Above image shows some data related to a walk. It says that the person has walked a distance of 7.05 km in 1 hour 8 minutes 49 seconds. Average pace shown here is 9 minutes 45 seconds per Km and the time taken in different kilometers are given just below that. This average pace can be simply computed by dividing the total time (1 hour 8 minutes 49 seconds) by the distance walked (7.05 Km) and doing the required conversions between hour, minutes and seconds. This means, if I walk each of the 7 Kms at the same pace completing them in exactly 9 minutes 45 seconds then the total time taken by me to walk 7.05 Kms would be 1 hour 8 minutes 49 seconds. In the last .05 Km too, the pace has to be same.  Time taken in each of the 7 Kms are given in the image. Let us check, whether the walking pace was higher or lower than the given average in the last .05 Km. Before reading further, pause a bit and think about the process you would like to follow to do this. I plan to check wheth...

  L et us talk about this Cycle. Those who know how to ride it know how easy and enjoyable it is to go for a long ride in nice weather and location. They can also recall;  how difficult it was to even hold it when they were not knowing how to ride them. Most likely, they didn't become comfortable with cycle immediately. They might have fallen few times, might have struggled to balance and might have even lost motivation to learn cycling. But  now they might be looking for opportunities to ride a cycle. Learning Mathematics is similar to learning cycling. You make errors, struggle to get the concept, lose interest and it becomes more difficult. But once you overcome these, it becomes a favorite subject. Solving Mathematics problems can even become stress buster. When someone is training you how to cycle, he may make you familiar with a cycle. He will tell you about seat, handle, peddle etc. He will tell you about how to sit on the seat, keep the foot on the peddle, ho...

  Here, we are taking an example to demonstrate how students are answering the questions right, getting good marks, letting the concept level problem continue and getting stuck in their studies or career at later stage. We also discuss, what approach can help in making learning right.  I hope, readers are aware of linear equations in one variable. Something like 15x+5=90, or 3x+5=2x+9.  Let, a student is asked to solve the 2nd equation 3x+5=2x+9. It's easy for most of the students. He solves this equation using right method and gets the answer as 4. Correct and full marks. Does it mean that he knows the concept of linear equations in one variable good enough?  Why should he solve such equations? Where can these concepts be used? Can he frame a question based on real life scenario where such equation may be needed? Can he visualize the impact of change in coefficients or constant values on the nature of the equation? If he is not clear about all these, then solving la...

  Here, we take a question and create three learning environments. You can check yourself, which environment offers what benefits. We talk about a formal learning environment where student is a part of school/ college/ coaching/ tuition etc. and is helped by the teacher in learning various topics as per the prescribed syllabus. These learnings are immediately helpful in getting marks in the examination but are also highly required in various applications and competitive examinations at later stage. So, learning them right at the time they are being learnt is necessary to avoid various blockages that can restrict the growth later. Let us take 3 scenarios: Scenario A:  Student asks a question. Teacher answers that. Student is now able to answer that question. Scenario B: Student asks a question. Teacher also asks few questions to understand why the student had to ask it. He determines the area of difficulty for the student and helps student to answer the question by addressing t...

Look at the image below: This image is about weather forecast. It says about chance of rain during coming few hours of the day in the city. Look at the number 30% at 7 AM. It means that there is 30% chance of rain at that time. In other words, probability of rain at that time is 0.3. It gives you some idea but can you conclude anything from this? You can expect to have rain on 3 occasions out of 10 with similar conditions and forecast. Mind it, you expect only. You are not sure. In fact, you will get rain on other than 3 occasions out of 10 more frequently than 3. Probabilistic situation is like that. It deals with uncertainty.  Let us understand this with some easier situation. Take 10 cards of same size and look, and write 'rain' on 3 cards. Write 'no rain' on remaining cards. Shuffle these cards properly and randomly select a card from this pack. What would you get? You can get any of the two 'rain' or 'no rain'. But you expect more to get 'no rai...

During morning walk, I saw a bench on the right side of the path, something like below image. As I walked further, I found another bench but on the left side of the path. Something like below image. I found that these benches were placed at some regular intervals. There were few places on the path with benches on left side and right side both. I found this quite interesting and useful. Persons walking on the path get place to sit and relax at some intervals with views of right side or left side. Whereas, there are places where people can sit in front of each other and relax.  I decided to get some idea about the distance between two consecutive benches on either sides of the path. I counted the number of steps required to move from one bench to other and got estimates of intervals between two consecutive benches. Left side benches were placed at interval of 200 meters whereas right side benches were 140 meters apart.  There can be several interesting questions in this scenario...

