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January 17, 2014

Of course we know algebra...

I have been introducing algebra to the kids in Udavi and Isai Ambalam schools. I have been doing this through puzzles that can be logically thought through to come up with a solution (which in many cases ties in one-to-one with the algebraic expression). For each new problem kind of problem a new way of solving would need to be thought of, till ultimately algebra can make it all easy (if you can write out the problem)... I had good success in motivating the 6th graders at Udavi that they absolutely demanded to know what this algebra business is all about. When introduced they were even able to write out the expressions though they got stuck not being able to solve it.

I had been doing something similar with the 6-7 grade kids at Isai Ambalam as well and I had used different variations of puzzles in each school:

Variation1: 120 biscuits are divided between 16 pets (cats and dogs). The dogs eat 9 biscuits each and the cats eat 7 biscuits each. All the biscuits are used up. How many dogs and cats are there?
Approach without algebra: Since each pet eats at least 7 biscuits. We given 16x7  = 112. Each dog now needs two more biscuits. The remaining 8 biscuits are eaten by 4 dogs. The rest 12 are cats.

Variation2: 110 biscuits are to be divided between cats and dogs. The dogs eat 9 biscuits each and the cats eat 7 biscuits each. There are two more cats than dogs. How many cats and how many dogs?
Approach without algebra: Give the two extra cats their 7x2=14 biscuits. The remaining 96 are divided into equal pairs of cats and dogs. Each pair of cat & dog eats 9+7=16 biscuits. There are 96/16 = 6 such pairs.
6 dogs and 8 cats.

The kids got the hang of the variation that we discussed in class and were even able to make their own puzzles and solve it changing the numbers. I wondered what would happen if they faced the other situation. The Isai Ambalam school was working through the Dec holidays after Udavi school had closed for vacation. A couple of kids Arc, Sub in 7th grade were at a point where they seem to have mastered what we had been working on in class and I asked them to take the exam of the other school as practice.

At some point I asked them about the algebra puzzle and they said that it was easy. I asked to see their solutions wondering if they had made an assumption or guessed the answer. It turned out they had  abstracted the puzzle accurately and were able to comfortably walk me through the steps of solving it as well. I must have had some look on my face because Arc smiled and said, Anna of course we know algebra, you taught us.

Arc soon had to figure out the logic behind the electricity bill at school and how the slab system works with algebra :)...but that's a different story.

How about a drama for math/science?

At the end of the term the children put up a cultural program. At the end of last term I had hinted on doing some experiments, but that didn't pan out. This time around the idea of doing a drama on Archimedes really caught the attention of the children.

I gave them one version of the story on dday-2 and they added characters, settings and created a drama out of it. They took up the roles - king Hiero, confidant queen, goldsmith, his unscrupulous sidekick, then enrolled others - friends of goldsmith who attended a party after the goldsmith thought he fooled the king, gatekeepers and soldiers of the king and put together some props, etc. They also modified the story from Archimedes being in a bath to it being a hot day and he drinking from a public water station in which he pushed the container in to see the water rise.

They were also kind enough to let me modify the ending with the king to thanking Archimedes from saving him from the wrath of the Gods by offering them a defective crown (from the more obvious one of the goldsmith's head rolling :)).

January 02, 2014

Butterfly says thanks...

Ani has been working on making some flower beds. Arham permitting, we go and collect cow dung in the mornings for the same. Her favorite bed are the hope flowers just outside our house. The buds are just starting to come out. Ani was sitting in front of the bed adding some cow dung when a butterfly came by sat on few of the buds. Ani didn't notice the butterfly till I mentioned it to her from the window and the butterfly flew did a circle around her and she saw it sit on another bud for a few seconds and then said goodbye. Perhaps, it was the butterfly's way of saying thanks for the time and effort she has been putting to get flowers to bloom at Isai Ambalam.

It was a nice moment and I wish I had captured it with a picture as its better than 130 words :).

The other story...

Multiplication: One man can eat 3 mangoes. How many mangoes can 5 men eat?
Inverting it into division stories
Division story: There are 15 mangoes, how do you divide it among 5 men.
Division other story: One man can eat 3 mangoes. How many men will eat 15 mangoes.

