Class 9: surface areas and volumes

Today when I was teaching surface areas and volumes to one of my students I was repeatedly telling him to not to do ratification (the process of pointless memorizing) the formulas. I told him that it is the only point of my teaching to you to make you understand that maths is not about ratification it's about understanding. this is the most reasonable subject you have all logical. So everything has a reason. You need to understand this, so if you forget them at a point you can revive it easily by the other way round. So here are a few things which I told him to remember maybe it can help you too

1. Start with 2 d shapes area and perimeter which includes shapes: square, rectangle, circle, semicircle (students need only these shapes in this chapter in 2 d)
2. Then tell them the basic rule in uniform figures:
volume= area x height
curved surface area= perimeter x volume
total surface area= curved surface area + area of bases
3. Let them derive the total surface area for all the shapes themselves and if you are a student please derive it yourselves
4. Let them derive the volume and surface areas for the right circular cylinder first and then tell them that the volume of a right circular cone is 1/3 of the volume of a cylinder of the same base and height. This way they can easily learn the formula for cone. And for slant height let them revise the pythagoras theorem so they can find slant height whenever they can.
5. Tell them why the total surface area and curved surface area is the same for the sphere.
6. And my last tip is please don't tell your kids about frustum soon. I know that you know but this is not in their syllabus. they already have a lot of different kinds of questions to do. don't make it complex until they are ready to deal with it which they will do when they will be in a higher standard leave it till then.

Good luck! and remember don't do rattafication.        

Japanese multiplication using lines

A few days back I have gone through a nice video about a method of multiplication, which is surprisingly very nice and easy. When I read about it more I got to know it is known as the Japanese method of multiplication using lines. I read quite a few articles about it and did some calculations too. I am really fascinated by this amazing use of lines and curves to do multiplication. This is a very good method which can boost the imagination power of the kids and let them multiply in an easy way without using any kinds of tables. I am not sure to use this method for young kids or whether we should teach this to our young kids, because I find it debatable. I think the way in which we are doing multiplication is good still we can learn more methods anytime. I am not here to debate about the origin of this method. Some people say it is originated in India, some say's that's not true. Let's not get into that.
I think we can teach our kids this method in a fun way. I suggest we should introduce this as to see the beauty of lines and curves that can even simplify algebra, instead of teaching our kids that this is a mere multiplication method. I found it quite lengthy sometimes when we take a bigger number although we don't need to memorize any kind of tables to use this method for multiplication as our traditional multiplication method demands. But for a longer run, later big issues, bigger mathematical problems we need our method, our more traditional methods as Vedic mathematics which are considered as obsolete nowadays but have great significance. So if you want to learn a new method which I felt that you should look at once, please go through some videos which are easily available on the net nowadays. It will hardly take 10 minutes of your precious time. Good luck!

When I realize I was doing tables wrong my whole life...

Me: Now it's time for your homework. What have you done in school today?

My son: Nothing. Just play.

Me: That's it. Anything else, like studies.

My son: Oh! yes. We were doing multiplication so my ma'am has started tables in school. she has given me a table of 2 to learn.

Me: Ok. Let's do the homework then. Show me your copy.

My son: Ok

Me: Why have you written all the other way round. It is not 1*2=2, it is 2*1=2, 2*2=4, 2*3=6 etc.

My son: No mom. This is wrong, ma'am told me this way only and in my book, it is the same.

Me: Wait! let me see in your book.

        Yes....You were right. It is the same. But we don't do it this way beta.

        I think there is something wrong with the book.

        Do one thing tomorrow you have an off so go and play we will do this tomorrow.

This is what my son and I discussed and then starts the discomfort. I am not the one who just sits and waits for someone to correct the problem, I think upon it again and again until I got a solution. Then I start looking for other books I have cause I have this in my mind that how can a book of such a good publisher has such a big mistake. then I saw two books, both of them have the same way of writing tables. Then I believe that the way is correct but why so? I have solved so many complex problems of very high classes before but this is something I was doing the other way, my whole life and on top of that this is something which I should have known in my first standard as the other children are doing nowadays. So I just saw that carefully and understood why this is this way. and it came out a very very simple logic which is actually right. this is the way it should be. Everyone in teaching pedagogy learns about mathematical modeling nowadays while doing any educational program or while studying about it. So how can I miss such a simple fact? 

I want to share with you this simple class 1 or 2 things which we were doing wrong when we were young. we all know multiplication is repeated addition.

2+2+2+2+2+2=6 times 2= so it should be written as 6*2=12

so here comes the table:

2                 = 1 times 2= 1 x 2=2

2+2             = 2 times 2= 2 x 2=4

2+2+2         = 3 times 2= 3 x 2=6

2+2+2+2     = 4 times 2= 4 x 2=8

2+2+2+2+2 = 5 times 2= 5 x 2=10

so now I guess we should unlearn what we have learned and start learning the way it should be. Believe me, it's not easy when you make learn the table to your 7-year-old the new and the correct way, because it's you who learned it the wrong way and doing it wrong your whole life.

Are you passing your maths phobia to your children????

"When I was at your age I was excellent in studies but my maths, oh my god! It was horrible. The most difficult subject. I always wonder how your uncle does it with ease. I do it daily but I never get good grades in maths and you are the same with your mind you need to do it daily for an hour at least and even more than that. It’s a difficult subject it requires a lot of time."

I know eavesdropping is really wrong but I couldn't help myself from doing it when I heard a bit of an argument between a parent his a child about how difficult is mathematics and the scary stories the parent has about his experiences. So the above is the small part of it which I felt I should write here.

Are you saying similar things to your children? Maybe you were not good at mathematics when u were young but were you good at handling computers, mobile phones, and everything,  the way they do at this young age? So please, stop comparing and stop manifesting the fears or phobia of your childhood to your child. Don’t project as if, if you have trouble doing this then your child has the same. You and your experiences may be different, absence of proper guidance, distractions, teachers, etc there could be hundreds of reasons for your phobia which you and your parents may be not able to identify. But for your child circumstances are totally different he or she is in a different setting at a different time. Now your duty is to address the problem he or she is having as their own, not related to their parent's past problems or some inherited phobia of mathematics. It should be their own to deal with not the one that you manifested. Many studies show that to overcome a phobia the best way is to first believe yourself that your fear was wrong and to laugh about it. Don’t tell your stories as if you were scared of it rather laugh about it and say you were wrong about scaring of something which doesn’t mean to be. Tell your child there is nothing to fear but we just need a bit of help to overcome this. Believe me, if you stop transferring your phobia into your kid it will help them a lot. This is one of the major reasons causing mathematics phobia as per different studies. Let’s think about it and never do it again.

Lets get started....

WORDS sometimes said sometimes written...

I am not good when it comes to pen down what I am thinking but maybe good while I type them, and maybe much better when I have to speak. Yes, that's my problem, I speak a lot. now I decided to type what I speak. As a mathematics lover, teacher, learner, I often come across a lot of people who talk about this subject differently. I myself experience a lot of things that I want to share with everyone. So here I am, a teacher, Mathematics lover, a mother of two decided to get started to write what I experience daily. These may be my current experiences, some old ones, any related issue or any good read I go through I will share with everyone. So hey, wish me luck. And I wish for myself to stick to what I have started.

next time....