tag:blogger.com,1999:blog-35651345632758283512020-05-22T01:27:36.578-07:00Math CoachI am an engineer-turned-school-maths teacher....
I love to see the sparkles of understanding in the eyes of my students.... It is really exciting to see I was part of this enlightenment process.... I find myself both inspired and inspiring!
I love doing math with children & sharing my love of math and children with parents and teachers... Check the websites www.about.me/rupesh.gesota and www.supportmentor.weebly.com to know more about me & my math-adventures...Rupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.comBlogger74125tag:blogger.com,1999:blog-3565134563275828351.post-61829884425468799532019-10-21T04:50:00.001-07:002019-10-21T04:50:38.437-07:00Part-2 : Re-learning and Enjoying Polynomial Division with students.
Last week I had shared my classroom experience of working with students on polynomial division, and these students were not yet taught the standard procedure of solving such problems in their school. This is the link to the blog:
http://rupeshgesota.blogspot.com/2019/10/re-learning-and-enjoying-polynomial.html
I forgot to mention one more interesting thing that happened while working Rupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com0tag:blogger.com,1999:blog-3565134563275828351.post-57246017910134046072019-10-19T14:30:00.000-07:002019-10-19T14:30:05.591-07:00Re-learning and Enjoying Polynomial Division with students.
They had just learned how to multiply two linear binomial expressions like
(x + 2).(x - 5) , (3x - 2).(5 - 4x) , etc. in two ways - pictorially as well as symbolically (i.e. by expanding).
I now wanted to see their approach for the division problems, like for problems of the type:
(x^2 + 5x + 6) / (x + 2)
Polynomial division was not yet taught to them in their school. So I should Rupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com0tag:blogger.com,1999:blog-3565134563275828351.post-25012863229443748592019-10-02T13:27:00.000-07:002019-10-02T13:36:26.408-07:00Revisiting forgotten Arithmetic - with a new student - Part-1
It was her first day in our class... Both of us were excited as to what would unfold.....
Readers may scroll below to the first paragraph written in Bold, if they wish to know only the Math part of this post :-)
I had come to know that she hailed from a very challenging socio-economic background and was further (helplessly) doing her schooling in a language, which was not spoken by Rupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com0tag:blogger.com,1999:blog-3565134563275828351.post-47950862728233727842019-09-23T12:18:00.001-07:002019-09-23T12:20:01.660-07:00Known to unknown - Integer to Rational exponents - Part-1
I had not yet introduced them to the numbers involving fractional or negative exponents, like 6^3.5 (6 raised to 3.5).... So I was curious to know as to how they will solve this problem -
I would suggest you to make an attempt to solve this problem on your own first.... Don't worry, even if you don't remember any of such math that was taught to us in school :)
.....
.....
.....
Rupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com0tag:blogger.com,1999:blog-3565134563275828351.post-74075240781149107882019-02-07T04:01:00.001-08:002019-02-07T04:01:15.358-08:00"Sir, we have done this many times! ... 1/6 is Two one-twelfths....so (half)/6 is One-twelfth..."
Setting: Some 6th std government school students in an After-school Maths enrichment program
I knew that they had been taught the fraction arithmetic in their school. So when I gave them couple of problems to work out, either some of them arrived at non-sense answers (of course, not their mistake) or some of them were applying the 'bunch of rules' incorrectly and there were also some who Rupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com0tag:blogger.com,1999:blog-3565134563275828351.post-67042668375688657842018-10-17T09:47:00.001-07:002018-10-17T09:47:09.704-07:00Yes Sir, this answer is correct! :)
His approach to solve the problem was perfect. After a minute, there was a need to add the two fractions:
3/4 + 1/20
He started doing some 'cancellation' .. I could hear his mumbling - 'four fives are 20'... So after couple of seconds, he provided me his answer -
4/9
Right Sir?
He was waiting for my response, but there was only silence for few seconds. I kept staring at his Rupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com0tag:blogger.com,1999:blog-3565134563275828351.post-51266301409052298652018-09-25T13:24:00.001-07:002018-09-25T13:30:41.287-07:00Tussle of 2/3 and 3/4, again!
Some time back, I had shared how a group of students added fractions visually, without using any procedure or rule. This is the link to that classroom experience:
http://rupeshgesota.blogspot.com/2018/04/adding-fractions-through-visuals.html
The above post also points out how students (with weaker conceptual understanding of fractions) generally confuse or misinterpret 1/3 as sum of 1/4 Rupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com0tag:blogger.com,1999:blog-3565134563275828351.post-39007662370536015162018-09-21T11:30:00.002-07:002018-09-21T11:36:46.200-07:00Revisitng the forgotten lesson.. (on mental math)
The other day I did some mental maths with a new bunch of students. I noticed that they were highly dependent on the standard algorithms for basic arithmetic like addition and subtraction. Yet, it was interesting to note that most of them were already aware of 'many informal' ways of doing this manipulation. However they never used these (more sensible ways) during their school maths (why?)
So Rupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com0tag:blogger.com,1999:blog-3565134563275828351.post-1867592593267191552018-09-16T13:35:00.000-07:002018-09-16T13:36:47.227-07:00Solving one problem - Learning many things
It didn't take much time for them to figure out, with reasoning, that the total number of numbers in a given range is 'one more than the difference of boundary numbers.'
However, this 'formula' (of difference +1) became visible only when I gave them some 'difficult' numbers to deal with (from 32 to 75). You may also notice how the opportunity of generalization was grabbed at this Rupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com0tag:blogger.com,1999:blog-3565134563275828351.post-61138954714223184012018-08-06T13:59:00.001-07:002018-08-06T13:59:24.139-07:00Square of the size of Rectangle - PART-2
In my previous post, I had shared two methods figured out by students for Squaring the given Rectangle (area unchanged) with only compass & straight edge.
If you haven't read the previous post, you can click here:
http://rupeshgesota.blogspot.com/2018/08/square-of-size-of-rectangle.html
And If you remember I had also mentioned in the end of the post that -
I had also posted this problem toRupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com0tag:blogger.com,1999:blog-3565134563275828351.post-46031958182575319242018-08-04T13:18:00.001-07:002018-08-04T13:18:29.848-07:00Square of the size of Rectangle
This problem caught my attention while I was looking for something related to another geometrical problem on internet. And after studying it for a while, I was pretty sure that my students would love even this one.
"Given a rectangle of some size m x n, construct a square of area same as that of rectangle using only compass and a straight edge (not a marked ruler)"
To this, one of my students Rupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com0tag:blogger.com,1999:blog-3565134563275828351.post-4878713272166794162018-06-23T04:53:00.000-07:002018-06-23T05:09:01.027-07:00"Oh! This is Cross-Multiplication....!!"
I had given them enough time
to struggle and figure out how to evaluate 'x' from such equations,
where variable is in the denominator:
But
when I found that they were unable to do this for long, I decided to
intervene. In the above problem, it's easy to visualize that 2x-1 has to
be 3, so that we get quotient as 3, and for this 2x should be 4 and
hence x=2.
But I was aware that thisRupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com0tag:blogger.com,1999:blog-3565134563275828351.post-77211042213398205902018-06-11T10:46:00.000-07:002018-06-11T10:46:22.270-07:00When students are not directly fed the text-book methods - A.P. - Part-2
Hello folks,
So as I had said, I am back again with the Part-2 of this story :-)
Hope you remember about the onset of an unusual activity in our class? - my (lower grade) students have started doing (& enjoying) Maths from (higher-grade) text-books. Its an unusual activity not just because of the different in the class-levels, but because we had never used any text-books till now! :-))
Rupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com0tag:blogger.com,1999:blog-3565134563275828351.post-34636884268463700552018-06-09T09:40:00.003-07:002018-06-09T09:40:47.405-07:00When students are not directly fed the text-book methods - A.P. - Part-1
I have been Playing Maths with a bunch of marathi-medium municipal school students after their school-hours.
As I can now see them approach and solve quite challenging (out of the text-book) problems comfortably, I decided, for a change, to now pick up their text-book for a while and see what unfolds...Of course, I cannot make them solve the problems from the school text-books of their age (Rupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com0tag:blogger.com,1999:blog-3565134563275828351.post-73637181704889459872018-04-08T10:36:00.000-07:002018-04-08T10:36:20.268-07:00Adding Fractions through Visuals/ Understanding
I really liked the visuals drawn by students while solving this problem.
The problem at hand was 4/3 + 5/2
Students had reached a point where they had understood the need / reason for fractions to be of same size i.e to have same denominators to add easily. However we had not arrived at any particular method yet to achieve this.
One of them said that each of the unit fractions above i.e. 1/2 Rupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com1tag:blogger.com,1999:blog-3565134563275828351.post-18839409109755309602018-04-03T10:52:00.002-07:002018-04-03T10:52:32.447-07:00An interesting date today :)
"Sir, tomorrow is an interesting day!", my students drew my attention to an old post-it note stuck on our notice board.
"Oh, really? And what's that?"
"Its 4th day of the 4th month (April), and its also falling on the 4th day of the week i.e. Wednesday."
