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Writing Sensible Word Problems
Creating meaningful, unambiguous word problems can be
difficult. When word problems involve
fractions and fraction operations, special care must be taken to avoid
strange or ambiguous part/whole relationships. For instance, although the original word
problems in Table 5.2 may sound plausible, they are mathematically
deficient.
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Original Word Problem
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Mathematical Issues
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Improved Word Problem
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Mrs. Smith’s fourth grade class has 28 students. A third of them are boys. How many of her students are boys?
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Deficiency: This problem is strange. Computing 1/3 of 28, an answer is
obtained that is not a whole number.
In the context of the problem, the answer “nine and one-third boys”
makes no sense.
Strategy:
Rephrase the problem so that the indicated product yields a whole
number of boys.
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Mrs. Smith’s fourth grade class has 27 students. A third of them are boys. How many of her students are boys?
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A cookie recipe calls for ¾ of a cup of sugar. Susan only has ½ a cup of sugar. How many cookies can she make?
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Deficiency: Not enough information is given. Without knowing how many cookies a full
batch contains, you cannot answer this question.
Strategy: Ask what fraction of a whole batch she can
make.
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A cookie recipe calls for ¾ of a cup of sugar. Susan only has ½ a cup of sugar. What fraction of a batch of cookies can
she make?
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Table 5.2: Writing
Meaningful Word Problems
Table 5.3 shows two word problems and their inverses. In general, the same attention used to
avoid ambiguity and strangeness when writing word problems should be applied
when writing their inverses.
Fortunately, if a word problem is well written, formulating a
satisfactory inverse is often easier than writing the original problem.
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Word Problem
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Inverse Word Problem
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Mrs. Smith’s fourth grade class has 27 students. A third of them are boys. How many of her students are boys?
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Nine of Mrs. Smith’s students are boys. If the boys constitute 1/3 of her class,
how many students does she have all together?
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Mr. Smith’s aquarium holds 25 gallons of water. How many gallons has he put into the
aquarium when it is one-third full?
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Mr. Smith pours eight and one-third gallons of water
into his aquarium. If, at that
point, the aquarium is one-third full, how many gallons of water does it
hold?
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Table 5.3: Word and
Inverse Problems
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Tech Resources
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Investigate Number
Line Bars – Fractions, Rectangle
Multiplication of Fractions, and Rectangle Division
at the
National Library of Virtual Manipulatives for
Interactive Mathematics
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http://matti.usu.edu/nlvm/nav/topic_t_1.html
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