ARITHMOMANIAC: 2012

Kendoku / KenKen / Mathdoku as a Way to Strengthen Math Ability and Logic

KenKen and KenDoku are trademarked names for a style of arithmetic and logic puzzle invented in 2004 by the Japanese math teacher Tetsuya Miyamoto, an innovator who says he practices "the art of teaching without teaching”. He intends the puzzles as an instruction-free method of training the brain. The names Calcudoku and Mathdoku are sometimes used by those who don't have the rights to use the KenKen or KenDoku trademarks.

As in sudoku, the goal of each puzzle is to fill a grid with digits –– 1 through 4 for a 4×4 grid, 1 through 5 for a 5×5, etc. –– so that no digit appears more than once in any row or column (a Latin square). Grids range in size from 3×3 to 9×9. Additionally, KenKen grids are divided into heavily outlined groups of cells –– often called “cages” –– and the numbers in the cells of each cage must produce a certain “target” number when combined using a specified mathematical operation (either addition, subtraction, multiplication or division). (www.wikipedia.com)

As of now, many are using Kenken to enhance the ability of students in dealing with integers. There's no harm to try introduce this in our class: a source of fun, learning and bonding.

You can click the following links for free online kendoku puzzle or you can play sudoku in this blog.

http://www.mathdoku.com/

http://www.conceptispuzzles.com/index.aspx?uri=info/news/281

Try if you Like... Prove if you want to Discover...

Multiplication means finding the product between two or more factors/numbers... I think, its one of the hardest operation that students encounter.... For that, there are many methods being introduced to ease the pain of multiplying..

There's no harm to try the new method being introduced but still encouraging to use the method where we feel comfortable...

http://www.youtube.com/watch?v=zvpLN5KJg0c

PROBLEM SOLVING IS DIFFICULT... OWS???

"Working separately, Kieffer, Albert and Onofre can accomplish a piece of work in 14, 7 and 6 days respectively. Albert and Onofre begin working together for 2 days. Then, Kieffer joins them. In how many days will it take them to complete the work? "

It is one of a sample problems where most students will shook their heads, circled their eyes, cross out their notes, and the like.

The questions of our students could be : is it really difficult? do our teachers taught it? do our teachers can answer this? how can i answer it?... And arriving to the statement "Teacher, why do we answer it orally?"... Without realizing that, the teacher is the one who really answer the problem and not knowing if the student understand how to do it.

Most Filipino students or teachers will answer such type of problems on using let x be the... and so on... and students or teachers only see the equations, the variables, and saying "Haay, algebra, huuh"... Where in fact, many students troubled on the use of variables, simplifying equations, evaluating equations, etc. So the point of using Algebraic Equations in answering problem solving would create another trouble.

Focusing on how other will solve it... Maybe they will use the AREA OF RECTANGLE METHOD in part of analysis and simple calculations... or BLOCK MODELLING in easy visualization of the problem and simple calculations, and many other easy method.

Let us save our students or even our self in solving complicated math problems.
Area of Rectangle Method

Model Method
Method

HOW FAST CAN YOU SOLVE IT?

Try to test your ability to perform the basic operations. Test how fast can you answer the given!

Play Games at freeworldgroup

Play Virtual Rubik's Cube

The Rubik's Cube is named after its inventor, Erno Rubik.

Magic Cube (Puzzle game) | Play more games

Learning Math From the Rubik’s Cube (by Jennifer Lee)

Can a Rubik’s Cube boost student confidence?

About a dozen New York City schools have introduced a child-friendly Rubik’s Cube-based math curriculum devised for students as young as 8.(Read more of the article at http://cityroom.blogs.nytimes.com/2009/11/16/learning-math-from-the-rubiks-cube/)

BLOCK MODEL APPROACH IN SOLVING WORD PROBLEMS

The Block Model Approach was introduced in 1983. In the present, the method remains a powerful problem-solving tool to solve many challenging arithmetic word problems. Mathematical models help pupils gain concrete experiences which are pre-requisites for understanding abstract symbols of mathematics and their manipulation (Kho, 1982).

