• Take for example the number 51236 X 11.
• First, write down the number with a zero in front of it.051236The zero is necessary so that the rules are simpler.
• Draw a line under the number.
• Bear with me on this one. It is simple if you work through it slowly. To do this, all you have to do this is “Add the neighbor”. Look at the 6 in the “units” position of the number. Since there is no number to the right of it, you can’t add to its “neighbor” so just write down 6 below the 6 in the units col.
• For the “tens” place, add the 3 to the its “neighbor” (the 6). Write the answer: 9 below the 3.
• For the “hundreds” place, add the 2 to the its “neighbor” (the 3). Write the answer: 5 below the 2.
• For the “thousands” place, add the 1 to the its “neighbor” (the 2). Write the answer: 3 below the 1.
• For the “ten-thousands” place, add the 5 to the its “neighbor” (the 1). Write the answer: 6 below the 5.
• For the “hundred-thousands” place, add the 0 to the its “neighbor” (the 5). Write the answer: 5 below the 0.
  That’s it … 11 X 051236 = 563596

Practice it on paper first!

source from http://www.angelfire.com/me/marmalade/mathtips.html

Try this:
Take 15 x 13 for an example.
Always place the larger number of the two on top in your mind.
Then draw the shape of Africa mentally so it covers the 15 and the 3 from the 13 below. Those covered numbers are all you need.
First add 15 + 3 = 18
Add a zero behind it (multiply by 10) to get 180.
Multiply the covered lower 3 x the single digit above it the “5″ (3×5= 15)
Add 180 + 15 = 195.
That is It! Wasn’t that easy? Practice it on paper first!

- source from http://www.angelfire.com/me/marmalade/mathtips.html

Many math team coaches from across the United States often ask me about the secrets to having a successful competitive mathematics organization because of the success that we have had at Rickards High School. I am very flattered by these questions and comments because I don’t consider myself to be an expert on such matters, and I know there to be other organizations that are far more accomplished than we. Nevertheless, because of the positive impact that being involved with competitive mathematics has had on my life, I am very delighted to provide the abridged story of Rickards’ math team from my perspective with hope that it will inspire more students, teachers, and volunteers to become enthusiastic and motivated to start or improve their own organizations.

Starting and supporting a competitive math team is not easy, and there is no hard and fast formula for success; unlike mathematics itself, running a math team organization is more an art. As a well-trained artist may have the paint and canvas to create a great portrait, a lesser-trained artist could have the same paint and canvas, yet attain strikingly different results. To this end, a great deal of Rickards’ success stems from adversity experienced in its early years with a lack of continuity, belief, and positive energy. Moreover, we have been strong advocates of inspiring students to become involved with mathematics at an early age. Finally, dedicated faculty, parents, students and volunteers with understanding school administrators are fundamental for this type of organization to prosper.

I started competing in the Florida Association of Mu Alpha Theta, the Florida chapter of the National Mathematics Honor Society, as a seventh grader at Deerlake Middle School in Tallahassee. As a middle school student taking rigorous high school level courses (Algebra I in seventh grade, and Geometry in eighth grade) I was exposed to mathematics concepts for Mu Alpha Theta that were above and beyond the requirements for the courses, and both courses moved at a rapid pace. Through this experience, I gained a great appreciation for mathematics and mathematics competition; Deerlake was the top school in the city for Algebra I and Geometry, and we were very confident as we participated in competitions. We knew that we would go to the competitions and be successful because our courses were top notch, and in addition, we were well prepared with appropriate supplements by our teacher. At the end of my eighth grade year, a group of my friends and I decided to attend Rickards High School for its International Baccalaureate Program. We recognized that the program was the most rigorous and comprehensive program available, and we were confident that we would receive the highest quality education in all subjects, including mathematics.

