Lazymaths Blog

The New York Times recently (Sep 16) published an interesting article – “Gut Instinct’s surprising role in Math”. The article shares an interesting view about human mind’s ability to instinctively solve math problems. It shows how the mind is wired to perform some seemingly complex math tasks with ease.

To quote it from the article “Whenever we choose a shorter grocery line over a longer one, or a bustling restaurant over an unpopular one, we rally our approximate number system, an ancient and intuitive sense that we are born with and that we share with many other animals. Rats, pigeons, monkeys, babies — all can tell more from fewer, abundant from stingy. An approximate number sense is essential to brute survival: how else can a bird find the best patch of berries, or two baboons know better than to pick a fight with a gang of six?” It’s interesting to know that not only the human brain works this way but even baboons’ and rodents’ work in the same manner.

In fact, research has shown that new born babies if found to be good at deciphering approximations with ease, will carry on the same trait when they grow up and have to deal with abstruse mathematical problems. NYT states: “One research team has found that how readily people rally their approximate number sense is linked over time to success in even the most advanced and abstruse mathematics courses. Other scientists have shown that preschool children are remarkably good at approximating the impact of adding to or subtracting from large groups of items but are poor at translating the approximate into the specific.” In fact, it goes further and suggests that Math teachers should emphasize on the power of approximation early on in the child’s education so he can hone this natural skills to an advantage. To quote “Taken together, the new research suggests that math teachers might do well to emphasize the power of the ballpark figure, to focus less on arithmetic precision and more on general reckoning.”

At LazyMaths.com, we precisely try to encourage our students to leverage these skills of approximation. We have found that with practice, the line between approximation and precision can be diluted if not fully erased. In the section of Don’t Solve, LazyMaths offers a large number of examples of a variety of Math problems attempted using the techniques of approximation.

If you are interested in checking out how good your natural approximation skills are, here’s a quick test.
http://www.nytimes.com/interactive/2008/09/15/science/20080915_NUMBER_SENSE_GRAPHIC.html

A lot of mathematics exams nowadays, e.g. GMAT, SAT, etc, are either completely multiple choice or they have multiple-choice components. These exams required students to solve a stipulated large number of questions within a small amount of time. Students break a lot of sweat over solving these questions, by trying to solve them completely like other questions, and not utilizing the information that is in front of them. 

One of the basic difference between multiple-choice questions and other questions is that for multiple-choice ones you have to just figure out the answer, and for achieving this objective, you need not necessarily solve the question completely, as the answer is right in front of you, among the 4-5 choices that have been provided.

Ball-park, or possible range strategy, is one such very effective method to quickly solve a multiple-choice question in arithmetic. In order to use it, you first make a quick guess of what the possible range of your answer will be. Once, you have made such a guess, you can easily eliminate all the other answers, which don’t fall in that range, and so can be ruled out as a choice for the possible answer. You are now left with just 1 or 2 choices, which you can just plug-in to confirm which one is the correct answer.    

This strategy doesn’t work well if all the choices are in the possible range, and it is particularly useful when the answers are scattered over a large range, as in the following example:

If 0.303z = 2,727, then z =
a) 9,000
b) 900
c) 90
d) 9
e) 0.9

We can notice that the range of answers is too large, so we can use ball parking to solve this question. .303 is very close to 1/3, which means 1/3 of z = 2,727, then what answer could be possibly correct. You don’t even have to do the math. 2,727 is about 1/3 of 9,000; therefore, the answer must be 9,000, according to the Ballpark Strategy (note that there are no other answers even in the 9,000 range.

If you don’t use the ballpark strategy, you could multiply both sides by 1000 to eliminate the decimal points, and then divide 2,727,000 by 303 and get the same answer, although after spending much more time.

Another important use of this strategy is to double-check your answer.  Once you have solved a multiple-choice arithmetic question, you should confirm whether the answer lies in the ballpark of what the answer could be.

So, invest sometime in learning and practicing to use ball-parking. This will allow you to solve the arithmetic questions much faster and will save you precious time, enabling you to score much higher.

LazyMaths.com focuses on this strategy and has hundreds of examples to show how and where one can use ballparking. Visit the Don’t Solve section of the site to know more about it and check out some free examples.

