"Word-Problems"

Supriya and I are sitting at the kitchen table. She is eating her breakfast and asks me for math problems. She cannot do big numbers in her head yet, so I think up problems that are a little complicated yet do not involve big numbers.

"If you go trick-or-treating to 10 houses and you get 2 pieces of candy at each house, how much candy will you have?"
"That's easy. 20, because 10 and 10 is 20."

"If we invite Robbie and his family over and each of us eats 2 cupcakes, how many cupcakes will we need?"
"20. 8 for us and 12 for them."

"We invite Robbie's family over. Now the kids eat 2 cupcakes each and the grownups eat 3 each, how many will we need?"
"24. 12 for the adults (3 times 4) and 12 for the kids (6 times 2), and 12 plus 12 is 24."

Manisha and I always amused when people talk about "word-problems," as if they are different and inherently more difficult creatures than symbolic problems. Since we know that math is just a way of representing reality using symbols, in our minds
there is no difference between word problems and the "other kind" of problems. The whole discipline of formalized mathematics developed because we wanted to solve problems in the real world - and as a matter of fact, the real world poses only word-problems!

Evidently Supriya thinks like we do. She effortlessly translates word-problems into their symbolic form and solves them.

I also asked her, "If 5 + M = 10, what is M?" She had no problem finding the answer.

At this stage Supriya has learned the essence of basic math, that it's a way of representing operations on quantities in real life. The rest is just details...