Packets to balance your weight

Situation: Practical assessment (grade-6 student of a government school)

Reason: To gauge his understanding of various math concepts that will serve as a vital input to my instruction plan later.

"Can you estimate the weight of this chikki packet?"

After thinking for a while --- "It must be around 30 grams."

"Let's check it."

He turns the packet around (seems he was already aware of the whereabouts of the weight). He shows the number to me with a smile -- "It's 50 grams."

"Oh.. your estimation was quite good.... Tell me Sidharth, have you seen a weighing balance?"

"yes"

"Imagine - I make you sit on one of its sides, while keeping this chikki packet on the other side....What will happen?"

While controlling his laughter, he replies -- "I will come down, and the packet will go up."

"Hmm... What if I add some more packets?"

"Then I will start moving up..."

"How much packets will be needed so as to balance you on the other side?"

He thinks for a while...and picks up the tools -- pen and paper. While I was happy to see his systematic work, I was also bit pissed off by the slower pace of the multiplication algorithms that he was using.. I wanted to stop him and ask him about the alternate approach... But doing that now would be 'harmful' to him.. I watched him work patiently, while figuring out what must be going on his head for the next set of moves..

This is how his work looked finally, before he just raised his head to tell me -- "600 packets."

​

I have labelled the work for you (from 1-6) to so that you can study his thinking process.. 

"Ok.. I watched you work Sidharth, But can you plz explain me you thought about this?"

What is 76 - 20 --------- 56, 55 or 54 ?

Two days back I was assessing one of the 6th grade students......

(Purpose? -- same as before -- to know her level of conceptual understanding).... So my role at that time was more of an examiner/ assessor than a maths teacher/ guide........but as you will find ahead, the teacher in me couldn't curb his urge to help and hence, I have eventually ended up teaching her, but fortunately, in a way that she could identify her mistakes on her own and then even correct those.. (I did not tell her that she has erred).... 

Also, I ensure that when I do such assessments, me and the student are no longer strangers to each other..... Such assessments are done only after enough contacts.... i.e. after I have conducted few 'Fun with maths' sessions with them and when I am confident that the student jells well with me and trusts me.... Also the purpose of assessment is clearly communicated to the students and hence they too are always eager to go through this diagnostics process honestly and fearlessly because they are now confident that this process is to help their favorite teacher to teach them better....

We had reached the section of 'Mental Math'

Q.1) "What is 50-20?"

"30" (in a flash)

Q.2) "What is 20-7"

No wonder, this time there was a pause. But the sadder part being, I found her using her fingers for this problem. Her lips and tongue moved, but there was no sound... After about 10-12 seconds, she said ---

"It is 11"

"Hmmm... And how did you get this?"

"I counted back from 20"

"Ok.. Is it possible to verify your answer using other method?"

Silent stare....

"Okay... Tell me what is 20-10" ....While I asked this, I also wrote this expression on the table.

​"10"  (and I wrote her answer too)

While writing further, I ask her what will be 20 - 9 then?

She continued to look at the two similar expressions for a while and then looked up with confidence -- "It is 11"

"Hmmm.... How did you do this --- without fingers this time?"

"Sir, 20 - 10 = 10, then if we remove just 9 from 20, then we will have one more left as compared to the previous case i.e. 10+1 = 11"

"Interesting. You have used the logic this time.. So tell me then.....20-9 = 11  and 20-7 will also be equal to 11 ?"