Spilled Juice (Missing digit) problems

The video below is only first (Part-1) of the Four videos. It captures the process that the two students (of classes-3 and 4) go through while solving the following problems posed to them:

Students were shown the above image and were asked to solve these problems. No time limit was set. But they took around 20 minutes to solve these 6 problems. They were also allowed to discuss among themselves in case they wanted to.... 

To check all the four videos of this problem, click on this link:
https://www.youtube.com/playlist?list=PLZBBZFls_2nEffHLet8RjYnfTPwGTYXrI

Thanks and Regards
Rupesh Gesota

Distributing money : Two methods -- Mentally v/s Long division

The other day I was assessing a middle school student one-on-one.

I asked her 'If you wish to distribute Rs.4,000 equally among 5 people, how much will each of them get?"

She thought for almost 1-2 minutes. I guess, she was working out mentally. I generally don't open my mouth (interfere) when students are thinking. Then I noticed that she resorted to pen and paper. I could see her work and she was trying out this problem using long division method. 

"Sir, each one will get Rs.800."

"Ok. I saw that you gave enough time to think before using pen and paper. Can you please share what were you thinking?"

She replied with a smile -- "Sir, I was trying mentally but I messed up somewhere."

"Oh... and Where?"

"I first did half of 4000, gave 2000 to two of them, further halved this 2000 and now 4 people got 10000. I then took 200 from each of the 4 people and gave the collected amount to the 5th person. So each got 800."

"Wow !! You have worked out correctly. What made you feel that you have messed up?"

"Yes, now I did correctly. But in the beginning, I had, by mistake, taken 300 from one of the 4 persons, and hence, had given 900 to the last person. So four of them got 800 and the 5th person got 900."

I paused for a second. 

"Would each of the 4 guys get 800, if the 5th one has got 900?"

She thinks for a while. " No..No... I took away 200 from the 4 guys but I did a mistake in adding four 200s... I calculated the sum as 900 instead of 800... So I thought I have done a mistake as each of them have not got the same amount. So I switched to pen and paper (log division method.)"

"Okay.."

"Shall we try one more similar problem?"

"Yes Sir", she happily agreed. :)

"How will you distribute Rs.2,500 equally among 4 people?"

I wanted her to do this mentally, but she directly jumped to pen/paper. I did not interrupt her (will push her for mental work after this).

"Sir, each person gets Rs.435." 

I was happy with her confidence, but was also disappointed to note that she was victimized!  This is how she did.

​I would request you to hold on for a while and..... Reflect...... Think what will be your reaction to such a situation -- i.e. if possible, write down sequence of steps -- statements/ questions/ actions -- you would take when your student (s) err out this way.