Flash back - we had figured out this special day many months back, but I could not recollect the specific instance that had triggered us forRupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com0tag:blogger.com,1999:blog-3565134563275828351.post-68209360926612124252018-01-04T12:09:00.001-08:002018-01-04T12:10:39.700-08:00The 1729 Hangover :)
So I was really surprised when this familiar number showed up; unexpectedly, while I was computing for something else.....
Incidentally, I was with my students when this 'accident' happened... And I could not contain my excitement, but had to call them to celebrate this...
I shouted -- "Hey guys... Did you all know that 1729 can be made using the first five natural numbers, and that Rupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com3tag:blogger.com,1999:blog-3565134563275828351.post-37964897841341597562017-12-25T08:23:00.000-08:002017-12-25T08:23:34.407-08:00Easy, yet interesting problem...
I think this is one of the rare problems where all the students solved it in the same way (whoever could solve it :)
While they were still working on this problem, I asked them about their opinion. Most of them guessed that the two areas will be equal. Couple of them thought the greener one might be bigger :)
Vaishnavi was the one who cracked it first...... She proved it beautifully that Rupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com1tag:blogger.com,1999:blog-3565134563275828351.post-49096235934528831152017-12-24T12:06:00.002-08:002017-12-24T12:06:56.287-08:00Area of Flower
It seems I am getting addicted to listening to (& learning from) the different beautiful approaches of my students... :-)
And I am also delighted to see the growing interest of my students to solve more of the Geometry problems these days...
So the above problem I saw on facebook and I was quite sure, they would like it - Area of Flower :) The bounding shape is Square of side 2 Rupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com0tag:blogger.com,1999:blog-3565134563275828351.post-42524764310833694792017-12-02T11:27:00.004-08:002017-12-02T11:29:22.944-08:00Another Geometry Problem (Extension) : Part-2
I was pleasantly surprised to know about the amount of interest / attention drawn by my previous post on the geometric problem on various facebook groups... So many people had not just read and liked it, but had even left their comments with their approach of solving this problem. I would first like to thank all these people for sharing their methods.
I did share some of the different Rupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com1tag:blogger.com,1999:blog-3565134563275828351.post-28623847358572696732017-11-27T18:57:00.000-08:002017-11-28T07:13:31.898-08:00Another Geometry problem...
I knew that this problem can be solved in various ways.. And hence was curious to try it with my students...
They stayed up to my one expectation fully that they could solve this problem quickly. However I got only 3 different approaches (as against my expectation of 5 to 6 !)
But when I realized that there are still 3 methods from just 7 students, Rupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com5tag:blogger.com,1999:blog-3565134563275828351.post-60192182161071303662017-11-21T19:02:00.000-08:002017-11-21T19:03:02.231-08:00My students solved it better than me :)
This is an interesting problem that was given to about 30 Maths Teachers in one of the PD workshops that I attended recently. I must confess that almost all of us, baring very few, struggled quite a lot and for quite a long to find its solution.. In fact, many of us could not even arrive at the desired solution :) However, I had a gut feeling that my students 'will' be able to reach the Rupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com0tag:blogger.com,1999:blog-3565134563275828351.post-8232985358881343072017-11-02T10:21:00.001-07:002017-11-02T10:21:16.323-07:00Simple Puzzle (Tin of Biscuits) - multiple approaches
I was sure they will crack this puzzle quickly, but I was more curious to know their multiple approaches.
"A tin full of biscuits weighs 5 kg 200 gm. The same tin half full of biscuits weighs 3 kg. Calculate the mass of empty tin."
Almost all of them were done in about a minute.
*************************
Give this problem a try before you read the solutions below.
*************************Rupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com2tag:blogger.com,1999:blog-3565134563275828351.post-37052700667693319312017-10-23T13:33:00.002-07:002017-10-24T08:59:30.441-07:00Simplifying Algebraic Fractions : Part-1
Could you find the mistake in her first step of simplification of LHS expression?
I am sure many algebra teachers would agree with me that this is one of the most common mistakes students do while simplifying algebraic expressions.
So, why would be they doing so? What could be the cause(s) for this effect? Why is it that this nonsense does not seem nonsense to them?
(I am Rupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com1tag:blogger.com,1999:blog-3565134563275828351.post-62175045273915583172017-10-08T12:51:00.000-07:002017-10-12T10:59:52.646-07:00Relooking at stack of Tables (Triangle Numbers)
The manner in which tables were stacked up in our classroom that day , it suddenly caught my attention.. I counted them 4+5+6= 15 and Aha ! It's a triangular number.. I was somehow amused by the fact that how come 4+5+6=15? because the triangular expression for 15 is 1+2+3+4+5
I usually include my students too in such investigations when they are around.. and hence this seemingly Rupesh Gesotahttp://www.blogger.com/profile/09059947826181197064noreply@blogger.com0