RATIONAL NUMBERS - INTRO STORY (2)

What does the word "Rational" mean?

Well the dictionary says:
 /'in accordance with the principles of logic or reason; reasonable; of sound mind/'
and the translations are as follows Hindi  विवेकपूर्ण , Tamil பகுத்தறிவு.

Whenever I think of Rationality, this story of Birbal comes to my mind.

One day Akbar asked his courtiers if they could tell him the difference between truth and falsehood in three words or less.
The courtiers looked at one another in bewilderment. "What about you, Birbal?" asked the emperor. "I'm surprised that you too are silent." "I'm silent because I want to give others a chance to speak," said Birbal.

"Nobody else has the answer," said the emperor. "So go ahead and tell me what the difference between truth and falsehood is — in three words or less."

"Four fingers" said Birbal. "Four fingers?" asked the emperor, perplexed. 

"That's the difference between truth and falsehood, your Majesty," said Birbal. "That which you see with your own eyes is the truth. That which you have only heard about might not be true. More often than not, it's likely to be false."

"That is right," said Akbar. "But what did you mean by saying the difference is four fingers?'. "The distance between one's eyes and one's ears is the width of four fingers, Your Majesty," said Birbal, grinning.




A rational number is a number that can be expressed as a fraction or ratio.  
The numerator and the denominator of the fraction are both integers.

An irrational number cannot be expressed as a fraction.

RATIONAL NUMBERS - INTRO STORY (1)

Carl Friedrich Gauss was the famous 17th century German Mathematician. 
His mathematical skills were clearly visible from a very young age. His elementary teacher Büttner, one day asked all his students to add numbers from one to hundred. this was to keep them engaged for some time. So the students started summing up the numbers,
 1 + 2 + 3 + 4 + ............... + 100
Within minutes Gauss was sitting idle. The teacher asked why he was not doing the sum, for which he replied he's already finished it! and the answer is 5050.
Wonder how he did that? Gauss observed that there is a pattern in these numbers, 
1 + 100 = 101
2 + 99   = 101
3 + 98   = 101
.
.
.
.
50 + 51   = 101
so there are 50 pairs of 101. i.e 50 x 101 = 5050. interesting isn't it? 

Now try this, 

Find the sum of integers from -10 to 10. what will be your approach?
Can you apply the same for adding consecutive fractions? what do you observe?

We are going to study more operations on fractions and integers combined together, called Rational Numbers (Q). Hope you remember the Number System and where Rational numbers fall!.

 A rational number is a number that can be expressed as a fraction  where  and  are integers and . A rational number  is said to have numerator  and denominator . Here, the symbol  derives from the German word Quotient, which can be translated as "ratio,"

A Story For a Topic in Math

It is wonderful to open your math class with a story. My children always appreciated the little tit bits of information along with the regular class. It helps even more when you have a math class just after the PT or lunch time. Am going to record here relevant stories and mind maps for every chapter for classes 8, 7 and 6 in that particular order.
Its also my firm belief that every math teacher and student should know about who discovered a concept or how it evolved - to - what you are learning about it - how it is applied today.
not very difficult for the middle school curriculum.

Teacher is part of being a Mother....

I am writing after two years,for the feeling is so intense and its like
"I actually knew this all along, that school is just an extension of home and I am a mother first and till the end".

When I started out as a teacher, it was a profession. I had to deliver and measured my SUCCESS by the performance of my students.
Oh! but what a beautiful feeling it is to grow gracefully into a mother. For now when I enter the class,
I am so sensitive to each and every expression on those faces.
I know when they smile or just nod their head,
I am more concerned when I see a kid tired,
I am particular that they first relax after their PT period before they open their math books,
We should be comfortable as a group inside the class room and when all those facial muscles are relaxed, I know I can start. Its ok to loose few minutes.
I am particular that if the kid is not feeling up to it, he/she should put their head down and rest. You can always learn it when you are fine...

And guess what a reward I got, for the first time in my 5-6 years of teaching math this kid came and said "thank you mam, I really enjoyed today's class". Well obviously, we had revision worksheets done under the trees, in the park.

Learning :  When my kids are cared for, learning happens naturally!

Number System - The Whole Picture

Presenting a whole picture before explaining the concepts helps children have a complete idea about what they learn.
Like any other classification (animal kingdom, plants etc.) numbers too have a system.