Its interesting that almost all children in 6th grade have only heard or said the first division story, but can't associate using the other information i.e. how much one man eats with a division story. Much like:
Story: A car covers 60 km in 2 hrs. What is its speed.
Other Story: A car travels at 30 km/hr. How long does it take to cover 60 km.

I find they are too used to multiplication stories being associated with one man, one hr, etc that they are unable to move beyond this experience.

Its also interesting that in younger grades teachers use only one story for subtraction
Story: There are 6 pebbles, if you remove 3 how many are left. 
Other story: There are 6 pebbles, I take away some and there are 3 left. How many did I take away?

What is your favorite other story?

Let's put a games stall

As part of my effort to create an engaging atmosphere for kids to think I had introduced many board games requiring strategy to the 6th grade at Udavi. With Christmas was the annual fair at Udavi and the kids put stalls with games involving luck and concentration. I proposed to the class if there were any kids who wanted to put up a stall for the board games and puzzles. I thought it would be an interesting exercise to increase the mental stamina of the kids to be able to play with different people throughout the morning (9:30 a.m. to 12:00 p.m.). The teacher had also informed me that the kids tend to abandon the stalls in order to try out other games so I had to have backups (and play myself if all else failed :)). Seven kids volunteered and even spelled out the games that they like and would like to host. Four for the games and 3 for the puzzles.

We had a practice session in which we polished the puzzles while solving it and renewing our understanding of the games and the strategy of each game. Though polishing the rust off games is an effort, the kids generally had a good time and talked about the posters they were going to make.

I got busy with trying to make a game to make a baloon through come game day the kids had made posters about their games, one had dropped off, but one had joined. The boots had visitors almost all the time. The kids kept up to their booths. None of the girls in the puzzles counter budged the whole time, older kids, alumni, those from other schools tried their tricks, but the girls held firm - kept to the time allocated for a puzzle independent of taunts, pleads, muscle men who tried to pull things apart. They also and kept rotating the puzzles to avoid the passerby who may have been waiting to see the solutions.

The kids had been practicing the games and  had mastered it by then. They played some practice rounds with the 10th graders and one of the kids quietly told me in a surprised tone that the 10th graders are actually smart. One kid who had not volunteered initially saw the fun and joined in. They kept to it till around 11:30 when a couple of them really wanted to try the other games. I relieved the kids in one set of games and the 10th graders followed to play with me. I then handed over the stall to the 10th graders.

The kids had interesting feedback about their experience. One of them said that he only got beat twice, but he gave tokens to kids who had played well especially the younger ones. One kid admitted that he was beaten when he was distracted. Another mentioned that one kid from the other school I teach was good at puzzles and tried to help other kids out. One of them had mentioned that they didn't play any of the games, it was ok, but they didn't get dairy milk chocolate. One of the kids said that he learnt that he made up good strategy and was difficult to beat. Still another talked about the game that didn't get used and said he wanted to use that. One child recalled an experience in which an older child called him a cheat after he won the game. they had a rematch and he won again and the person still called him a cheat, he let her play again and this time when he won the person quietly left. One child said that she will try to be more relaxed and have more fun, another said that she would be more serious.

When school reopened today I took 20 chocolates to class. I told the ones who had maintained the stalls that since they missed out that day they can have the packet and decide how to disburse the same. It would be nice if everyone got something, but even that was up to them. I only wanted to know the fraction of the total each of the 15 children finally got. The kids decided to give a chocolate to everyone and then realized that there were more. They asked me how to disburse the rest. I told them it was up to them. One of them suggested that they keep it, another pointed out that there were only 5 chocolates and 8 of them. The next suggestion was that there were 4 pieces in each chocolate and we should split it evenly, another intervened and said that this would not work. Still another suggested that this was a fraction problem and each dairy milk needed to be split into 3 parts for each person to which a child pointed out that the chocolate had only 4 pieces. At this point I walked out of class with a smile. For all the puzzles and problems we make up, nothing beats real life!