This post is part of LazyMaths’ Math website review series. Dedicated purely to help math students, the review highlights tangible learning that the website offers to its visitors and users. If you would like to have your website considered for review, drop us an email – contact(at)lazymaths(dot)com.

Review in a Tweet
Comprehensive set of interactive math lessons, with unlimited practice

About the website
AAA math features a comprehensive set of interactive math lessons, categorized well in terms of levels (Kindergarten through Eighth) or according to topics, like Addition, Algebra, Counting, Decimals, etc. This allows the user to use the site for class related work, as well as reviewing or learning any particular topic that he or she needs.

The most striking part of the website is the focus on interactivity.  Fully interactive lessons enable illustration of key concepts through visual animation, reinforcement of important points through challenging fun math games, and prevention of learning of wrong ways of solving through immediate feedback. Also, interactivity engages the students, and makes learning math a fun activity.

Moreover, availability of unlimited practice questions allows the students to try out enough questions till they feel confident in a non-threatening environment. This has a huge impact on their self-esteem and confidence.
The content is available in two languages “English” as well as “Spanish”, allowing for a wider reach. Also, all the website content along with some additional stuff is available on a CD version. The CD version is completely advertisement free. It helps the students in avoiding distractions, and focus completely on learning.

What’s on the website?
AAAmath offers the following:
• A wide range (Kindergarten through Eighth) of lessons
• Unlimited practice questions on each topic
• Math Games
• Immediate feedback to the students
• Links to other mathematics resources

What’s the best part about this website?
No registration is required, and the site is very well structured, making navigation intuitive.

Any $$$?
Only if you buy the CD version – ranges from $24.95 to $240.95 depending on Home, Classroom or School editions

Review Disclaimer: This is an independent review of the given site. It only reflects the opinion of our site reviewer(s). Views and opinions expressed may not be representative of the site or its owners or its users and visitors. LazyMaths.com and its reviewer(s) cannot be held responsible for any damage caused to hardware or any other problem caused by visiting this site or misuse of this information. Any errors or omissions should be brought to our attention by contacting the site administrator.

Learning math on Twitter? Is this just a thought, a dream or mere wishful thinking? Not anymore!

LazyMaths.com has been sharing Free Speed Math shortcuts with its Twitter followers since the beginning of this year. Yes, One Free Shortcut a Day. Could it get better than this?

This has been so popular with our followers that they have been wanting for more! So, we plan to now offer something else for free too! More Math on Twitter!!

Starting June 15, we plan to offer one free Smart Math technique for our Twitter followers. If you are taking the GMAT, GRE, SAT, CAT, CET or any multiple choice based Math tests, this is an absolute must for you. All Smart Math techniques are in the Don’t Solve section of LazyMaths. The techniques are based on concepts of approximation, elimination and reverse substitution. Not only does using these techniques, save a ton of time to get to the answer, but it also helps in avoiding silly mistakes.

The Don’t Solve section contains problems in areas of Algebra, Percentages, Average, Ratio Proportion, Time, Speed & Distance, etc. Check out free samples here.

Eager to learn a new kind of Math right now? Go ahead, sign up with LazyMaths.com and select your choice of membership. We guarantee that you would not regret.

While we publish free speed math shortcuts and free smart math techniques, we also publish math puzzles, downloadable math learning resources like Number classification. All of these are available to our Twitter followers as well as on our blog – Zzzlog.

In short, learn math the web 2.0 way – right on Twitter! Simply follow LazyMaths on Twitter and become a pro in Twitter Math!!

This post is part of LazyMaths’ Math website review series. Dedicated purely to help math students, the review highlights tangible learning that the website offers to its visitors and users. If you would like to have your website considered for review, drop us an email - contact(at)lazymaths(dot)com.

Mathkinz.com – Rule the World (of Math)

Review in a Tweet –
By students for students – Download Math practice sheets for free from Mathkinz.com

About the website –
Mathkinz is a unique site that’s entirely run and managed by kids. Yup, school kids of grades 4 through 8. They develop the content, in this case worksheets, test material, etc. and host it too!