• Zero with Natural numbers form WHOLE NUMBERS
• Whole numbers with negative numbers form INTEGERS 
• Integers with fractions form RATIONAL NUMBERS 
• Rational numbers with irrational numbers form REAL NUMBERS 
• Real numbers with imaginary numbers completes the NUMBER SYSTEM

When you understand this it becomes easy to build on concepts one after another. Else the concepts sland as isolated ideas, difficult for the child to comprehend and remember.

talking place value...

Consider this scenario, you are shopping in a supermarket and have a long list of items. You want to do a quick check of the approximate value... This is where your place value comes in real handy.how?
Let the cost of items be like,
rs.1034
rs 973
rs.450
rs.228
rs.1005
rs.824
rs.2000
the best and perhaps the easiest ways to add is by splitting them according to their place values.

thousands - 1000+1000+2000 = 4000
hundreds - 900+400+200+800 = 2300
tens - 70+50+20+20 = 160

total it up = 6460 (approximately)

the actual value being = 6514

The importance of place value is very much underplayed in to-days schools. Practical examples, used to explain the addition based on place value will help better understanding.
we are taught a mechanical way of addition which obscures the basic principle. Memorizing addition values of the single digit numbers and applying them with carry overs helps us only so much as doing a sum correctly. Of-course this is necessary, but try and do your checking by using place value. I am sure you will enjoy the process.

oh so sweet... (typo)

http://goodtypography.tumblr.com/post/29617334883/bookspaperscissors-alphabet-plushies-by

For the love of numbers - D.R.Kaprekar (1)

Once upon a time (January 17, 1905 to be precise), there was born a boy named Kaprekar. He played with numbers like you and I would play solitaire in our pc. Maths was his entertainment. He went on to become a maths teacher and spread the joy and fun of playing with number to others. He was a maths teacher in the beautiful hill town called Devlali or Deolali (1929-1962). A number theory addict, he was invited in many colleges to talk about his unique methods.

He would say of himself:

A drunkard wants to go on drinking wine to remain in that pleasurable state. The same is the case with me in so far as numbers are concerned.

Well ofcourse, many Indian mathematicians laughed at his number theory ideas and called it trivial. After his retirement in 1962 he found it difficult to survive with his pension. He was forced to take maths and science tutions to make enough money.

International fame only came in 1975 when Martin Gardener wrote about Kaprekar and his numbers in his 'Mathematical Games' column in the March issue of Scientific American.

His discoveries in number theory include

• Kaprekar constant
• Kaprekar number
• Devlali or Self number
• Harshad number
• Demlo number

Let us make him our hero by entertaining ourself with these fun methods...

Can you imagine...the integers? (student)

If numbers are just numbers and operations (+, -, x, /) just symbols, oh... then maths is really boring.
Well, actually numbers can be imagined as values which make sense. HOW????

I was walking up the stairs with my lil chaaru behind. I had climbed 5 steps and she was still in the first step. Mummy come and hold my hand, lets walk up together. So i came down 4 steps.
Which step am I in? 1st step right.
This is how we should start learning integers, where down, below, back, wrong , etc generally denote the negative value of a number.
The above incident can be numerically written as 5+(-4)=1.

In a snake and ladder game I was in the 15th block. I gained 3 steps in the ladder and fell down by 7 steps. Where am I now. 15+3=18, 18-7=11. Here I have to come down by a total of 7 steps.

Draw the number line in a chart or a paper and stick it next to your bed. Try different jumping actions in the line till you understand the working of negative and positive numbers. 

Whenever you work on the integers, visualise the number line (?), imagine it in your mind. The figure should be stuck in your mind. Remember that zero lies between the positive and negative numbers. Well, Iam sure you know that zero has no value, positive or negative.

There you got it!!!

The "CRAP" principle

A term very interestingly coined by the design course at http://www.colorado.edu/.

The following is my version of the CRAP principle, which can be used in both graphic and web designs.

Contrast contrast brings in visual int rest and focus to the design.contrast can be brought in through fonts, colors and dimensions.a focal point (CVI) can be brought in the design using contrast, which is very essential in guiding the user through the design.contrast should also be balanced. Else it can create chaos.

Repeat repetition is a major factor in UI design to bring in consistency.repetition of elements like font color, header size, layout structure etc., tell the user that they are in the same web site.repetition also goes a long way in brand identity, repeating a particular style, by way of graphics, bylines or quote create a brand recognition.

