Tussle of 2/3 and 3/4, again!

[Rupesh Gesota]

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 and (Half of 1/4)... this guess probably gets triggered because the small extra amount (corresponding to 1/3 - 1/4) seems to be quite close to Half of 1/4, if the figures are drawn roughly or not so accurately.....and they dont have enough experience / exposure that looks can be deceptive over here and there can be two different fractions with very small difference......

I would suggest you to read that post (if you haven't yet) to know about the argument given by one of the students as to why this extra amount (i.e. 1/3 - 1/4) cant be Half of 1/4. It was music to a maths teacher :)

Little did I know that I would be facing a similar situation so soon... However, what motivated me to share this experience with you is - that there is some twist in this tale :-)

The problem at hand was -- (about proportional reasoning)

If  a group of workers can make 4 walls in 6 days, then how long will they take to make 1 wall?  

This is how some of them started -

6 days    -->  4 walls

3 days    -->  2 walls

1.5 days --> 1 wall

1 day      --> 3/4 wall 

I am sure you would have noticed the (common) flaw in the last step...

So I asked them how to verify this result... One of them suggested lets trace back...

1 day   -->  3/4 wall

2 days --->  1.5 walls

6 days  ---->  4.5 walls

So they realized that since we didnt get back to the given condition from 3/4 wall, it means its incorrect. 

So then they were stuck.. How to figure out?

To read the full post, click here:

http://rupeshgesota.blogspot.com/2018/09/solving-one-problem-learning-many.html

1) I will be thankful if you can share your comments / views about this post...

2) If you find this post helpful, then you may even share it with other teachers and parents in your circle...

Thanks and Regards

Rupesh Gesota   Maths Educator, Program MENTOR
Mobile: +91 9594 02 03 04 Email: rupesh...@gmail.com Website: www.supportmentor.weebly.com Blog: www.rupeshgesota.blogspot.com

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