kids, I’ve been doing my own part to make sure they never need to spend valuable school time figuring out the math on the board, they already got it at home. Note, this doesn’t exactly make me a favorite parent with their teachers; making kids “bored” in school doesn’t endear me to them, but teaching them is such fun I can’t really help myself.
Counting from 1 to 10 is something kids get from many sources; television, children’s books, etc. I won’t cover that here, and my kids could count a bit higher than that when I started with these exercises. The following are several good methods to used to give kids the tools to solve most any math problem they can think of.
Number Line: The first basic math technique you should teach a child is the number line1. This gives kids a handy way to compute sums and differences without breaking out the fingers and toes. Try creating several worksheets where each row has its own number line followed by a single-digit addition problem.
Continue reading Making more math geeks
By The Count, on July 5th, 2009
Ah, there’s nothing quite like the geek joke. When you hear one, you’re torn between not wanting to look stupid and not wanting to look too smart! I’ve heard a lot of them in my time, and thought I’d share some of my favorites with you here.
There are 10 kinds of people in this world. Those who understand binary, and those who don’t.
Not only does this joke require some small bit of knowledge to get, but this classic example of the geek joke even refers to the separation between those who will get the joke and the rest of humanity. Not a bad start.
Continue reading Classical Geek jokes
By The Count, on July 1st, 2009
For the past 20 years, I’ve been going to Las Vegas for a weekend here and there and, just like everyone else, I couldn’t even stop gambling to eat; and why should I? The casino owners so graciously offer to take even more of my money as I munch on the buffet of the day with the lottery alternative, Keno.
In case you’re unfamiliar with the game, its basic version goes like this. On a grid with 80 spaces labeled with numbers 1 through 80, the player may choose between 1 and 20 spaces and mark them. The computer then randomly chooses 20 spaces (regardless of how many the player chose). A win is determined by how many spaces marked by the user were chosen by the computer (these are called matches).
| Matches |
Payout |
| 1-2 |
$0 |
| 3 |
$2 |
| 4 |
$5 |
| 5 |
$150 |
| 6 |
$3000 |
A possible payout table for picking 6 numbers in Keno.
People from all over the casino turn in $2 and a card containing their marks for the next game and the computer’s same 20 chosen spaces are played against all of them. Note that the more spaces the player marks, the more spaces must match in order for the player to win. In this example, the player chose 6 numbers, then hoped for 3 or more of those number to match. Please note the marked increase in the payout as the number of matches increases, this is what first got me interested in the game. I also wondered how the computer could control the total payout (in some cases a player can win over $100,000) when so many people are playing, and the computer must pick the same 20 numbers. I knew there was no way a casino would run a game where the odds weren’t in their favor, so I set out to determine the actual probabilites involved.
Continue reading Keno: an odd game
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