Align alignment brings in rhythm and grace to the design.print designs like news paper and magazines generally justify the content and have a column alignment web pages favour left alignment and majority have a single column structure.every element in a page should be connected and aligned w.r.t each other. never have elements standing alone.always align a image with captions or baseline text.

Proximity group related design units in close proximity, thereby separating different units of the design.a single unity structure without proper grouping, results in a boring layout.there should be enough white space between one group and the other. maintain consistency in spacing different groups.

UI Basics - Few gudelines

“A good designer knows the user and designs for the user”

The user interface is the aggregate of means by which people (the users) interact with a particular machine, device, computer program or other complex tool (the system). The user interface provides means of:
• Input, allowing the users to manipulate the system
• Output, allowing the system to produce the effects of the users' manipulation.

- Wikipedia encyclopedia

The following list is a compilation of some basic guidelines every designer will follow and some of my personal experiences.

Even before that, there is one point which I would emphasize -
It is not enough if a design is aesthetically pleasing it should also be technically flawless.

1. Know your user and understand their profile (requirement gathering, persona creation and other usability tools)
2. The client is not always the end user. If you feel a certain element is essential in terms of the user, let the client know about it.
3. Follow consistency in terms of placement, color, functionality etc.
4. Make visual cues clear.
E.g. if link text are underlined, do not underline submenus or titles. This will confuse the user.
5. Know how to attract attention. Animated gif or a promotional tool should be attractive at the same time be in sync with rest of the page.
6. Use css and html to give optimum results. Understanding of SEO basics and css2 go a long way in making a good website.
7. Provide Help to the user.
About boxes, help documents, tool tips, visual cues etc (feed back to say action is complete).
8. Visually define the context. Cancel and refresh buttons placed together in a form generally created confusion.
9. Give importance to typography. Defining correct font size for headers, sub-headers and other text help the user to a great extent.
10. Use proper metaphors when you design icons.
11. Use controls effectively. (Radio button, check box etc.)
12. User testing is an absolute essential.

This is not an exhaustive list. Comments and suggestions are welcome.

Favorite Fonts of 2004 and 05

A must read... Gr8 insight into different typefaces.

Some favourites fonts of 2004
Some favourites fonts of 2005

some key factors...

I was browising through a article in the digital web magazine - "The Business of Blue", by Stephen Van Doren.

Few basic concepts which I thought will be of help to review.

Saturation is important to strong colour scheme because it is the primary criterion by which a reader or viewer will assess the work. Stronger saturations call for a much louder voice, where desaturated schemes lend themselves to a much lighter touch.

Visibility, of course, pertains to how the colours "jump" from the page. It is important to note that not all colours need to do this; they can be as transparent as you wish. At the same time, if you place a premium on visibility the choice of colour must be evident to the viewer, or the implied message is lost.

Hierarchy refers to the levels of colour utilized in a scheme: in each swatch combination, there are three colours.
The first is the primary colour, used in major washing of objects and blocks to give the first "punch."
The second is the subordinate colour, which is used to substantiate the claim the primary colour holds on the viewers attention.
The third the accent colour, which should be used sparingly within reason so that the viewer's eye can jump from place to place to ascertain what is truly important about a particular project.

Stephen Van Doren is a software developer and graphic designer from Denver, Colorado.

Typography and CSS2

CSS1 vs. CSS2

A designers dream will always be to bring some amount of typographic aesthetics into a webpage.
Because the main challenge online is that, people to a great extent tend to scan the content that actually read it. So one has to judiciously use techniques to highlight important text. How different yet technically viable a site can be made in terms of text, will be the top of mind concern for any designer.

With little extra time spent on style sheet authoring, all these can be achieved to a great extent with the CSS2 techniques.

The effect of judiciously exploiting CSS2 can be seen in the following links which Garrett Dimon in his article "CSS Typography" in the Digital web magazine.
http://www.Kottke.org
http://www.RobWeychert.com
http://www.Subtraction.com
http://www.AListApart.com

In CSS1 fonts used were assumed to be in the client's system and were identified solely by name. Alternate fonts were specified through the properties. CSS2 gives the liberty to the author to describe the font that is to be used. And the user to select a font when the author's requested font is not immediately available.