Watch the sample video created by www.mathplayground.com.

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MATHEMATICS & ALICE'S ADVENTURES IN WONDERLAND

Alice's Adventures in wonderland, written by Lewis Carroll, is recognized by almost everyone as a classic in children's literature. What many are are surprised to learn is that Carroll was a professor of Mathematics, whose real name was Charles Lutwidge Dodgson. Dodgson used his real name only when writing on mathematical topics and his pen name when writing children's literature.

One of the unique qualities of Alice's Adventures in Wonderland is its appeal to children and adults as well. For decades, mathematicians and logicians have tried to look beyond what appears to be children's nonsense and find a logical meaning in much of it. Some believed that Alice's Adventures in Wonderland is full of symbolic logic, a topic on which Carroll often wrote as a mathematician. An example of this can be found in the story when Alice says, "Let me see: four times five is twelve, and four times six is thirteen, and four times seven is-oh dear! I shall never get to twenty at that rate!"

Mathematicians propose different explanations for this passage, such as the use of bases other than base 10. Perhaps the simplest explanation is that the multiplication table traditionally stops at 12. If you continue the nonsense progression, 4x5=12, 4x6=13, 4x7=14, and so on, you will end with 4x12=19, which is one short of 20. So Alice's fear that she will never get to twenty may be well-founded.

~Chua, Simon L. et.al., 2005
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SMARTER WAY to multiply numbers close to 10

http://www.glad2teach.co.uk/fast_maths_calculation_tricks.htm

PLATEAU & DEPRESSION PRIMES

Plateau primes are palindromic prime where all the interior digits are alike and smaller matching end digits. Examples are 1777771 and 355555553.

Depression Primes are palindromic prime where all the interior digits are alike and have larger matching end digits. Examples are 322222223 and 722222227.

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THE STORY OF 1729

When Srinivasa Ramanujan, the great Indian mathematician was ill with tuberculosis in a London hospital, his colleague G.H. Hardy went to visit him. Hardy, trying to initiate conversation, said to Ramanujan, "I came in taxi-cab number 1729. That number seems dull to me which I hope isn't a bad omen."

"Nonsense," replied Ramanujan. "The number isn't dull at all. It's quite interesting. It's the smallest number that can be expressed as the sum of two cubes in two different ways." (Ramanujan recognized that 1729 = 1^3 + 12^3 as well as 9^3 + 10^3).

http://mathworld.wolfram.com/Hardy-RamanujanNumber.html

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THE MAGIC NUMBER IN YOUR NAME

A-1    B-2 C-3    D-4    E-5    F-6    G-7 H-8 I-9      J-1 K-2 L-3    M-4 N-5    O-6    P-7 Q-8    R-9       S-1     T-2 U-3      V-4    W-5     X-6    Y-7    Z-8

People who lived during the ancient times believed that there was a kind of magic in numbers. They thought that numbers could tell about the future and many other things. So, they worked out what they thought were in magic ways to tell them what these numbers mean.

How would you like to know your "magic number" and what it is supposed to tell you about yourself? Here's how to do it.

Use the number assignment for each letter of the alphabet:
   C L A R I S A     E L L A
   3+3+1+9+9+1+1      5+3+3+1
          27              +      12            = 39

Now, add up all the resultant numbers per name and then, per whole name. If your get a number from one to nine, that's your "magic number." If you get a number that is higher that nine, you must add up the numbers.
For example, Clarisa Ella's numbers add up to 39. When she adds 3 and 9, she gets 12. So, she adds the 1 and 0 from her 12, and gets 3. That's her magic number.

