Can 24/3+5 be interpreted as 24/(3+5)? I remember my very favorite
problems from fifth grade math. We would get a string of operations (like
the above, but often longer) without parentheses, and a number it was
supposed to equal. The problem was to put in parentheses to make it work.
I believe these were good, educational problems, in addition to being fun.
They drive home the point that order of operations matters. Eventually, I
was taught, explicitly (maybe later in that section, maybe in a later
grade, I don't recall) what the standard rules are for order of operations
in the absence of parentheses. But those "fill in the parentheses"
problems laid a firm groundwork for it.
(my personal gripe is with many of the new calculators with "improved"
algebraic order, where you type (sqrt)X but X(squared). After a group of
us puzzled with how to remember which operations precede and which follow
the operand, one of us realized that it was the way they are commonly
written!! You know, the square root symbol is placed in front of the
number, but exponents come after. While I suppose these calculators make
it easy to type in a written equation, they can only confuse someone
actually trying to solve a problem.)
I also agree with a previous poster to CASNET that intonation and pauses DO
make the problem work
when spoken. This problem was meant as a fun arithmetic drill, and as
such, I think it was, at worst, harmless.
Ginda Fisher
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