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Wednesday, July 25, 2012

Thank you, Math!

Journal writing in mathematics education is often perceived as a boring activity in getting students to reflect on their own mathematical thinking. Perhaps an appealing way to assess students' mastery of mathematical concepts is to encourage them to write "mathematical letters" to a buddy in the form of "thanks goodness for anything numerical or mathematical."

Let's look at a sample of these math-lite correspondences.

Dear Numbers

© mashable.com 
Thank you for being such a buddy I can always count on. You don't change because of geography or history. A while ago, you gave me an idea to blog on "Singapore Math by Numbers." Without you, the world would come to a standstill. You numbers don't just rule the world; today, you've been semi-elevated to a god—with all your metrics and analytics.

Numerically yours


Dear Calculus book

Thank you for letting me use you as a weight or support. Your thickness scares the hell out of so many otherwise intelligent mortals, especially those who have had an unpleasant experience with their high school math teachers. Besides, I use you as an inexpensive cure to help my friends and loved ones, who are suffering from insomnia—your deltas and epsilons are sufficient to hypnotize the hardcore sufferers.

Infinitesimally yours


Dear 1001
© shashindrasri.blogspot.com

You're a mirror to my numerical soul. Indeed, you provided me with so many oddities and idiosyncrasies about the Palindromic Family. In fact, I've started writing the first few chapters of "The Joy (and Pain) of Palindromic Numbers."

Palindromically yours


Dear LOGIC

Thanks for being such a reliable companion in my dealing with irrational and illogical folks. Your cold, austere character has put off many egos, who would otherwise have trampled over the rest of us.

Logically yours


An i-protractor
© 1mobile.com



Dear Protractor

I hope you won't go the way of the abacus or slide rule, because I'm seeing lesser use of you these days. Anyway, I promise to keep you as a vintage math instrument for my grandchildren.






Dear Compasses & Unmarked Ruler

Thank you for frustrating and humbling thousands of our mathematical forefathers in their futile attempts to constructing a square with the same area of a circle. To revive your popularity, I'll be conducting an enrichment math lesson on The Lost Art of the Compass.


Product Details
Dear 25

Thanks for confiding with me some of your innermost secrets, which allowed me to write some parallelisms between the king of the public holidays and the queen of the sciences. Don't worry, I'll dedicate CHRISTmaths to you on its silver edition.

Joyfully yours



Dear Boring Math Teacher

You provide jobs to half a dozen tutors, as they try to teach the most disliked subject in school in a less parrot-like manner! And your boring test of artificial questions only serves as a filter to separate the nerd from the herd—the mathematical goats from the sheep.




© business.mcmaster.ca
Dear Probability

Thanks for mocking my intuition and flawed logic. The answers to your problems have humbled the mathematical brethren, as you tease them with your counter-intuitive results.



 © tower.com

Dear FRENCH

Thank you for making me pronounce the first part of the word "factorize" to sound like the four-letter word. To test my hypothesis, I tried that trick on my French female teacher many moons ago, and the class then couldn't control themselves but burst into laughter*. 

Fact-ally yours

* Try this trick on your French-speaking friends and fans who speak English as a second or third language.


Dear Math Editor

Thank you for introducing me to so many conceptual and linguistic faux pas—I couldn't have fabricated them without your poor grammar and punctuation, and shaky grasp of some difficult mathematical concepts. Some are jaw-achingly funny. My collection of your blunders is growing, and I couldn't wait to compile them in a book for green editors. If only I knew earlier that "poor writes" could open up the doors to many freelance assignments. 


© 123opticalillusions.com

Dear Dice

Thank you for feeling so good in my hand and for showing me so many different possible outcomes. You've taught me a lot about chance and probability, and you look pretty sitting on my book shelves. That's where you'll stay. Love, Leah.




Dear Sex

Thank you for revealing to me your intimate liaison with the most boringly taught and disliked subject in school. And for giving me enough materials to writing and getting "Mathematics And Sex" published.  Indeed, MATH is a four-letter word! 


© mathandchess.net
Dear Chess

Thank you for using me to beat those older and smarter chaps. Mentally satisfying to "humble" them! But I can't stand you when you used the same trick on me years later—when those young geeks refused to let me win or draw even one game.


Dear Calculators

Although you had atrophied my mental calculation abilities, however, you're a God-sent tool to working out those tedious and mindless computations. I'm totally dependent on you for my everyday numerical chores—from calculating the waiter's tip to finding the amount I owe to the credit card companies. On the negative side, you've upped my innumeracy index by a dozen points. On a positive note, I wished you'd upgrade yourself to becoming an instrument of desire, just like the iPad. 