The beauty of CSS2 is that, it defines the information in the client/user agent database and allows stylesheet authors to contribute to it. To display a character with a particular font, the user agent first identifies the "best fit" form the data base. Then retrieves font data locally or from the web to display the character using the particular glyphs.

So in css2 there are basically two mechanisms, font specification by the author and font selection by the user agent.

css2 specifies fonts according to the following characteristics
Font family, font style, font variant, font weight, font stretch and font size.
As a fall back mechanism generic family name is always specified as in css1. The five generic font families are serif, sans-serif, cursive, fantasy and monospace

In font selection by the user agent, there are four possible actions. Font name matching, intelligent font matching, font synthesis and font download.

This is just a snap preview of the concepts. Elaborate details are available at w3c

Creativity in cartoon channels...

How things can be made simple and easy, I got to understand today. Actuall my neighbours kid was watching POGO channel and I happened to be ther in his house that time. This is the program call "Mad". It is really very intresting wher a host of art activities are introduced to the kids in a playful and funny way. Not just POGO but almost all cartoon channels have a program like this, i was told by my lil friend. How intresting... there is always something to learn, even from kids!

Who is a UX Designer

Been quite some time since I last visited my blog. Wanted to write about a very interesting discussion over the HCI-IDC group mails. The topic was about the very identity of designers. Who is a UX designer and what is his/her exact profile? Interaction design, visual interface design, information design, usability analyst, IA, emerging tech design are different roles of a UX dessigner. As Mr.Dinesh Katre rightly put it, to claim oneself as a UX designer and not having your fundas right will be over claiming and under performing. A designer according to me should be conversant with at least all the basics and specialize in a couple of UX concepts. Today people who choose this field is luckier that they have these specialized subjects offered at their graduation levels. This gives them more confidence about the subject when they enter the industry. Rather people like me learnt in the process of experience and on a larger scale on requirement basis of projects we worked in. Learning is a ongoing process and one way or other you get into it if you have interest in the subject and wish to improve.

Teak wood carving...

I've been going to this carpenter shop next door and for the past few weeks and understand the way they create/carve the furniture designs. This is Bakur Bose and he's been working on a intricately carved sofa. The models are selected by the customers and the carpenters go ahead with it. Giving here few snaps i've taken during the process...

1. The 3 seater piece assembled
2. Top corner close-up
3. The model on which he's working on

Learning to Love Letters--and Leading

A very interesting article on typography. Enjoy!
http://www.creativepro.com/story/feature/21163.html
Well, now i know what my next project is going to be. Fonts from nature... how intresting.

Center of Visual Impact

Imagine yourself reading your daily with that favorite cup of coffee in your hand or browsing through a webpage at free time on your favorite subject. Do you start reading from the left to right, top to bottom, or there is this one thing that attracts your attention first? A colorful photograph or a headline in a comparatively larger font which might not exactly be placed at the left top.
A good designer can actually guide you through the page in a particular way by using different design elements as an attention grabber. This attention grabber is termed as the CVI – Center of Visual Impact, a concept that Mario Garcia writes about in his book Pure Design. CVI is about the use of one visual element that is at least three times larger than others on the page. http://poynter.org/dg.lts/id.33/aid.3251/column.htm
The CVI concept is very important as it plays a major role in shelf visibility of the product. It is not only restricted to News papers or magazines but also proves to be of use in web designing, package designing and Interior designing.
And, yes there should be only one CVI in a page. Else it will lead to confusion.

Of Header and Sub header...

Header and Sub header plays the role of introducing the subject line to the reader. Besides the choice of words or phrasing of the headers, their presentation in a print or web medium has great significance.

The cover design
The main aim behind the cover design is to give a glimpse of what’s there inside thus prompting the reader to buy and browse through. A Serif/Slab Serif is an obvious favorite choice for the title or the name of the magazine. With strong finishing strokes and extensions, these help grab the attention from a distance. Supported generally with a photograph or illustration (very rarely) the cover design template demands attention grabbers. I have rarely seen any magazine follow a standard color pattern on their covers. The color choice will obviously depend on the image the designer chooses. The ideal pattern for the highlight text will be to stick to a single font family with the headers in bold text and the detail text in at least three points smaller in size. Going for different font options or fully upper case creates confusion.

The font size variation (Main text atleast 3points bigger than the rest of the text) plays a important role in the visual appeal of both the cover and the inside pages, be that print or web. I will next talk about a important concept dealing with size variation.