The website was started by Nirlesh Jain, a father that takes keen interest in his kids’ education. While teaching his kids, he came up with the idea. After speaking to his friends and family, he gathered all the neighboring kids and encouraged them to start developing math content. And in just a few months, Mathkinz.com was born. To keep the interests of kids alive, he offers Mathkinz points for the content they develop. This encourages them to keep developing more content and also build up a competitive spirit amongst them.

Mathkinz also conducts Math competitions in the central New Jersey area to encourage local students to develop better math skills.

What’s on the website?
Mathkinz offers the following:
• An online Math Quiz (By Grades – 1 through 8 – US Standards)
• Math Practice sheets (By Grades – 1 through 8 & By Subjects )
• Math Jokes
• Math Games
• Math Resources (Other math websites links)
• Math News
• Math Forum (for parents to network, ask questions, provide suggestions, etc.)

What’s the best part about this website?
You don’t have to register or sign up. Just visit the site and start printing your Math worksheets at home for your kids!

Any $$$?
Mathkinz is free, yes really!!

Review Disclaimer: This is an independent review of the given site. It only reflects the opinion of our site reviewer(s). Views and opinions expressed may not be representative of the site or its owners or its users and visitors. LazyMaths.com and its reviewer(s) cannot be held responsible for any damage caused to hardware or any other problem caused by visiting this site or misuse of this information. Any errors or omissions should be brought to our attention by contacting the site administrator.

It was Darwin who first revealed the world, the concept of ‘Survival of the Fittest’, but the norm was practiced long before Darwin coined it, and it does prevail now too. Be it the animal world or the world of humans, survival is always of the fittest. And, to succeed; you have to be still fitter than the fittest. In modern parlance, this is now called ‘Competition’.

It won’t be completely incorrect to say that competition is omnipresent. The world over, right from the ivory towers of huge corporate houses, to the annals of schools and colleges, it is sheer competition, and the only means to survive it is by being fit enough to win over your opponents. For those who are the challengers, competitive environment offers a challenge to show their mettle and for the meek, it is the burial ground.

As the month of November draws near, a new challenge is approaching for those who aspire to rise above their colleagues and make a mark in the world of business. It is the Common Aptitude Test, commonly called CAT – the only gateway to the top B-Schools of India. A springboard for many to jump in the corporate world of Blue-chip companies by getting the most sought after degree – the MBA.

There are many aspirants to this luring opportunity, but very few will actually manage to make their dream come true. With the past statistics showing more then 100,000 applications for a seat strength of just over a 1000, the ratio of candidates to capacity is dreadfully competitive. It is like 1 guy fighting 100, all on his own! And, as time passes by, year after year, the ratio is going to get tougher and tougher. In this scenario, what makes the 1000 plus guys get to their dreams? Is it IQ, as many people think? Or, is it Luck? Or, is it sheer practice? Well, if you ask a successful CAT candidate, he would say, a mix of all, but in different proportions. And, yes he would also drop in a word from corporate parlance – Strategy.

To many, this may sound a bit out of place, but remember, all wars on the battlefield are lost for lack of clear strategy. Nevertheless, Strategy alone does not do the miracle of winning. This article attempts to bring forth some of the most important strategies of winning a competitive exam like the CAT and also tells you when to use them.

To begin with, as most readers would be aware that most of the competitive exams have about 200 questions to be solved in around 2 hours. The exact number of questions and the time availability, of course, differs from exam to exam. With 200 questions and 120 minutes, you have a jaw dropping 36 seconds per question. This means that you have to read the entire question, understand it fully, get the right answer and mark it, all in 36 seconds flat! So, how do those guys mange to succeed and score appreciable marks? Well, they use 3 techniques.

1. Brute-Force Method: this is the most common and basic technique used by any student. It simply says  – actually sit and do the calculations to arrive at the answer – no short cuts allowed. In fact, every one in the beginning uses this technique – for it more or less guarantees a correct outcome. However, it also guarantees incomplete attempt of the test in the given time! As this method of solving takes more time than any other method, it is suicidal to use this technique to solve all questions.

Nevertheless, it is the only technique to solve real tough Math questions. It is good for guys who are comfortable with mathematical ability and can easily juggle around with numbers and do lightening calculations. Mostly, it is advisable to use this technique somewhere in the beginning to the test when you have the whole of test duration with you. But, one may avoid it consciously if he does not understand the question or does not know the formula or method of solving it.