When you know your "magic number", look at the list to find out the kind of person are. Ofcourse, numbers can't really tell you about yourself-but it's fun to pretend that there is "magic number".
1 - You are sure of yourself, make friends easily, and like to keep yourself busy.
2 - You are quiet, rather shy, but can work easily with others
3 - You are clever, artistic, sociable.
4 - You are hardworking and dependable. You do not change your mind easily.
5 - You are smart, active and adventurous, but you lose your temper easily.
6 - You are fair, unselfish, and careful of other people's feelings. You like to keep things neat and organized.
7 - You like to be by yourself and you don't like to do what everyone else is doing . Yout think things out very carefully.
8 - You like to plan things out and to make sure you are right. You are kindhearted and people know they can trust you.
9 - You like people and you believe strongly in freedom. You are a clear thinker.

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PARALLEL AND PERPENDICULAR LINES

You may have heard about a train bound for Bicol that was derailed from its path. The accident happened because some parts of its railroad were stolen or dislocated, and it claimed so many lives, including those of children.

Buildings are designed to be perpendicular to the horizontal ground so that the gravitational pull will be directed perpendicularly to the ground. On the other hand, the railroad of a train is designed to form a pair of parallel lines. These are some important designs that use the concepts of perpendicular and parallel lines.

Share what you know about parallel lines and perpendicular lines.

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THE MAGICAL MYTH OF NUMBER 7

Seven has always been considered a special number. To the Egyptians, for example, the Earth was represented by a four-sided house in which three Gods dwelled, which added up to seven. This became their lucky number.

Seven really came into its own with the Christian interpretation of Creation:
The world was made in seven days.
There are seven days a week.
There are seven graces.
There are seven stanzas in the Lord's Prayer.
There are seven ages of man.
Christ uttered seven last words.

Most of the above beliefs are ruled by the different phases of the moon, which change every seven days.

The Romans believed that the mind and the body changed completely and were renewed after seven years. They also started the seven year's bad luck concept.

Seventh-Heaven is an Islamic concept, and it represents the best of all possible places. It is the heaven of heavens, the residence of God and his angels. There is also a very early Islamic belief that there are seven heavens, one lying right above the other, graduating in degrees; depending upon how good a person was on Earth, he or she could say, "I'm in Seventh-Heaven."

Seven is especially lucky for gamblers.

The seventh son born to the seventh son is thought to be doubly blessed. He is believed to be a clairvoyant, with natural healing powers. Throughout the Middle Ages, the seventh son usually practiced magic and administered the laying on of hands to the sick.

(Ymas et.al. 2002)

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What makes Mathematics beautiful?

Its language – clear and concise;

its discipline – profound and alive;

its usefulness – diverse and practical;

and its continuous contribution

to the unraveling and understanding

of life’s mysteries.

For mathematics to be appreciated, one has to see beyond the ideas,

concepts and skills presented in the confines of the classroom.

It has to be made real, relevant, tangible and enjoyable at the same time.

And how do we do these?

We can only do so by presenting our learners all the possible different

connections and applications Mathematics has.

(Blanco, 2005)

This is what the Learning Activities aim to achieve-

To show how Mathematics can be made alive in its simplicity.

To supplement and deepen the classroom instruction,

various activities that the teacher and students

may enjoy and find meaning in are presented.

It is hoped that teachers get use of the activity

that will inspire students to get a glimpse

of the importance of Mathematics.

NUMBER ODDITY

Make a number of all the digits 1 to 9 leaving out 8 : 12 345 679
Now, multiply it first by any single-digit numbers : (say for instance 5) 12 345 679 x 5 = 61 728 395
Multiply the product by 9. 61 728 395 x 9 = 555 555 555

YOU SHOULD GET YOUR SINGLE-DIGIT BACK NINE FOLD.

LUCKY 9

Think any number. Say 123456
Reverse the Order of the Digits. Gives us 654321
Subtract the Lesser from the Greater Number. 654 321 - 123 456 = 530 865
Now, add up the sum of the digits in the remainder. 5 + 3 + 0 + 8 + 6 + 5 = 9.

Try other numbers.

You will find out that no matter what number you choose,
THE ANSWER WILL ALWAYS BE 9!