Consider this problem, written by a third grader (in 1957!)...
My father is forty-five years old. My dog is eight. If my dog was a human being, he would be fifty-six years old. How old would my father be if he was a dog? How old would my father plus my dog be if they were both human beings?
Try to solve this problem using (1) algebra and (2) pictures. You may be surprised at how one method seems so much clearer than the other.
Source: Clifton Fadiman's Fantasia Mathematica, 1958, p. 292
Hint: For the algebraic approach, set up a proportion or an equation.
Solution Commentary: Because 7(# dog years) = # human years, we have that # dog years = (1/7) (# human years) = (1/7)(45) = 6 3/7 dog years for the age of the dad. Also, the sum of their ages in human years is 45 + 56 = 101 human years.
Now, for the visual......imagine two thermometer-like line segments (equal in length). At one end, make a marking of "0 dog years" and "0 human years," each on one of the two lines. At the other end, make a marking of "8 dog years" and "56 human years" respectively. Then, find the appropriate location of 45 years on the "human" line. Placing it next to to the other segment, with the ends even, what is the equivalent in dog years? Note: The situation should sound like "stretching"...in fact, do you see how you could solve this same problem using a meter stick and a length of elastic tape?