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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.

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