Dear Amazon.com

A trick-and-tricky math book 
Thank you for showcasing our math titles on your site, but we hate that 55 percent you're charging us every time there is an order for our books. When we factor in the time we need to dispatch them, and the shipping freight, most of us are only operating at a negative profit! Plus, your payment in US dollars, and your reluctance to link with PayPal, makes authors living outside the US hesitant to promote their titles on Amazon.



Dear ZERO
© spaceadventures.com

Thanks for sharing with me how you're once marginalized by your fellow numerals, and how you're even ostracized by the Catholic Church for calling you the "infidel zero." Your forgiving spirit towards the Pope and his bishops, and your revelation to Newton and gang regarding some of your oddities and idiosyncrasies, had earned you a numerical place in the Mathematical Hall of Fame. However, your critics never cease to call you the "troublesome zero."


Dear NOTHING

Pictures of Nothing: Abstract Art since Pollock (Bollingen)Folks always mistake you for the numeral zero—both of you are like faux twins. Zero is nothing, and nothing is zero. In fact, you're anything but nothing—you're something! Philosophers and mystics curse or deify you, with their ever-convoluted arguments—they've almost elevated you to the status of an atheistic religion. 

There's almost an alphabet for your name: abyss, chasm, emptiness, hole, pit, void, nothingness, nada, naught, …, nil, nix, zilch.

books.google.com

Dear Empty Set

Thank you for causing so much confusion among school kids. Do you exist or not? Are you really a set? Are you like a club with no members? Or, a bag without items? You're like something with zero nothings.




© shop.cafepress.com 
Dear Imaginary Numbers

Once upon a time, they denied your existence, just like your rejected, dejected, and ejected cousins, the negative numbers. But today, like zero, you're having the last laugh; in fact, we often take you, guys, for granted, albeit you prefer to keep a low profile. I wished school teachers won't tell the kids that you're complex, when you're really simple to manage.




Dear May 1

This is the only date in the year, when working folks don't have to labor. A day of protests and political rallies, you remind the masses of Karl Marx's words that workers of the world must unite—that they have nothing to lose but their chains.


© eoagh.com

Dear Black Hole

It's beyond my reasoning ability to understand the math that predicted your existence. Thank God, He produces a few Hawkings among His creation every century or so to reveal your galactic existence and importance. 




 © abqjournal.com
Dear Sudoku

You give me hope that in my golden years my chances of dying from schizophrenia or dimentia are significantly reduced if I indulge myself to playing with you more often.


Dear Numerology

© geocaching.com 
From the simple idea of digital root, you manage to bluff tens of millions of numerically challenged folks into believing that they can predict their good and bad days, and that they can take control of their future from their birthdates. Indeed, a pseudo-equation of yours is: f(birthdate) = lucky/unlucky days 


Dear iPhone

Thank you for saving me the trouble of having to carry a scientific calculator around. Yes, by a mere 90-degree turn, you magically turn yourself from a four-function to a scientific calculator. I look forward to seeing you functioning as a graphing calculator in a-not-too-distant upgrade. Hope you can strike a deal with Texas or Casio, just like you did with HP.


Dear Statistics

Thank you for revealing to me all your curves and standard deviations. However, I'm still confused about your three musketeers: mean, mode, and median. Which mean do you mean? Now I understand why some folks call you "Sadistic Statistics" for torturing hundreds of thousands of students every day.


Dear 13

© sabotagetimes.com 
I know you didn't deserve that awful publicity surrounding your name, especially when those superstitious folks wickedly try to associate you with some black Friday. You're just an innocent-looking prime who had suffered so much—far worse than 666 and 4444.

Thank you for providing me with rich materials to write about, every time you fall on a Friday. We, recreational math enthusiasts, feel a bit like "numerical hypocrites," when we can't help but gossip about the numerical quirks of Friday 13.

Un-triskaidekaphobically yours



Dear Death

Thanks for being the great equalizer. You won't let the rich and the powerful, or the arrogant and the haughty, live beyond their undeservedly numbered days. Three scores and ten, or a billion odd heartbeats—that's your deadline to them, all!




It's now time to write and e-mail some math-lite letters to the rest of us to read and enjoy!

Mathematically yours

Reference
Dieterich, L. (2011). thx thx thx: thank goodness for everything. Kansas City, Missouri: Andrews McMeel Publishing, LLC. thxthxthx.com

© Yan Kow Cheong, July 24, 2012

Thursday, February 9, 2012

Social Media Math

Here are some questions that might appear in future National Assessment of Educational Progress (NAEP), Third International Mathematics and Science Study (TIMSS), or Scholastic Aptitude Test (SAT) papers, to reflect the interests or changing habits of students, who are spending an unhealthy amount of time, Facebooking and Twittering friends, fiends, or foes, rather than doing their homework.

