Known 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 :)

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do not read further unless you have solved it  :)

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As expected, I found all of them perplexed when this problem was posed to them.... But after some time, one of them came to me saying - "the answer is 1000"   and this was with Confidence !

I was surprised. So I asked him for the approach and rationale, to which he replied -

"All the other options are incorrect.... So it has to be 1000."

To be honest, I was least expecting this approach. I was more keen to listen to his explanation now...

The expression inside the bracket evaluates to 100....  and the exponent 3/2 means 1.5, which means more than 1.... 

-- It cannot be 100 because 100 raised to 1 (and not 1.5) is 100

-- It cannot be 10 because if 100 raised to 1 itself is 100, then how can 100 raised to 1.5 be less than 100?

-- It cannot be 1 because 100 raised to 0 is 1.

-- So it has to be 1000..... Further, as 1.5 is more than 1... hence (the answer of 100 raised to 1.5) should be bigger than the ( answer of 100 raised to 1).

I wonder if the people (like me) who already 'know how to' evaluate fractional indices would (even pause to ) think and reason this way...... Rather we would (almost instantly & probably even proudly :-) use the 'Laws of Indices' given to us (& accepted & memorized by us).

one of the conventional ways would be this - 

He asked me if his answer is correct. 

I looked at other students and asked them about their views about this. All agreed with this argument.  So I had to congratulate him, but how can I let him go away so easily :-)

"What if, I would have not given you the options? How would you solve it then?"

He looked at me with a smile, knowing very well that his teacher has caught him this time !

"It would have been difficult in that case", he said... "let me go & think about this....."

I could see couple of his friends giving him a teasing smile while he was returning back, loaded with the new challenge.......and while one of them started consoling him, "Don't worry, I will solve this part now :-)

And soon, everyone was again engrossed with this new problem now ...

How did they work on this ? Could they solve it ?  

We will see this in the part-2 of this post..... let me also say that the next post will talk about how these students looked at the negative indices.....   :-)

Meanwhile, you too can try out this with your children / students (who know how to deal with integer indices but haven't been introduced to fractional indices yet) and do let me know how they worked on this problem..... 

You may even share your views about the approach adopted by the boy in solving this problem and how did you solve it :-)

Thanks and Regards

Rupesh Gesota

www.rupeshgesota.weebly.com

PS: Students belong to class-7 marathi medium government school in navi-mumbai. I work with them voluntarily after their school hours as a part of maths enrichment program. www.supportmentor.weebly.com