Guessing and estimating

AASHALATA BADAMI, Mumbai

Students in every math class are constantly reminded about the correct answer, the exact answer, the perfect answer. Math is after all an exact science.

But the moment the child steps outside the classroom into the real world he more often than not has to know 'ABOUT' how much of something is required. Is that Rs. 20 my grandma gave me enough for a coke, two samosas and a packet of Uncle Chipps at the canteen? Will I be able to finish my homework in half an hour, so that I can watch 'Friends' tonight? This is true for adults too. "About" how much money should I carry for the weekly grocery shopping? Does that total on the vegetable bill look approximately correct?

We need to teach our children the skill of estimation, as a finely honed estimator will arrive at the exact answer quicker than the one who is not. I must emphasise here that the idea is not to make a wild guess, but instead an educated, trained guess.

Rounding up numbers to the nearest ten, 100 or even 1000 is routinely done in schools. But this is not used as an aid to do other sums. Rounding up skills can be used to check the approximate correctness of answers without going into detailed checking. For example, multiplying 97 by 68 cannot give you an answer more than 100 x 70 which is 7000 - so any drastic errors can be spotted right away. Similarly for addition and subtraction. 732 minus 318 has to give you an answer that is around 400. These are not fool proof checks or even meant to replace accurate checking - but merely tools to check the reasonableness of an answer.

Estimating helps in checking out whether the answer to a formal problem sum makes sense. If I have to find out how many books should go into each of three book shelves, given that I have 24 books - and I have multiplied instead of dividing - the answer cannot be more than the books I have. Encourage the habit of looking at answers critically.

Estimating of weights and measures is possible only after studying weights and measures. An inch is about this much on my finger. A metre is about the length of my arm. A kilometre is about the distance from home to my friend's house. My school bag is approximately five kgs (sad but very often true), a pencil is about three grams, and so on. Children with this kind of exposure and estimation skills will never be confused as to whether 1,000 metres make a kilometre or the other way round. But remember there always has to be a reference point. It is difficult to estimate how many stamps there are in that huge pile without knowing what a pile of say 20 stamps looks like. If there is no reference point then it is a wild guess with no real skill involved or developed.

There is no right way to estimate. Different children may use different methods according to their own comfort levels - we are only looking at the development of judgmental skills as opposed to blind application of solutions, formulas and computational methods. We need to develop a discerning mind through a system that uses approximation in order to arrive at that all-important single correct answer in a subject as exact as mathematics. And giving your child the freedom to judge and more important decide for himself is perhaps the singularly most important skill that you will teach him - not only for math but for also for life. Whoever said math was only numbers and meant only for the classroom?

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