Upon arriving at Rickards, my friends and I were also interested in continuing with Mu Alpha Theta at the high school level. Much to our surprise, our experience at the high school level was very different from what we experienced at Deerlake. The math courses that we took were not as challenging, and we had a very poorly planned math curriculum sequence; mathematics at the highest International Baccalaureate and Advanced Placement levels were not offered, and the mathematics faculty did not provide us with a clear and correct road map for the way in which the top students would progress. Throughout high school, the concepts that were presented in honors mathematics classes were not aligned with what we needed for mathematics competition or any traditional honors course, and the math team was devoid of a positive culture of expectation. While Rickards’ Mu Alpha Theta was in its infancy, the teachers involved in the program did not drive the students to excel and reach their maximum potential in mathematics and mathematics competition; instead of encouraging us to go above and beyond the minimum and reach for new heights, we settled for mediocrity. Rickards was not well respected at the competitions; students who went to the competitions from Rickards accepted this status, and internalized this belief to the extent that it became a self-fulfilling prophecy- Rickards students couldn’t do well, so Rickards students didn’t do well.

Since my friends and I were not accustomed to this type of mediocrity, we tried very hard to improve the culture of expectation. I felt that I had personally gotten too far behind in mathematics to compete, so I encouraged those around me who were gifted in mathematics to try harder, and we set incremental goals for Mu Alpha Theta: first, to be one of the top three schools in the region, then to be one of the top ten schools in the state. In my senior year of high school, we reached those goals, as we became the top school in the city, beat every team in the region, and placed 8th in the state. As more students and parents realized that Rickards was making strides, we began to attract more talented students for the math team.

When I graduated from high school, I intended to leave Mu Alpha Theta behind, but I formed relationships with new students and maintained relationships with old ones that kept me involved. Since my college was in the same city as Rickards, I continued to ensure that the students had access to math competitions and study materials to become better math students. A lack of continuity and historical involvement often impeded our program; our practice materials were incomplete and unorganized, we were not aware of the importance of participating in competitions such as the American Mathematics Competitions or National Mu Alpha Theta because they were deemed “too hard,” and our curricula were still not aligned with the most rigorous mathematics standards for fear of difficulty. We realized that we were behind, and gained this understanding through benchmarking- looking at what the well-coached teams did and making changes accordingly. We needed more support to make these changes, and we were very lucky to get it.

One of those avenues of support has come through starting students with mathematics competition at an early age. Since Fairview Middle School opened a Pre-International Baccalaureate Program, we have formed a very close, positive and cohesive relationship with them to ensure that there is a continuous pipeline of students who are interested in mathematics. Terry King, hired at Fairview shortly after the program opened, encountered the same lacking culture of expectation that I did when I started as a student at Rickards. Instead of settling for mediocrity, she also encouraged her students to excel, and Fairview has consistently been amongst the top teams in the state in Mu Alpha Theta, Mathcounts, American Mathematics Competitions, and a host of other mathematics activities since her arrival. The partnership that has resulted from our relationship with our primary feeder school has helped to ensure that students are acculturated to high expectations before they enter high school; we set goals as a single entity, and we reach them together.

Though Fairview was successful and provided Rickards with the majority of its high caliber students, Rickards did not have a faculty member who understood the dedication that being involved with mathematics competitors requires until Jason Wiggins was hired. A Rickards alumnus, his experience with the culture of mediocrity in mathematics at Rickards led him to earn a mathematics degree. Eager to teach, Mr. Wiggins has been the key force in revamping the math curriculum sequence; Rickards now offers the highest levels of Advanced Placement and International Baccalaureate mathematics, and he is knowledgeable about what it takes to be successful in mathematics competition. Mr. Wiggins and Ms. King both realize that working with gifted mathematics students is a great honor; teachers will learn from the students and, in turn, become better mathematics students themselves. Parents and administrators have also been supportive of the time commitment that it takes to be competitive, and have given time and resources to ensure that the students have access and are successful in competitions.

In developing and sustaining a mathematics organization, a culture of expectation must be prominent, and stakeholders must be dedicated and willing to sacrifice mornings, afternoons, weekends and sometimes vacations to be successful. We’re also very lucky to be based in Florida, where mathematics competition is very popular and experienced teachers provide wonderful examples for running math teams. As time has passed, Rickards has gone from being a laughingstock to becoming a well-respected, well-run organization to which the best students are attracted. While people often point to me as the reason behind the organization’s success, I honestly believe the major thing that I am responsible for is helping to create a culture of expectation and helping students gain access to these ventures. Though I am no longer involved, I still believe that both Fairview and Rickards have a long way to go; since neither has won every competition attended, I am not yet satisfied. Nevertheless, as we get our students involved early, participate in more competitions, and have a better curricular sequence with dedicated faculty, I predict that Rickards will reach new heights and continue to rise as time passes, and that any school that learns from our mistakes and follows our positive example can also be very successful.

