Wednesday, June 7, 2017

Discovering the Formula for Area of Trapezium

I was thinking of writing the 2nd part of Fraction story tonight....But did not know that something more interesting would emerge in our class today.... :)

It was completely unexpected as there was nothing that we were doing on geometry today..

Rohit walked up to me asking for a method to find the Area of hexagon... I just hinted him that a hexagon can be sliced into triangles, and that we had already 'discovered' the formula for area of triangle... He looked at me for a while and then left, while I too got engrossed with my work...

Soon, I heard him talking to his peers - "I still need to find the formula for area of trapezium. Its pending since long..."

I turned around to find him trying out some constructions around a trapezium, drawn on the floor. I usually don't disturb my students when I see them doing such research. However, I desperately wait for the moment to be invited by them to see their work...Why? - Because it's an authentic learning source as well as opportunity for me!

This time I am trying to share the story in a different way... I will just share the photos of the work of the student as he continued with his work.. I will allow you to figure out what's going on the floor and even in his mind :-)

But before we embark on this game, I invite you to solve a problem --

1) Forget the formula for Area of trapezium, (if you still remember it :) And
2) Try to find its formula using any method that makes sense to you.

The only rule is -- you cannot use any rule or formula whose derivation/ proof you are not aware of or you don't understand... In short, your work should be based on Understanding and not rote-learning of the knowledge that you will be using..  This is the rule we follow in our class...

Ready?  :-)

Take enough time.. 

Don't worry..... there is no race in our class :-)

And when you are done......

You can scroll down to see the approach of Rohit.....






So...... How was it?   :-)

I don't know about you friends....  But let me make an honest confession... Despite being a person who enjoys learning and exploring about many ways to solve the same problem, I have still not thought of or came across this particular innovative method of finding the formula for area of trapezium..... He just won my heart.... !!

-- What are your views about this method?
-- What was your method? (Was it different than the method taught to you?)
-- Why do you think was Rohit able to find out this method?

Would like to hear your response to these questions :)

PS: Rohit has just passed his class-7 from a marathi medium municipal school and lives in the slums surrounding his school, with his parents and younger brother. He loves maths very much and is part of the program - MENTOR.  To know more about this program, check the website

Rupesh Gesota


  1. I love that your students can draw in chalk on the floor! I've never had a classroom with a flooring surface where that would work.

  2. A very interesting idea indeed. And the fact that he understands why the area of a triangle is half the product of the base and the height.

  3. Well done Sir. You are awakening the mathematical, logical spirit, inspiration to explore and above all thinking process to be converted into practical things. Kudos to your students for their innovative methods. Bowing my head to salute for your great services. The pictures shows the involvement of Rohit in full spirit. Best wishes Rohit.

    T.R.Jothilingam, B.Sc.,
    Retd Railway Station Supt., Madurai
    5/111, Raja Sethupathy Street,
    Pasumpon Nagar,
    Tamil Nadu.INDIA

  4. Wonderful

    I am also an Iitian turned maths teacher, and I look forward to more interactions with you.

  5. On Thu, Jun 8, 2017 at 11:33 PM, Jean-Jacques DAHAN wrote:

    Hi dear ​colleague

    I was quite impressed by the investigation and reasoning of Rohit. So I have modelled his solution dynamically with CAbri 2 Plus and recorded this solution in a Youtube video of my channel

    Congratulations to Rohit and thanks to you for sharing such experience.

    Best regards

    Jean-Jacques DAHAN

    in charge of the dynamic geometry research group

    IRES of Toulouse

    Paul Sabatier University

  6. Wow!! That is just fascinating. And that sentence, "I still need to find the formula for area of trapezium. Its pending since long..." says so many things about him. He is truly interested in mathematical thinking and is far above average in it for his age group. I don't think even a graduate can do that.

    I was always skeptical whether we can teach higher level mathematics by allowing children to work on their own. Though this is not the right expectation, but now I think we can. It is very much possible. The teacher's job is to ignite the process, the rest can be left to the child. Rupesh, you have done that exceptionally well. Hats off!

    I am waiting for the day when such kids will be seen in every school, every where, solving problems on their own.


  7. From one of the Parents ---

    This is simply amazing... The way Rohit, at this young age, could visualize the problem, extend it to make it simpler, transform it to make it easy and solve this complex problem is just outstanding.... Hats off to his approach... And a grand salute to you once again for bringing out these abilities in children like Rohit... This is simply awesome...

  8. This is inspiring. What Rohi has done is no doubt great and very one has written about it. But what you are doing is such a rarity in these day rote education. You are "teaching then to learn". Leo Tolstoy said or maybe it is an old russian saying that a spark neglected burs the house, but here a spark lit is lighting up the world one life at a time. I like the fact that you waiting for the permission to e let into the child's work very inspiring. Keep up the good work.