1. N stands for the number of hours Dennis spends on Facebook each day. Which of the following represents the number of hours Dennis spends on Facebook every week?

a. N + 7           b. N – 7           c. N × 7           d. N ÷ 7                        [Grade 4]

2. If the number of Facebook members in a school is F and the number of Twitter members T, and there are 40 times as many Facebookers as Twitterers, write an algebraic equation that shows this relationship. [Grade 8]

3. For next year’s Singapore App Annual Show (SAAS), a child pays $x per ticket and an adult pays $y more than a child per ticket. If p children and q adults buy tickets, find the total revenue from the sale of tickets in terms of the variables. [Grade 8]
  
4. Sam has twice as many Twitter followers as Ruth. If Ruth has r followers and Sam s followers, and Sam helps Ruth to gain a dozen followers within a week, how many followers does each have in terms of r? [Grade 7]

5. In the following, write an expression in terms of the given variable that represents the indicated quantity.

(a) The cost of having an IT repairman spend t hours at your house if he charges $40 for coming to the house and $50 per hour for labor

(b) The time (in minutes) left to use the mobile phone with a battery life of 8 hours, after t minutes of SMS-es and k hours writing e-mails 

(c) The resale price of a laptop after t years if its initial price is $P and the resale value of the laptop halves every year

(d) Arthur’s total earnings as an ICT tutor after three years if the first year he earned $x, the second year it was $8,000 higher, and the third year it was twice as much as the second year [Grade 8]

6. Last month, Jack, a hardcore ex-convict,
· illegally downloaded a pirated blue movies;
· secretly watched b YouTube adult-themed clips;
· sneeringly “defriended” c Facebook members;
· insincerely clicked “Like” d times;
· angrily unfollowed e followers on Twitter;
· anonymously left f mean comments on blog posts; and
· vengefully spammed g e-mails to his ex-math teachers.

How many on-line transgressions did he commit in the last month?           [Grade 7]

7. Tom recently set up a Facebook account for his dog. Freakie has now more friends than his owner: x canine friends and y feline friends. Tom has z friends. Which of the following is true?

a. x + y < z           b. xy > z           c. x + y > z           d. z > x + y        [Grade 7]

8. @cobrakill tweeted the following to @MathPlus and @Zero_Math:

Scared off 3 bullies; had x mice & y ostrich eggs for breakfast. Gobbled up a piglet & a wild cat for lunch. And terrified a trio of oldies!

How many fell prey to the king cobra?                                                   [Grade 7]

Selected Answers
1. c
2. F = 40T
3. px + q(x + y) = (p + q)x + qy dollars
4. s = 2r; Sam has (2r – 12) followers, and Ruth has (r + 12) followers.
5. (a) 40 + 50t dollars     (b) 480 – t – 60k     (c) P/2t     (d) 4x + 24,000 dollars
6. a + b + c + d + e + f + g
7. c

© Yan Kow Cheong, February 8, 2012.

Saturday, December 17, 2011

25 Christmaths Toughies from Singapore

Here are 25 non-routine fertile questions for friends and relatives to solve during this festive season:

1. The Recurring 25

Convert 0.252525... to a fraction.

2. The Sides of a Polygon

If the sum of the interior angles of a polygon is 2525°, what is the maximum number of sides the polygon can have?

3. December 25, 2025

On what day of the week does Christmas Day fall in the year 2025?

4. Number of Diagonals in a 25-gon

What is the number of diagonals in a 25-sided convex polygon?

5. How Many Ways?

In how ways can you arrange the letters of the word CHRISTMASTIME?

6. Merry Xmas & Happy New Year

If the value of MERRY CHRISTMAS is 189, the value of A HAPPY NEW YEAR is _____.


7. Santa's Routes

Determine the total number of distinct shortest routes from point A to point B in the following diagram grid map.
A
 































B
 

8. A Sum of 25 Powers

Find the sum of S = 2 + 21 + 22 + 23 +⋯+ 225.

9. Writing 25

What is another way of getting the number 25 using the numbers 2 and 5 only once, other than equating it to 5²?

10. Time Needed

Determine how long it will take to return all the gifts mentioned in the song “The twelve days of Christmas” if the gifts are returned at the rate of one gift per day.

