Posts tagged ‘decimal’
“200?” asked the shepherd. “But we only have 196 sheep.”
The dog replied, “Well, yeah, but you know I like to round up.”
Rounding up has been a topic of conversation in college basketball this week.
Marcus Keene, a guard for the Central Michigan Chippewas, scored 959 points in 32 games this season, giving him a points-per-game (PPG) average of 30.0.
Technically, his average is 29.96875, just shy of the highly coveted 30 points-per-game mark that’s only been attained by a few dozen players in NCAA history. Since 1981, only 8 players have reached 30 PPG, most recently Long Island’s Charles Jones in 1996‑97.
But the controversy swirled this week because Keene didn’t actually average more than 30 points per game. He was one point shy. His lofty accomplishment was nothing more than smoke-and-mirrors due to round-off error, or so the critics say.
Per-game statistics are used to compare players with one another, because totals can’t be compared for players who have played a different number of games. And let’s face it, no one wants to get into the habit of comparing per-game stats to seven decimal places. The NCAA reports all per-game statistics to the nearest tenth, and the truth is that Keene’s PPG average would be reported as 30.0, 30.00, 30.000, and 30.0000 if rounded to tenths, hundredths, thousandths, and ten-thousandths, respectively.
It’s been a good year for math and basketball. Anthony Davis can have an asterisk for his record-setting 52 points in the NBA All-Star Game because no one played defense; and now Marcus Keene can have an asterisk for his 30.0 points-per-game average.
In related news, it was reported that 53% of men say that they will watch the NCAA Division I Men’s Basketball Championship (aka, “March Madness”). And just to prove the men are the dumber sex, 61% of them admitted that they’ll watch while at work. Simple math says that 32.3% of men will watch the tourney at work. Which means that if you’re a man with two friends who don’t like basketball, then you’ll be the one killing office productivity next Thursday.
Today is 7/11/13, and boy, have I got a great math trick for today! You’ll likely need a calculator.
- Multiply your age by 12.
- Now add the age of your spouse/brother/sister/friend/uncle/aunt/whomever.
- This should yield a three-digit number. Now, divide by 7.
- Then, divide by 11.
- Then, divide by 13.
- The result should be a number of the form 0.abcdef…, with a 0 and a decimal point in front of a long string of digits. Add the first six digits after the decimal point.
Here’s the cool part. I don’t know your age, nor do I know the age of your spouse, brother, sister, friend, uncle, or aunt. But I do know that after you completed those steps, the result was 27.
Pretty cool, eh?
There are myriad math tricks of this ilk, but this one is my favorite. It’s based on a trick I learned from Art Benjamin, though I think the one above has more panache than his original. Decide for yourself.
- Choose a number from 1 to 70, and then divide it by 7.
- If your total is a whole number (that is, no digits after the decimal point), divide the answer by 7 again.
- Is there a 1 somewhere after the decimal point? I predict that the number after the 1 is 4. Am I right?
- Now add up the first six digits after the decimal point.
Just as with the trick above, the result will always be 27.
Regardless of which trick you prefer, have a happy 7/11! And if you’ve got a few hours to kill, you can try to solve the 7‑11 problem.
I used to dislike math, but then I realized that decimals have a point.
For instance, they separate dollars from cents in prices, as shown on the price tag of a Black Brown 1826 shirt that I received as a gift from my mother-in-law:
Like me, you may be wondering: Why would they include four zeroes instead of just two after the decimal point?
My first thought was that Black Brown 1826 was a London-based company. The tag shows the price in U.S. dollars, so it would make sense that a British company would display the price in U.S. dollars to four decimal places — currency pairs are often expressed to four decimal places.
But that’s not the case. Black Brown 1826 is a clothing line at Lord + Taylor, which is a North American company.
My second thought was that the designer of the line might be European. But nope. The line was designed by Joseph Abboud, an American designer.
My third thought was… well, actually, I didn’t have a third thought. And I still have no idea why the price is expressed to four decimal places.
Do you know why there would be four decimal places shown in the price? If you have a theory, leave a comment.
The location of the decimal point is often a mystery to kids, too, but not for this student…
A math teacher wrote 15.1 on the board. “This is what happens if we multiply by 10,” she said, and then erased the decimal point.
“Now where’s the decimal point?” she asked.
A student answered, “On the eraser!”
But decimal points can also pose problems for adults…
A colleague noticed a new spot on the carpet in the hallway. “Quick! Call the accounting department!” he yelled. “See if they misplaced a decimal point again!”
“Patrick, I have to ask you a question,” said Martha. “You have written a book of math jokes… so, how are you so very serious?”
In my 41.82 years, this is the first time that anyone had ever used the word serious to describe anything about me.
Clearly, Martha doesn’t know me.
Then again, perhaps Martha’s perception is based on me doing things like stating my age as a decimal to the nearest hundredths.
Martha and I had only been introduced two days earlier. We were both asked to participate in a quality review session for the Math Snacks project at the Learning Games Lab at NMSU — which, by the way, is a great project; I particularly like the Bad Date video and the Gate video game — so she hadn’t really had much time to get to know me.
