|
Writing Sensible Word Problems
When word problems involve decimals and/or percents,
special care must be taken to avoid strange or ambiguous part/whole
relationships (See Table 6.11).
|
Original
Problem
|
Mathematical
Issues
|
Improved
Problem
|
|
Jimmy partitions his land
into 0.5 pastures, each of which contains 0.75 acres. How many acres of land does Jimmy
have?
|
Deficiency: This problem is strange. One would expect to count pastures the
same way one counts rocks or cucumbers, using whole numbers.
Strategy:
Rephrase the problem using an integral number of pastures.
|
Jimmy partitions his land
into 3 pastures, each of which contains 0.75 acres. How many acres of land does Jimmy
have?
|
|
Mr. Smith’s fifth grade class
has twenty five students. If 30% of
the students vote to go to the zoo and 70% vote to go to the museum, how
many students voted to go to the zoo?
|
Deficiency: This problem is strange. 30% of twenty five equals 7.5
students. In the context of the
original problem, “7.5 students” has no sensible interpretation.
Strategy: Change the percents so that they
correspond to an integral number of students.
|
Mr. Smith’s fifth grade
class has 30 students. If 30% of the
students vote to go to the zoo and 70% vote to go to the museum, how many
students voted to go to the zoo?
|
|
In a local election, 40%
of female voters and 30% of male voters supported the proposed school
levy. What percent of all voters
supported the levy?
|
Deficiency: This problem is ambiguous. The given percents, 40% and 30%, do not
refer to the same whole. Without
more information, there is no meaningful way to use these statistics to
answer the question.
Strategy: Change the problem so that the percents
refer to the same whole.
|
In a local election, 40%
of voters went to the polls before 5pm. 35% went between 5pm and 8pm. The
remainder submitted absentee ballots.
What percent of all ballots submitted absentee ballots?
|
Table 6.11: Writing
Meaningful Word Problems
Table 6.12 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.
|
Word
Problem
|
Inverse
Word Problem
|
|
Jean has $4.50 to spend
on candies. If each candy costs
$.75, how many candies can she purchase?
|
Jean purchases 6 candies,
each costing $.75. How much did she
spend in all?
|
|
Every year, Mr. Jones
donates money to State
University,
specifying that …
§ 80% of his gift must be used for undergraduate
scholarships;
§ 60% of the amount used to support undergraduate
scholarships must be awarded to women.
What percent of Mr.
Jones’ annual gift is used to support undergraduate scholarships for women?
|
Every year, Mr. Jones
donates money to State
University.
§ 48% of each gift is used to support undergraduate
scholarships for women
§ Women are awarded 60% of the undergraduate
scholarships
What percent of Mr.
Jones’ scholarship support is awarded to undergraduates?
|
Table 6.12: Word
and Inverse Problems
|