2. Method of Approximation: This method is a balancing method for it gives a decent chance of getting to the right answer as well as saves a lot of your time as one doesn’t have to do hard core calculations. Thus you compromise with trueness of answer as against time taken. The technique takes help of approximations to reduce time and ease up calculations. An example would make it clearer. Let’s say, you have to multiply 59 with 41, if you use Brute-force method, you will actually multiply both the figures and arrive at 2419, but if you make approximations of 59 to 60 and 41 to 40, you will arrive at an answer of 2400 and save a lot of time.

One may argue that the answer arrived at is not correct. Yes, it is true; the answer should have been 2419. Now take this scenario that the options available are 2426 / 2419 / 2359 / 2519. We already know that the first two digits are 2 and 4 (by approximation) and commonsense says that the last digit must be 9 as 1 multiplied by 9 is 9, we can fairly zero down to the correct answer of 2419 even if we actually have not known that this is the correct product. And, all this in a far lesser time then it would have taken to get to 2419 by actually multiplying 41 and 59.

Method of approximation is a bit tricky method and needs a good deal of skill to approximate. Very broad approximations can defiantly lead to a wrong answer, hence, one needs to have the skill to approximate the right numbers up to a correct degree to get most close to the right answer. Normally, this technique can be used in the middle of the paper when you have exhausted tough math questions and are approaching the middle tier and easy math questions. The best place to use it is on the data interpretation type questions. A word of caution – if the options given at pretty close, like 2429 / 2419 / 2439 / 2449, it is advisable to use brute-force method.

3. Method of Elimination: This is the last and final resort of the warrior, the last weapon in the armoury, when the battle draws to a decisive end. It is simply, marking answers randomly. Many may ask, how you call it strategy? Well, isn’t it said ‘Discretion is a better part of valour’? When, you know that nothing is going to remain, it is better that you collect whatever comes in you hand, instead of planning and thinking. This method assumes that there has to be at least 1, if not 2 options in the list that you know for sure that they could not be right. Now, once you have eliminated those definitely wrong options, you are left out with 2 or at most 3 amongst which one is definitely correct. Now, just close your eyes and mark one of these. Remember, you are not marking anything blindly though. Had, you marked anything blindly; the probability of getting the right answer is 0.25 (1 out of 4), but by eliminating the definitely wrong ones, you increase the probability to 0.5 (1 out of 2) or 0.33 (1 out of 3).

This technique has to be used on questions that you can’t solve, either due to lack of time, or because you do not know how to solve. Mostly, the tough ones should be tackled by this technique. However, in those tests which have negative marking for a wrong answer, you have to use this method cautiously else, you will end up wiping of a sizable chunk of marks you earned on right answers.

With the competitive environment so heated up that one can move a college up or a college down in the admission list by just 1 mark, the above techniques definitely helps one to gain at least 25% more then he would have otherwise got. This means, that if followed religiously, a jump of 4-5 colleges is guaranteed by this method.

The Last word:
The article in itself is no way self sufficient to be a complete guide to strategies for competitive exams, but just provides a general guideline to the methods used by successful candidates. However, the best technique still is and always will, is PRACTICE. Sheer practice on a daily basis helps one to speed up as well as helps in knowing when and on which type of questions should the above techniques be used.

Here’s my story on how became an MBA in a matter of seconds –

I was just a mediocre guy on the street dreaming to one day become an MBA from an Ivy league college. Well, nothing wrong in dreaming. But my dream soon turned into a wish that rapidly became a want and before I knew morphed to a desperate need.
The next thing I did was to get in touch with some of my college mates, who I thought liked me , and could possibly help me. My stray chats with them on the how to’s, the do’s , the don’ts, the caveats, the carrots, and everything in between became a thorough research on how to get to a great B-school.

Based on the grand PhD kinda research, I opted to join an Institute for classroom coaching over taking a correspondence course. I knew that I am not the kind of guy who could study on his own, but can, upon prodding.

My initial days in the classroom were more exploratory, but those ended abruptly, when I gave my first mock test. It was that day – the day of realization – an apocalyptic day that opened up my head, popped out my easy and scared the #*@# out of me. My percentile score was in the dumps and along with it were my dreams, wishes, wants and all kinds of desperate needs too. The figure 48 made my head spin.