The records

One of the things that keeps baseball fans coming back, tuning in and going to the stadium is to watch records be made and broken. It’s interesting to know the top record holders in each category and watch their achievement pursued. Look up a baseball record sheet on the Web and you may be spending a long time running down list of everything from most hits by a left-hander in a single-season to the highest number of steals from a pitcher. Watching somebody approach and take a record is an exciting visceral experience, as we hold out hope to see a record challenged. Currently, baseball fans are fixated on whether or not Barry bonds can beat Hank Aaron’s 755 homerun mark. Nerds, who love memorizing and categorizing numbers, find themselves right at home watching records stand and predicting their fall.

Statistics

Of course, you don’t have to wait for a major record to be broken to get excited about numbers in baseball. Every single game, every single player, and every single pitch has been placed in categories for you. Listening to the baseball announcer is a lot like listening to a very excited math professor most of the time. They tell you batting percentages, pitching averages, field lengths and times at bat. Many baseball parks offer free scorecards to fans so that they can track the pitches and hits themselves. Statistics are attractive in baseball, because they help remind us that beyond the sport there is a science. Baseball is made of angles and force, physics and math. Now who wouldn’t want to go out on a sunny afternoon and watch all that?

Money

Unfortunately, the things that make you can also be the things that break you. Another set of numbers has become prominent in baseball that doesn’t add so much to the joy of the game. That would be salaries, trade-offs, endorsements and other things involved with money. While sports are fun to watch, somebody must pay the athletes to do it. And when money changes hands in amount that it does in baseball it’s bound to have an effect on what goes on the field. When a batter is averaging .125 and he is getting paid $1.8 million to do it suddenly every missed pitch seems like a stab to the wallet as well as the heart.

Overall, baseball has been America’s pastime for a long time and that it will probably continue long into the future. However, when you look around at the crowds of folks who attend the games don’t be surprised to see people with laptops, glasses and polo shirts. The nerds are drawn to numbers and they are here to stay.

Answer :

1st Year Student : say  ’4′ , without any thinking.

2nd Year Student: say ’4′ exactly, after a moment of thinking.

3rd Year Student : takes a scientific calculator, press some button and say ’4′.

4th Year Student : designs a new programming language that perfectly fits for solving such problems, implemets it, writes a program, and answers: `It says “4″, but I doubt if I really fixed that ugly bug last night…’

Student just before the final graduation exams  : cries in desperation: `Why, why do you think I must know all that bloody constants by heart?!’

The very start of modern algebra began with the ancient Babylonians. They were the very first people who used an advanced math system for their time. This math used an algebraic system to do calculations, and it enabled the Babylonians to utilize formulas and calculate the answer using unknown values for a problem class that would be solved in the modern day by quadratic equations, linear equations, and indeterminate linear equations. During this same time period in the first millennium BC, most of the mathematicians in India, China, Greece, and Egypt were using geometric methods to solve such equations. The word algebra comes from the Arabic word al-jabar, which means reunion of the broken parts. A Persian Muslim mathematician named Muhammad ibn Masa al-khwarizmi wrote a book in 820 whose title is translated to mean The book of Summary Concerning Calculating by Transposition and Reduction. There is debate in math circles on whether the mathematician Diophantes, who has always been known as the father of Algebra, or Al-Khwarizmi should actually be named the father of Algebra. There is support for Al-Khwarizmi instead of Diophantes because a lot of his work on reduction is still currently in use today. He also explained how to solve a quadratic very extensively.