  My fitness app gives me monthly challenge related to exercise each month. In June, the challenge was to complete 3600 minutes of exercise in the month. This averages to 120 minutes/ day as there are 30 days in the month of June. That means, If I do 120 minutes exercise each day of the June month, I total 3600 minutes which is equal to the challenge minutes. Average does this only. If average monthly expense in first 8 months of this year in your family is ₹25000, that means the total expense is ₹25000*8 = ₹200000. It is not necessary that the monthly expense is ₹25000 each month to keep the average same. Expenses may be high in some months and may be low too in some months. If the total expense in 8 months is ₹200000, then the average monthly expense is same ₹25000. Coming back to the exercise challenge. Doing 120 minutes of exercise each day was good enough for the June challenge. But, it's quite uncomfortable to keep doing that each day for 30 days. So, I divided the target of ...

  I purchased 7 mangoes from a nearby fruit seller yesterday as there were that many persons in my home. There are plenty of fruit sellers around, so there is no reason of purchasing more and storing. The fruit seller was a lady in her seventies and probably had no formal education. She sold those mangoes at ₹140/kg. She weighed the mangoes selected by me. It was 1 kg 750 gm. She asked me to pay ₹245 while transferring the mangoes into my bag. I was surprised as the time taken by her to do this calculation was practically nothing and she didn’t use calculator or pen-paper. I took more time than her to do this calculation manually and found the amount to be right. I thought, she might have got another customer earlier purchasing same quantity of mangoes, so she might just remember the amount! But, it was not so. I was curious to know her process of doing the calculation. She said; 14*7 = 98 for 700 gm, +₹7 for 50 gm = ₹105 for 750 gm. Add 140 for 1 kg. So, 140+105=₹245...

  Have you noticed that most students know how to get better marks than what they have been getting but they don’t seem to be improving on that? Similarly most of the sales people know how to sell more than what they are selling at present. What holds them? There are many people who are constantly in debt. They know how to come out of that but they don’t. Why?  Most people know how to do the job better than what they are doing. But they are not able to do so. Their actions and what they know do not go together. The reason is that they haven’t applied their knowledge to form good habits. They know, but they don’t have the habit to work as per that. Bad habits are holding them. In truth, the only difference between those who have failed and those who have succeeded lies in the difference of their habits. Good habits are the key to all success. Bad habits are the unlocked door to failure. Thus, the first law I will obey, which precedes all others, is--"I will form good habits and...

 This post discusses about temperament control issues during preparation for IIT entrance but it holds true at earlier level as well. So, consider this as something related to habit which affects different aspects of life. The single reason that contributes most in failure to qualify for IIT for good students is poor temperament management. Some of the situations described here may look familiar to you. You make too many unintentional errors. You are suggested to be careful. You prepare hard but forget important points at crucial moments. You know things well but are too slow in applying them; perhaps you are not sure whether you are applying right or not. You get hold on the issue and suddenly lose concentration. Mind becomes either blank or starts wandering. Sometimes you feel confident—JEE is well within your reach. Sometimes you feel just the opposite. Everyone else seems to have prepared better than you. You keep changing your strategy with every suggestion you rece...

  We drove our Car in rural Konkan area recently. Distance was about 160 miles. Roads were good and bad in patches. On good patches, we enjoyed driving at speed of 60 miles per hour. Whereas, on bad patches, it was difficult to go beyond 10 miles per hour. A general feeling was that we were at the slower speed for about 4 hours and at the higher speed for only 2 hours. Roads were bad; that was the conclusion. You can understand that about two-third of the travel time, we were struggling to get a speed of 10 miles per hour. Let us see another aspect of the journey by getting idea about length of the bad or good road. Since, we had 4 hours of drive at a speed of 10 miles per hour, the length of such roads was 10*4 = 40 miles. Similarly, length of the road travelled in 2 hours at 60 miles per hour can be computed as 60*2 = 120 miles. So, total distance travelled was 120+40 = 160 miles, out of which 120 miles were good and only 40 miles were rough. In terms of %, only (40/160)*100 ...