11. Join the Xmases Family

A mother who was born on December 25, married to a husband also born on December 25, gives birth to their first baby on December 25. What are the odds of the mother doing that?

12. Four Fours to Make 25

Using four fours, the four basic operations and, if necessary, √4 and/or 4!, form the number 25. [Note: 4! = 1 × 2 × 3 × 4]

13. The Largest 25-digit Integer

What is the largest 25-digit number that can be divided by 2 and 5 without any remainder?

14. Number of Zeros in 1 × 2 × 3 ×⋯× 24 × 25

How many zeros are there at the end of the product 1 × 2 × 3 ×⋯× 24 × 25?

15. The Chocolate Bar

Given a 25-piece square chocolate bar, how many snaps are required to break the bar into its individual pieces?

16. A Creative Thinking Question

It is late on Christmas Eve and little Noel is waiting the Christmas tree to be finished. At exactly what time will this happen?

17. Christmas and Halloween

Prove that Oct. 31 = Dec. 25.

18. Divisibility by 25

Show that, if n is a positive integer, 16n + 10n – 1 is divisible by 25.

19. A Pair of Christmas Alphametics

In each case, replace each letter with a digit, different letters being different digits.

(a) SANTA - CLAUS = XMAS

(b) A + MERRY + XMAS = TURKEY

20. A Sum of Squares

Find the value of 1² – 2² + 3² – 4² +⋯+ 25².

21. Number of Rectangles

A board has 25 squares. How many individual rectangles are there in all?

22. A Christmas Party

At a Christmas party, each child brought a present. Presents were put in a large basket. All presents were different but identically wrapped. Going home, each child randomly selected a present from the basket. What is the expected number of children who carry home their own presents?


23. How Many Lines?

Using only horizontal and vertical lines, what is the most number of straight lines you can draw between the dots in a 5 × 5 grid without lifting your pencil?

24. A Table of 25 Boys and 25 Girls

A total of 25 boys and 25 girls sit around a table. Show that it is always possible to find a person both of whose neighbors are girls.

25. All n's End in Zeros

For what values of n does 1 × 2 × 3 ×⋯× (n – 1) × end in 25 zeros?


A Merry CHRISTmaths to all!

Selected answers

1. 25/99     2. 16 sides.         3. Monday.      4. 275 diagonals.     5. 778,377,600 ways.
6. 158.       7. 252 routes.      8. 2^26 - 2      9. 5 ÷ .2 = 25          10. 364 days.
11. 364/1         12. 4! + (√4 + √4)/4             13. 999…99990     14. 6.         15. 624 snaps.

16. Midnight.       18. 600.       19. (b) 2 + 97,445 + 6,928          20. 325.         
21. 225 rectangles.                    22. 1.                 23. 34 lines.      25. 105, 106, 107, 108, 109

For full solutions, consult the title in the Reference.

Reference
Yan, K. C. (2011). CHRISTmaths: A Creative Problem Solving Math Book. Singapore: MathPlus Publishing.

© Yan Kow Cheong, Dec. 16, 2011.


CHRISTmaths: A Creative Problem Solving Math Book
Now available as an iPad app
http://tinyurl.com/7pn8pau



Thursday, December 15, 2011

25 Things You Wished Were Untrue about Christmas

25. Toys are made affordable for millions of parents thanks to the appalling working conditions endured by under-aged children in Santa’s sweatshops, in China.

image photo : Fractal Christmas trees
Fractal Christmas Trees
© Dreamstime.com
24. Proud CEO: “My time in looking for a five-dollar present for my company Christmas party is worth more than US$2,525—I’d rather issue a check 100 times the amount for the gift.”

23. An e-card costs much less than 25 cents—maybe a mere 2.5 cents plus or minus a few bits and bytes.

22. There are fewer joyful people on Christmas Day than on any other day of the year. Do you know why?

21. Men dishonor Christ more in the 12 days of Christmas than in all the 12 months of the year—by their boozing and carousing.

20. Even staunch Christians may not be aware that Christmas is a pagan feast, originally meant to worship the Sun god, instead of the Son of God.

19. There may be more non-believers celebrating Xmas than believers every year.

© teachercreated.com
18. Singles, poor people, and entrepreneurs could not wait for Christmas to come and go—not a happy time to be alone or be lonely.

17. Many believers and non-believers celebrate Christmas without a genuine understanding of the meaning of the public holiday—probably the most celebrated and the least understood festival of the year.

16. Retailers rely on Xmas significantly on the festive sales to remain financially afloat.

15. People merry so much on Xmas Eve that they don’t have time to open up their Xmas gifts—Boxing Day often becomes a sleeping day!