]]> http://math2u.wordpress.com/2009/08/19/cont-what-is-algebra-old-and-new/feed/ 0 math2u http://math2u.wordpress.com/2009/08/18/what-is-algebra/ http://math2u.wordpress.com/2009/08/18/what-is-algebra/#comments Mon, 17 Aug 2009 17:29:11 +0000 math2u http://math2u.wordpress.com/?p=11 ]]> Algebra is one of the three wings of mathematics, the other two being arithmetic and geometry. While most of the common calculations done are though arithmetic and geometry, algebra plays a crucial role in exemplifying the abstract and unknown entity.

Algebra is derived from two words “al-gbr” which is Arabic in origin. Al-Khwarizmi born and brought up in Baghdad the capital of Iraq was a great mathematician and a renowned astronomer of his time around 789 A.D., is known in contemporary mathematics world as the father of algebra. However Babylonian legend promulgates us that the word algebra was in some form present in form of algorithms, linear and quadratic equations were frequently used to calculate the production of grains, position of stars and other forms of estimates. ‘Al-Jabr wa-al-Muqabilah’ was perhaps the first book to be written on algebra in the later stages algebra got due attention from the famous English scientist Sir Isaac Newton in his book Arithmetica Universalis.

Two most famous forms of algebra commonly used are 1) General form of quadratic equation

Ax2 + bx +c=0

2) A,b,c are variables and x is a constant

General form of linear equation

Ax+by+c=0 The basic terms used in algebra in the contemporary education system are x,y,z and a,b,c. Algebra uses a number of different sets of equations such as linear equations and quadratic equations.

Algebra uses same standard sets of operational addition multiplication division and subtractions as in arithmetic. However the integer’s multiplications are different and can be comprehended with an example,

Let “a” be a number which has to be multiplied by a negative integer “-b” the outcome will be a negative “-ab” Similarly a negative integer “-a” when multiplied by a negative integer “-b” the result being a positive “ab”.

The key being a negative and a negative will give a positive result, a positive and a negative will give a negative result and a positive integer when multiplied by a positive one will give a positive outcome.

]]> http://math2u.wordpress.com/2009/08/18/what-is-algebra/feed/ 0 math2u http://math2u.wordpress.com/2009/08/17/how-to-improve-your-learning/ http://math2u.wordpress.com/2009/08/17/how-to-improve-your-learning/#comments Mon, 17 Aug 2009 01:29:47 +0000 math2u http://math2u.wordpress.com/?p=7 ]]> Have you ever wondered why on some occasions you can remember information easily while on other occasions you aren`t able to recall it at all? Well it could have to do with the fact that in one situation you are in an environment which is compatible with your personal learning style, while in the other case the teaching is just not presented in a manner which is right for you. Every human being has a certain learning style which is connected with a certain strength. In order to make your learning as effective as possible anyone should know the own learning style which is based on his strongest intelligences and talent structure. His intelligences? There’s only one intelligence in the person, right? Well, following the theorie of Harvard professor of education Howard Gardner there are seven different intelligences. Those are: 1. Linguistic : good in reading, writing, listening and talking, spells easily 2. Logical-Mathematic Intelligence: good in abstract thinking, counting, performing calculations, orderly note-taking 3. Spatial Intelligence: thinking in pictures, good in reading map, likes arts, good sense of colour, uses metaphors 4. Musical Intelligence: sensitive to rhythm, the composing and singing 5. Bodily-Kinaesthetic Intelligence: good in control of one’s body, good timing, good reflexes, learns good by moving, skilful and purposeful movements (dancers, athletes and surgeons) 6. Intrapersonal Intelligence: good negotiator, empathy, enjoys company, likes to mediate disputes, good self-understanding 7. Interpersonal functioning: good understanding of others and one’s relations to others, intuitive, self-motivated wants to separate from mainstream, being high in social skills (psychologists, teachers and politicians are often equipped with this type of intelligence). Gardner states if we all had exactly the same kind of mind and there was only one kind of intelligence, then everybody could be taught the same things in the same way and assess them in the same way and that would be fair. Once it is realised though that people have very different kinds of minds, different kinds of talents, like some people are good and thinking spatially, some in thinking language, others are very logical, other people need to be hands on and explore actively and try things out, then education, which treats everybody the same way, is the most unfair education. He adds, then we have this myth that the only way to learn something to read in a textbook or hear a lecture on it. Gardner admits himself and those seven intelligences are not definitive, but can show the facets of the human mind and each human will have combinations of those. Not all experts agree with this theory as you can read yourself here (Howard Gardner Under Fire: The Rebel Psychologist Faces His Critics). Each reader may find out for himself whether this knowledge about the different intelligences helps understanding and learning a new subject in the future better. So knowing about your special talents and intelligences is the first step in helping you to advance your learning. Obviously it would be helpful to use as many of those talents while learning as possible. At the same time you should leave out the channels which don’t fit your preferred intelligences, may it be reading, hearing or something else. The second step to improve the learning would be finding out about the own learning style. For that we need to acknowledge three different sectors which are relevant for the learning: * how do you receive information easily (kinesthetic, auditory, visual for instance)? * how do you organise and implement information more easily (step by step approach or big picture)? * what circumstances would help you to receive and implement information you are learning (being alone in library, study buddies, calm or music playing? How do you find your own learning style while using your strongest intelligences? Actually there are several tests available these days to find out about your preferred learning style. Here I found a site for you where you can take the test and find out your learning style for free and print it out; simply click this link (click on learning styles in the second paragraph of the site). Its is pretty close to the intelligence types Gardner is using with slight differences, but you will be able to find out your strength easily. Anyone interested in improving his learning exponentially should go and take that test now, because it brings valuable insight for the rest of the life. People who are interested in finding out even more about Gardner and his seven intelligences finds some excellent references here:

