Number & Operations for Teachers 

Copyright David & Cynthia Thomas, 2009

Word problems

As with addition and subtraction, teachers must be prepared to create multiplication and division word problems (and their inverses) that

· Are situated in contexts and situations familiar to children;

· Avoid use of ambiguous and/or confusing language; and

· Avoid unconventional, unrealistic, or nonsensical uses of numbers and/or operations.

 The examples in Table 3.2 illustrate the relationships between different exercise formats and related word and inverse word problems.  What assumptions does each word/inverse problem make with regard to students’ background knowledge?  Which concept model would you use to illustrate each problem? 

Original Exercise	Word Problem	Inverse Exercise	Inverse  Problem
3 x 5 = 15	Three friends each have $5.  How much do they have together?	15 ¸ 5 = 3	$15 is to be awarded as a prize.  If each award is $5, how many awards will be made?
12 ¸ 6 = 2	A cook has 12 eggs with which to feed 6 people.  How many eggs will each person receive?	2 x 6 = 12	Two friends each have $6.  How much do they have together?

Table 3.2: Sample word and inverse problems 

Of the two division problems in Table 3.2, one is partitive and the other is measurement.  Which problem is partitive?  Which one is measurement?  [Answer: The egg problem is partitive.]