Solving one problem - Learning many things

[Rupesh Gesota]

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 moment. It was students who made me write 'b - a +1'.

So now I encouraged them to find the number in the Center of this range 25 to 30. I did not use the words 'mean' or 'average'. 

Kajal quickly answered it as 27. While Tanushri said, there is no one number, but two numbers 27 and 28 in the centre. She figured out this by writing down all the numbers and then cancelling out numbers in pairs - one from left and one from right - while approaching the centre. And to this, Yash immediately said that the central number would be 27.5

I asked others, if they agreed with this result. One of them related this situation with the cm / mm markings of a ruler and explained to the class how 27.5 would be between 27 and 28. I ensured that also knew the meaning of 27.5 i.e. 27 and half.

I asked them to solve the next problem: Central number in the range  45 to 60. All of them quickly resorted to the previous method (cancelling numbers from both the ends) and figured out the answer as 52.5

So now I challenged them to figure out the central number in the range 32 to 75 without making the list as above. This slowed them down to think. I could see some just staring at the problem while others scribbling something on their book.

After a while, Yash came forward to show his solution:

There are 44 numbers from 32 to 75. Now half of 44 is 22. So there will be 22 numbers above and below the central number. Hence the central number is 22.5

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

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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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