2008 to 2009 saw the first cohort of Every Child Counts (ECC) schools beginning their work with Numbers Count. The research phase of this scheme found that a “Particularly strong impact was achieved by the multi-sensory teaching approach (Numicon). (p2)” and the ‘Standardised score gain per lesson available’ was the highest of all interventions (see Impact headlines table, under ‘Evidence Base’). Our website has a feature on some of the very impressive results from Leeds LA and we are waiting for the national results for this year’s intervention work.

April 2009 saw Ann Dowker’s report on ‘What Works for Children with Mathematical Difficulties? The effectiveness of intervention schemes’, which looked at the ways in which LAs and schools can best introduce a layered approach to intervention. As a result of Ann’s research, three approaches have been highlighted as having a solid evidence base and a national infrastructure of training provision. The three approaches are Numicon, Mathematics Recovery and Catch Up Numeracy, and we have developed our Closing the Gap with Numicon Intervention Programme to support this layered intervention approach. The programme is specifically for TAs and a supporting teacher for work with children in Wave 2 and ‘lighter touch’ Wave 3 which supports teachers using Numicon in Quality First teaching and across all 3 Waves of Intervention.

In June 2009 Sir Jim Rose and his team submitted their ‘Independent Review of Mathematics Teaching in Early Years Settings and Primary Schools’. On describing Numicon and multi-sensory resources in general, they kept with the recommendations of the Williams Review in that: “it would be regrettable if such clear enhancements to the learning process for those struggling with mathematics were not readily available in all schools” (p54).

Finally, at the Educational Awards 2009, Numicon were awarded the ‘Educational Supplier of the year’! Plus our Closing the Gap Kit specifically for older pupils struggling with maths was on the shortlist for an award too.

Numicon maths resources and numeracy teaching resources grew out of a classroom based research project where the authors sought to discover, why it was that so many children failed in arithmetic where they were successful in all other curriculum areas. 10 years on and primarily as a result of teachers recommending Numicon to other teachers, the benefits of using Numicon are now starting to achieve national recognition.

Through the use of abstraction and logical reasoning, mathematics evolved from counting, calculation, measurement, and the systematic study of theshapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records go (see: History of Mathematics). Rigorous arguments first appeared in Greek mathematics, most notably in Euclid’s Elements. Mathematics continued to develop, in fitful bursts, until the Renaissance, when mathematical innovations interacted with new scientific discoveries, leading to an acceleration in research that continues to the present day.

Today, mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new disciplines. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind, although practical applications for what began as pure mathematics are often discovered later.

MATH is

“the science that draws necessary conclusions”  - Benjamin Peirce

“as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” - Albert Einstein