Finally, when I returned back on good ol’ earth, I looked around. I knew that my peers were definitely doing something that I was not doing. I was just onto something… either something terribly wrong or something that will change the course of my future.

Befriending 2 guys from the top 10 percentile scorers group, I started talking, discussing and understanding from them their “secret”. In a matter of days, I had collected enough stuff to be ready to experiment it for the next mock test.

This time, I focused to only use the “secret” and see if it would become the fortune tuner for me. When the results were out, lo, behold, my percentile score not only increased, but it jumped. This time around, I was at 77! It had jumped by a leap! With it came a load full of hope. Hope of getting into a B-school. I knew I was back in the game.

I started honing on the new found skills and kept focusing on the further improving them. Test after test, my score kept beating the previous one. By the last mock test before the D-day, I was @ 97!!

To many, this might sound to be a great score, but let me tell you, I had my eyes on the top B-School and I knew that I had to be at 99.7 to be there…

…

After all the sweat and stress, after all the grind and grin, the day of reckoning arrived. The results were out. I got my score and… I was 2nd amongst all who gave the test. I had managed to get 99.9997 and far better score than what I had even dreamt about!!!

So, what were these “secrets”? Well, I shouldn’t be calling them “secrets” any more, as I am gonna reveal it out to the world 

Here there are –

1. Do not try to attempt problem in the order they are, rather, pick and choose the ones you can attempt in the shortest possible time first gradually moving to the ones you think you need the most time. This way you maximize the score in a shorter time, attack more problems in first half and build a psychological comfort level

2. DO NOT SOLVE – as much as you can, avoid solving. Simply attempt. Huh? Yup. This one’s the killer. When you solve, you spend time, when you attempt, you save time. Let me explain this one a bit more in detail. Every problem has options. It you would randomly mark one option for each question, your probability of hitting the right answers is 1/4 or 1/5 depending upon whether there are 4 or 5 options. But when you attempt, you read the whole question… along with its options. When you read the ‘whole’ thing, look at the options and you would soon notice that some of them cannot be the answers, simply because they don’t make sense. So, you would intelligently eliminate them. Now let’s say you are left with 2 options (as you have eliminated the others), you can do either of the two things

a. If you are nearing the end of the test and have less time, you can simply flip the coin and pick one. Don’t worry, this isn’t gambling with your future, but a strategic move to improve your attempts. When you randomly picked one, your chances of getting the right answer is now 1/2 or 50%. A jump from 20 or 25% to 50% while you save precious seconds!

b. If you are in the middle or the beginning phase of your test, try doing reverse substitution. This way, you would be able to pick the right answer (without flipping any coins) and still save more precious seconds!

3. So, what do you do with saving those precious seconds? Well, you would notice that all questions in a test cannot be solved using these smarty ways, so you invest those precious seconds to ‘solve’ those types of questions. Thereby maximizing attempts and maximizing score and achieving that dream B-school of yours!

It was those seconds that made me an MBA and it is up to you now to grab a bunch of them by signing up with LazyMaths.com.

In the Don’t Solve section of LazyMaths, we have over 100 math problems attempted without solving to get your head going in the right direction. And for those nasty ones which you have to ‘solve’, we have Zappers – some mind blowing speed math shortcuts to help you rapidly solve them and get more of those precious seconds.

Remember, when thousands are competing, even a score difference of 1 or 2 can move you up or down 3 to 4 B-schools. So, save those precious seconds – NOW!

In this category of Facts and Fun, along with Math Humor, you will also see what we call a Mathphrase. It is a kind of catch phrase but for Math.

For those of you who still can’t figure out what is it, here’s a Dictionary meaning of it from the LazyMaths lexicon!

Math·phrase [math-freyz]

-n. (2008)

1. an expression that is used repeatedly and conveniently to represent or characterize a Math idea in a new way or with a new point of view

2. a phrase that catches the Math essence

3. a phrase, as a slogan that comes to be widely and repeatedly used, often to covey a Math doctrine

Synonyms: rule of thumb (Math kind)

Hypernym: A quirky Math phrase

Here’s an example of it –

“A fraction is a whole with a hole!”

Look out for a quirky mathphrase every week…. only on the LazyMaths blog, we lovingly call Zzzlog.