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Word problems? Draw a picture!
 “This is devilishly hard for fifth grade, especially the second week of the year,” math teacher Stan Sterenberg told his students. The devils in this case had names — Andy, Ben, Carl, David, Earl, Frank, George, Harry and so on down the alphabet — and were all inhabitants of word problems that Mr. Sterenberg had created to show the girls that the key to solving such a problem is, often, drawing a picture.
Mr. Sterenberg first demonstrated the picture-drawing technique on a problem involving Isabel and Jen, two stamp collectors. Isabel has five less than two-thirds as many stamps as Jen has, and together they have 90 stamps. How many stamps does each girl have?
Mr. Sterenberg represented each girl as a column divided into parts, Jen with three parts and Isabel with two. Isabel’s lack of another five stamps was noted next to her. “I’m going to loan Isabel five stamps,” Mr. Sterenberg said, a magnanimous gesture that showed his students that math teachers aren’t all interested in hoarding numbers. His loan rendered the problem much easier: Isabel and Jen now had a grand total of 95 stamps between their five parts, and Isabel simply held two-thirds of what Jen had.
What next? “Division,” one student said, espying that the 95 stamps could be divided among the girls’ five total parts to obtain how many stamps each girl had in each part. With that figure in hand, quick addition and subtraction yielded the final answer. (We’re not going to give it to you; try it yourself!)
The girls then set to work on four similar problems. Mr. Sterenberg checked their work, offered advice (“Never erase!”) and sent them back, in certain instances, literally to the drawing board to sketch better representations of Ben or Carl’s holdings.
The lesson gave the girls a useful technique that made the abstract thinking of math more concrete, though one student found her thoughts drifting from the numerical realm to the cultural one, where she discovered a “word” problem of her own. She looked at her paper and declared, “You choose old names, Mr. Sterenberg. Who names their kid Earl?”
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