Shiralkar: The man who bought a hundred oranges

Columnist Parth Shiralkar explains the fun nature of word-based math problems. 

Parth Shiralkar

Commonly employed as a last-minute gift, the typical fruit basket arrangement contains about a dozen mixed fruits, all cut up and put nicely together. Some of the larger ones may contain more sliced fruits, catered to a larger number of people. These are normal proportions of fruit — one simply does not walk up to a fruit vendor and offer to purchase half the inventory. And yet, in an experience shared by students worldwide, we’ve come across a math problem with a person who does exactly that.

Word problems, or story-based problems, are used in the teaching of mathematics. Essentially, a word problem can be translated, stripped down into an equation (or multiple equations) to be solved. There are two parts to a word problem: the part that matters and the part that doesn’t. Without the proper wording to go with the constants (given arbitrary numbers) and variables (unknown values), we’re left with something like “if one envelope can carry two letters and one stamp, how old is the postman?”

The study of semantics aside, word problems have generally been fun to solve for years. Before we started using symbols to denote values in equations, there were only words — this made for fairly intricate wording and complex sentences. The Rhind Papyrus, a document that dates back to 1650 B.C., contains examples of such elaborate numerical questions. In addition to the early Babylonians, other civilizations also have had some or the other sort of word problem in their curriculum.

Some research suggests word problems are important aspects of a child’s learning process. In addition to teaching them about the math itself, these problems can serve as a tiny, abstract glimpse into their own lives. Word problems tug at one’s comprehension skills — unwrapping the equation from within the words and then solving it is a great mental exercise.

But does the chicken come first? Or is it the eggs? While developing a word problem, does the mathematical equation project itself onto a daily occurrence, or is it the other way around? Past studies point to the latter — seeing a flock of birds fly from one telephone line to another can be inspiration for the word problem — but the problem is always the math.

In a study from 1999, the very idea of a word problem is compared to a genre — a special form of problem. And word problems are special — they tell you how to dismantle complicated information and tell you that it’s OK to buy a bunch of things at once. This rare combination of words and math has led to many fun incidents in class too — if your name is picked for a problem or if your name appears in one of the fun problems, that’s always a pleasant experience. Wash your hands and wear a mask.