14. Even believers forget that Christmas needn’t be merry to be meaningful—it is the Christ of Christmas that needs to be celebrated, not Christmas itself.

13. Believers and non-believers are more and more expensively anxious or stressed to buy something to please others—as a sign of showing off their wealth, or exhibiting misplaced generosity.

12. New Christians do not want to be excluded from Christmas as they await for their employers’ Christmas bonus—that universally revered figure.

11. Employees are willing to work under unreasonable bosses because of the Christmas bonus—many at the same place, for the same boss, for more than 25 years.


The Search

© www.sodahead.com
10. Believers from other faiths often feel morally obliged to celebrate Christmas with their Christian colleagues and neighbors, all in the name of religious harmony.


9. Religious fanatics intolerant of Christianity wished Christmas were celebrated every quarter of a century instead of every year.

8. Some people would buy off a Christmas gift for their children on eBay for several thousand times the original price.

7. People max out their credit cards to finance the gift storm, as compared to their grandparents who saved money for Christmas.

6. Some allegedly US-friendly Arab nations tend to treat Christians worse than those living under dictatorial Muslim rule.

5. A month after Christmas, the holiday is only halfway paid off—credit card debt resulting from a borrowed merry Christmas. And a third of the money borrowed for Christmas spending is still not paid off two months after the holiday.

CHRISTmaths: A Creative Problem Solving Math Book
A Christmas gift for numbers lovers
http://tinyurl.com/7pn8pau
4. This Christmas over a billion people in the world are surviving on less than 70 pence a day.

3. Politically correct retailers have banished Jesus and Christmas from the mall to accommodate to the secular demands of agnostics and non-theists.

2. Christmas is celebrated today more like a sales frenzy than as the most important birth in history—the commercial mentality has robbed the message of giving.

1. The closer people get to Christmas, the pressure to give these (useless) unnecessary gifts goes up and they feel depressed and unworthy if they can’t give.

Merry X-W/g to all!



© Yan Kow Cheong, Dec. 15, 2011

Friday, November 11, 2011

11 Random Musings on 11/11/11

On this "auspicious date" for the superstitious, and "marriageable date" for those tying the knot, here are eleven random numerical thoughts for this year's most memorable date.


1. When Numerology Meets Biology
A possible aftermath for this year's hot date is to expect a slight increase in the birthrate this coming August—maybe some 11 percent points up for greying nations like Singapore and Japan, where the fertility rate is currently below its replacement level.


2. The Heck of a Date
Let's celebrate, or meditate on, a dozen 1's at 11 seconds past 11:11 on November 11, 2011: 11:11:11 11/11/11


3. Murder by Numbers
Health risks for both mothers and babies, resulting from induced births or Caesarean operations, as parents-to-be long for an auspicious birthdate—a union of superstition and innumeracy!


4. A Mental Stimulation
A mental calculation for lovers on a hot date: Find the value of 111111 × 111111.

Predict the patternful answer for 11111111111 × 11111111111.


5. Timely Birth, Untimely Death
What is the probability that one born on 11/11/11 will have one's last heartbeat on 12/12/12?


6.  Born on 11.11.11  Died on 11.11.11
What are the chances that someone born on 11/11/11 (2011) will also die on 11/11/11 (2111)—when he or she is a centenarian?


7. The 11:11 Phenomenon
Are you a superstitious, or faithful, believer in the numerology of the 11:11 synchronicity?

Do you wake up every night at the same time, sometimes 11:11 p.m., sometimes 1:11 a.m., 2:22 a.m., 3:33 a.m.? 

Your minor medical expenses from a minor accident: $11,111.
Your hospital room number: 1111
Date of accident: November 11

Your mileage read 111111!


8. Special Birth-dates
What percent of children (or twins or triplets) in the world would be celebrating their 11th birthday on 11/11/11?


9. A Mathematical Quickie
The product of the ages of Mr. and Mrs. Yan, and their daughters, is 111,111. If Mr. Yan is two years older than his wife, find the sum of the ages of their children. 


10. Expressing Oneself in Ones
Using 1's only and the four operations (+, —, ×, ÷), what are some ways of expressing 111111?

For example, 111111 = 11 × 111 × (111 - 11 - 11 + 1 + 1)


11. A Pseudo-Mathematical Toughie
Mrs. Ones bought a certain number of pens for $1111.11. She sold each pen at $1.21. If one pen costs more than $1.00, how much did she earn in total?

Selected Answers
9. 18      11. $200.20

© Yan Kow Cheong, November 11, 2011.