But it made me wonder… do other people think I’m too serious, too?
To correct this false perception, here are some non-serious things I’ve done:
- I regularly pretend that one button is broken on my calculator, and then have to figure out alternate methods to calculate the value of long expressions. (On one particularly zany day, I pretended that two buttons were broken. Boy, did that ever lead to some crazy misadventures!)
- One afternoon — when the curtains were not drawn — I danced if no one were watching. The tune that put my backfield in motion? New Math by Tom Lehrer.
- I once used the phrase “backfield in motion” in a math blog post.
- In an academic paper submitted to a prestigious journal, I once reported a result to three significant figures, even though I was well aware that only two significant figures were justified.
- At a bookstore, I paid for a copy of Innumeracy entirely with pennies.
- On my way to a lecture, I asked a passer-by for directions to the lecture hall. She pointed straight ahead… and I turned around and walked the other way.
- I regularly wear a hat that reads, “Shut your πhole.”
- When someone enters the elevator and says, “Seven, please,” I push the 2 and 5 buttons and say, “There ya go. That makes 7.”
- When a telemarketer asks, “How are you doing?” I usually say, “I’m great, thanks. And I’m glad you called, because — boy! — do I have an exciting offer for you! Do you like to laugh? Do you like math? For $12 — or the cost of just two venti, non-fat, no foam, no water, six pump extra, hot chai tea lattes at Starbucks — you can have a personally signed copy of Math Jokes 4 Mathy Folks delivered right to your door! That’s right, just $12! How many copies can I put you down for?”
Gee, I sure hope Martha reads this…
The summer is a great time for kids to hike, bike, swim… and forget everything that they learned during the school year.
The son returned to school after summer break. At the end of the first day, his mother received a call from the teacher about his poor behavior. “Now, just one minute,” said the mother. “He had poor behavior all summer, yet I never called you once!”
In Outliers, Malcolm Gladwell purports that poor kids lose ground to affluent kids during summer break. Their experiences and academic progress during the school year are similar, he contends, but their out-of-school experiences during the summer are very different. Though minor at first, the cumulative effect of those summer losses becomes noticeable as children get older.
The following are five games/puzzles that can be used with young kids to prevent summer losses and, possibly, even elicit some summer gains. Each has the characteristics that I love about a good game for young kids: It requires students to use and practice basic skills, but there is a higher purpose for doing so.
This is a game that’s kind of like SuDoku, but a million times better. If you don’t know the game, check it out at www.kenken.com. My sons noticed me playing it one afternoon and asked what it was. I explained, and they asked if they could do it with me. We now solve three or four games every afternoon. I used to help them a lot, but now they pretty much know all of their math facts up through 7 × 7. How do you not love a game that helps four-years-olds learn the times table?
This is a puzzle, not a game, and you can learn all about it at Math Pickle. The general idea is that you start with a sequence of numbers in a flower-like pattern. You then multiply two adjacent numbers, subtract 1, and divide by the number below. The cool and surprising part is that every intermediate result is an integer, so there are no ugly decimals for kids to deal with. And by the twelfth ring of petals, every result is 0. Happens every time.
3. Squares of Differences
The good folks at Math For Love reminded me of this great problem, and Josh Zucker discussed it at length on the NYTimes Numberplay blog. Draw a square, and put a positive integer at each vertex. Then at the midpoint of each side, write the difference of the numbers at the two adjacent vertices. Now connect the midpoints to form a rotated square inside the original square, and repeat. It seems that if you continue this process long enough, you’ll eventually get all 0’s. But does that always happen?
By the time kids test this conjecture with three or four attempts, they’ve done a hundred subtraction problems without even realizing it.
4. Decimal Maze
The Decimal Maze (PDF) comes from the lesson Too Big or Too Small on Illuminations. Trying to obtain the maximum value while traversing a maze with decimal operations, students learn about the effects of multiplying and dividing by decimals that are greater or less than 1. The activity is good for upper elementary and middle school students, but I’ve used modified versions with very young kids. For instance, a modified maze for kids in first grade uses single-digit positive integers while limiting the operations to just addition and subtraction; for older kids, a maze could include fractions or powers instead of decimals.
5. Dollar Nim
As I mentioned in a previous post, my wife created a great game that I call Dollar Nim. The idea is simple. Imagine you have 100¢, and on your turn you can remove 1¢, 5¢, 10¢, or 25¢. Players alternate turns; the player to reduce the amount to 0¢ is the winner. The optimal strategy is not obvious, and kids practice a whole lot of subtraction, especially as it relates to making change.
More generally, any one-pile nim game is great for the purpose of having kids practice subtraction without realizing it.
I hope you find some free time this summer to enjoy these games. I’ll leave you with a joke/truth about summer school.
I never understood the concept of summer school. The teacher’s going to go up there and go, “OK, class. You know that subject you couldn’t grasp in nine months? Well, we’re going to whip it out in six weeks.” – Todd Barry